doing hypothesis testing and today's session as well. It's a very long one, so I'm hoping if we're not done by half past four, we can continue until five o'clock, but we will see how far we get as well. What we're doing for the next one hour 30 minutes, we'll be looking at hypothesis testing for the mean and the proportion and this is towards helping you being able to submit your assignment for. Next week, we will do more activities because I realized that also this week and last week, we didn't do a lot of activities. So at least next week, it will allow us more time, one hour 30 minutes to do activities from both study units as well. Then the last week of August, we will do question and answer session. Are there any questions before we start with this week's session? Is there anything that you want to ask? Are you all good? I'm good. Thank you. In the absence of any questions, then that we can continue. We're going to look at firstly at the hypothesis testing for the mean, and later on we're going to look at the hypothesis testing for the proportions. By the end of the session today, you should be able to learn what are the basic principles of hypothesis testing that is very important to know that, and how to use the hypothesis testing for the mean to make a decision, and also how to make use of the hypothesis testing of the proportion to make a decision as well. Yes. Oops. My hearing still says confidence interval, but this is hypothesis testing with hypothesis testing. We're still going to look at two sections, hypothesis testing for the mean, and hypothesis testing for the population proportion. When it's for the mean, we need to also know that the populations that are deviation needs to be known, or it can be unknown. In that case, then it means they have given us the samples that are deviation, and how do we handle all three of them, and how do we do a hypothesis testing of all three scenarios as well. What is a hypothesis testing? Hypothesis testing is a claim that a researcher wants to prove. As a researcher, you will have a question that you want to answer, and that question you can state it in a hypothesis testing statement. Always when we want to prove something, we're always going to be using the population parameters. Therefore, it means in your hypothesis testing statement, you are always going to use the sign relating to your population parameters. Like for the population mean, we will use the mu in our statement, and for the proportion, we will use the pi for the proportion. When we state the hypothesis testing statement, now, because the researcher wants to prove something, there is always a case to be proven in a way, right? It's either you are guilty or you are not. It's either something is true or it's not. With hypothesis testing, there are those cases. With the research statement that they want to prove, or we want to test, we're always going to have an opposite of that statement. We will have two sides. We will have what we call a null hypothesis and an alternative hypothesis, which will be the alternative of a null hypothesis. Your null hypothesis is the statement that the researcher wants to prove, and the alternative is just another, or we can say it's the complement of that statement. If your researcher statement is not true, therefore, it means your alternative hypothesis will be true. The way we state the null hypothesis, which is the researcher's name, it will always contain an equal sign to it. For example, when we want to prove that the mean diameter of the manufactured bolt is 30 millimeters, therefore, it means we will say the mu is equals to 30 millimeters. We do not use the sample statistic symbol. We always use the population parameter symbol and not the sample statistic symbol. With your null hypothesis, we always begin, when we state the null hypothesis, it always begins with the assumptions that the null hypothesis is true, which is similar to what I just referred to, whether you are guilty or you need to be proven guilty or not. Always, like I said previously, just to reiterate on this, it always, in the null hypothesis, always has an equality sign. So you will notice that sometimes, when they state the null hypothesis, there's always an equal sign. They don't mind the sign of greater than or equal or less than or equal. But when we state your null hypothesis, they should always be an equality sign to it. So always, your statement will contain equal, less than or equal or greater than or equal. But generally, we can use just the equal sign statement. Your null hypothesis may or may not be rejected. So when we get to the end of the session, once you have done all your testing, then you need to make a decision. When you make a decision, you can either reject the null hypothesis or you do not reject the null hypothesis. And that's how you will state your hypothesis. What is very important in the null hypothesis is that when you make your decision and you conclude, you always refer back to your null hypothesis statement. Number two, the other thing that is very important with the null hypothesis is the statement you write on your null hypothesis statement, especially the parameter. It's very important that you use the right parameter when you are stating your null hypothesis and always your null parameter will correspond with the value of that parameter as well. Looking at the alternative, which is a complement of a null hypothesis, this is the opposite of that null hypothesis, right? If we stated in the null hypothesis that the mean diameter will be equals to 30, the alternative will say it is not equals to 30 millimeters. Always, what I also didn't mention with how we state the null hypothesis, we used a subscript O or subscript zero. For the alternative hypothesis, we use the subscript H1, some books or somewhere they use HA, some books they use HC, some books they use, yes, it's either they use HA or H1 or HC, which is the complement. Your alternative hypothesis testing always does not contain an equality sign. So it means the sign will be not equal, less than or greater than. Those are very important. These statements in your alternative hypothesis testing, they are very, very important because they will determine where you're going to find your critical value. They will determine what type of a decision you're going to be making and they will determine the type of test you are doing. Whether is it a one-tail test or a two-tail test and based on that information, it will tell you whether you do need to find two critical values. We know, we remember what critical values are. We did find the critical values in the last exercise study unit that we did with confidence intervals and it will also help us with the decision because if we're doing a two-tail test, then it will help us to know which sites are we making the decision to reject the null hypothesis and the alternative. Only the sign in your alternative hypothesis is that important to that effect. That is why in your null hypothesis, whether you put a greater than or equal or you just put an equal sign, it will not matter that much than when you do your alternative hypothesis. The statement you put there, it's very important. Now, some people might ask, what if the researcher wants to prove that it is less than? Remember, the statement that the researcher wants to prove has to have an equal sign to it. So if the researcher wants to prove less than, we're going to use the statement of the researcher in our alternative hypothesis and when we make a decision, if we go into reject the null hypothesis, we will be rejecting the false null hypothesis and those will create some errors and we will get to that just now. Your alternative hypothesis, we do not even have to worry about proving it whether it's right or wrong because we always, when we make a decision, we refer back to our null hypothesis statement. Right, like I explained, when the researcher wants to prove a less than, they say the mean diameter is less than 30, because we cannot put it in the null hypothesis, we can only put it in the alternative hypothesis testing, then when we make a decision, we are going to create an error because if we reject the null hypothesis, then we are rejecting a false null hypothesis. We're not rejecting the three null hypothesis because the true hypothesis that the researcher wants to prove, we placed it on the alternative. So we create what we call a type one error if we reject a true null hypothesis. So for example, most of the questions that you will get, you will be rejecting a true null hypothesis because if you get to the decision where you are rejecting the null hypothesis and that is what the researcher wanted to prove, then you will be rejecting a true null hypothesis. Like for example, with our null hypothesis that stated that the mean is equals to 30 millimeter. If we reject that null hypothesis, we are creating what we call a type one error. And the type one error is considered as a serious type of an error and the probability of a type one error is always going to be referred to as the alpha value or we call that a level of significance. So when we do hypothesis testing, we are always going to find that level of significance to use to find our critical value so that we are able to make a decision to see whether are we rejecting the null hypothesis or not. And your level of significance or your alpha value, it is set by the researcher at the beginning. So they will tell you that test at 95% confidence interval or test at 95% interval, you need to remember that your confidence level of 95% is the same as one minus alpha and you can find your alpha from there. Or you need to remember that a 95% confidence level is equivalent to the level of significance of 0,05. 0,05. We create a type two error if we fail to reject a false null hypothesis. So for example, like I did say, if the researcher wants to prove that the mean diameter is less than 30 millimeter and we put it in the alternative hypothesis, therefore our hypothesis testing, sorry, our null hypothesis will state that the mean diameter, if that one was less than, the mean diameter will be greater than or equal or we can just say the mean diameter is equals to 30 millimeter. And if we do not reject the null hypothesis then, then we are committing a type two error which is failing to reject the false null hypothesis and this is denoted by a beta value which is a type two error. Probability. Okay, we're now going to move into how do we then do the hypothesis testing? So we're going to look at how do we apply what we just learned now to state the null hypothesis and to use the level of significance, how do we make decisions? So we're going to look at a hypothesis testing for the mean and we're going to look at when the population standard deviation is known. Therefore it means we're going to somewhere to calculate using the Z test or we're going to find the critical values on the Z table or we're going to use Z table at some point to do all this. And we are also going to calculate what we call the Z test statistic which is what you have learned in sampling distribution and we will get to that just now. We are also later on going to look at testing for the mean when the population standard deviation is unknown when we use the T test. Remember to go find the critical value on the T table and also going to be introducing a new calculation which is similar to the Z test from the sampling distribution Z formula but using the T test. And then we're going to learn how to make a decision. Okay, so let's first start with hypothesis testing when the population standard deviation is known. You will need your calculator, your statistical table and the formula to remember this. On top of it, you need to know the steps of the hypothesis testing. And I'm going to tell you all the steps because they are very important that you know all six steps of hypothesis testing in order for you to get the questions right as well. So like I said, we're going to look at hypothesis testing for the mean and when the population standard deviation is known we know that we're going to use the Z table. And when we calculate the test statistics starting going to use to find either the probability value or we're going to use the Z test to make a decision using the Z test and the critical value we will use the Z test which is similar formula that we have learned and we worked with in study unit seven in the sampling distribution. And now we just in state of that only Z we put subscript state to show you that this is a Z test statistic which will be given by your sample mean minus the population mean divided by your standard error which is your population standard deviation divided by the square root of N. Now, the other thing before we forget always remember that your questions in the exam or assignment they might not give you the symbols. They will give you weights. You need to know how to interpret the weight into a mathematical formula or function or symbol. For example, if they ask you that it exceeds you need to know that it's greater than. If they say it's fewer than then it's less than. If they say it's not less than it is greater than or equal. If they say it's no more than it's less than or equal. If they say at least you need to know all those weights. If they say it is greater than or equal it should be easier to find the symbol that relates to that. So you need to always constantly remember all this. If you can't remember them, have them saved some way that you can always come back to them and refer back to them when it comes to the sides, right? Yeah, so now when we state the null hypothesis and the alternative hypothesis, the sign that sits on the alternative hypothesis it's very important. It tells you what type of a test are we doing and it also helps us to find the critical values which also help us to find the region of rejection for us to make a decision. So for a two tail test, your null hypothesis will state that the mean is equals to 30. Your alternative will state that the mean is not equal to 30. Immediately you put the null equal to 30 and the alternative hypothesis testing you know that you are doing a two tail test. Therefore it means you will have two regions of rejection. Therefore it means you will have to find the critical value by dividing your alpha value. Your critical value you will find it by dividing your alpha value by two because you will be splitting it into two regions of rejection. When we make a decision because now we I always like to write or draw this very same graph that you can see here. I always draw the belly calf shaped graph which is the normal distribution graph. And I highlight my regions of rejections based on the critical value that I would have found on the table. So if I use the z table I will find the critical value if for example it was for 0,95 a level of significance or sorry not level of significance but the confidence interval which means my alpha value would have been 0,05 and therefore I will take my 0,05 and I will divide it by two and I will get 0,0250 and I will go to the table to go find my critical value of 1,96. When I find that critical value I'm just gonna use it 1,96 and it will be on the negative side it will have a negative and on the positive side it will have a positive value and this will be my region of rejections. Anything that falls above or below so this side it will be below the critical value I'm going to reject anything that falls above the critical value I'm going to reject. So when we come to the decision this is very important because it helps you to visualize where your areas of rejections will be. Anything that falls in between the two critical values we do not reject. What happens when you have a one-tail test? So when you have a one-tail test it is when you have only one side of where you're going to do your rejection. So for example, if your hypothesis testing states that you're especially your alternative hypothesis testing it states that the mean is less than three therefore it means we are going to have our region of rejection in the lower side. So the sign is very important it will be in the lower side and you will see how we state the null hypothesis and the alternative hypothesis you can see you can either use greater than or equal in your null hypothesis or you can write it as your mean is equal to three and your alternative will state the mean is less than three as long as it has an equal sign in your null hypothesis that's right. The most important sign is what you place on your alternative hypothesis because that will tell you where your region of rejection is and when we find the critical value because it is a one-tail test and it's one-sided we're going to find our critical value at zero comma zero five and one we don't divide our critical value by two for a one-tail test it's always going to be alpha value and go find the critical value of an alpha value. When it's in the upper tail it will say it is greater than and your alternative can sorry your null hypothesis will say less than or equal and your alternative will say greater than or you can say your null hypothesis is equal to three your alternative will state greater than and then your original rejection will be in the upper tail area which means once you have your critical value of one comma nine six and on this one if our critical value will not longer be one comma nine six it will be something else at zero comma zero five you will find the critical value for that and it will you then create the origin of rejection and you will make your decision anything that falls below you do not reject anything that falls up after critical value you reject. So now let's look at how the steps now comes together. Okay, so there are six steps that you need to know and always remember and this statement or these six steps can either be the options in your question for example option A, B, C and D or option one, two, three and four can be one of the statement. So the first step of doing a hypothesis testing is to state your null hypothesis and your alternative hypothesis and I've shown you how to state your null hypothesis and alternative. Remember null hypothesis always contains an equal sign your alternative which is very important for your sign it has no inequality or it does not have an equal sign. Step number two, you need to choose the level of significance state whether is this for hypothesis testing for the mean when the population standard deviation is known or unknown you need to also state your sample size and you need to go and find your critical value that will be step number four. Okay, so you need to find your level of significance which is your alpha value. Step number three, you need to calculate or determine and calculate your test statistics. So now if you found that in step number two your population standard deviation is known then you need to find or calculate your test statistics for Z. If it's unknown you're going to use the T test statistic. Step number four, it's very important. If in step number one, step number two and step number one you did something wrong there you will get step number three or step number four wrong. Step number four it's very important to know that the sign you put in your alternative hypothesis is the correct one because it will determine how you find your critical value. In step number two, how you find your level of significance it's very important as well that you need to make sure that your alpha value is correct and whether you determine whether the population standard deviation is known or unknown because in your critical values calculation on step number four where you're going to get the critical values to determine your original rejection you will use your alpha value and the sign you got. If the sign said it's a two tail test which means it's not equal then you will divide your alpha by two and go find the critical value. If it is less than or it is greater than then you only use your alpha you don't divide it by two you use your alpha to go find the critical value. If your population standard deviation is known you find your critical value on the Z table if your population standard deviation is unknown you find your critical value on the T table and therefore it means you will need to find the degrees of freedom and the degrees of freedom you use your N minus one to find the degrees of freedom. So it's very important that you follow the steps because they link to one another and once you have determined what your appropriate test statistic is and you found your critical value the step number five says you can calculate your test statistic. So if we determined that it was a Z test then we need to calculate the Z test. If we determined that it was a T test then we need to calculate the T test. And once we done with that then we can come to step number six which is to make a decision and conclude. When making a decision we make a decision by using the critical value and your test statistic. So you need to make sure that your step number three is correct, sorry, step number four is correct and step number five is calculated correctly because then you will use both of them to make a decision. And you make a decision referring back to your null hypothesis testing or statement to say whether you reject the null hypothesis or do not reject the null hypothesis. Very careful. In the hypothesis testing for your module there are two statements that you make. You will say we reject the null hypothesis or you say we do not reject the null hypothesis. No other statement you need to make like for example we may not, we are not rejecting. The way you stated we reject the null hypothesis or we say we do not reject the null hypothesis. That is the format that you will need to use when you're stating your conclusion, right? Okay, so let's look at an example. Let's test the claim that the true mean diameter of a manufactured bold is 30 millimeter and yeah, I'm going to say at 95% confidence level. That is the case. So let's test this hypothesis. Remember our six steps, step number one is to state our null hypothesis and our alternative hypothesis. Stating the null hypothesis, our mu is equals to 30 because the statement said test the claim that the true diameter of the manufactured bold is 30 millimeter. If they could have said it is greater than then I will be doing something else. If they said it is less than then I will be doing something else because the statement said is, it means it's equal. So the null hypothesis state, the mu is equals to 30. The alternative will state that they are not equal to 30. So your mean is not equals to 30 and this because of the sign that I put or I have placed on my alternative hypothesis testing then it means I am doing a two-tailed test and that is very important because it tells me when I get to the critical value, how am I going to find that critical value? When it comes to the rejection areas, it tells me that I'm going to have two regions of rejections, okay? Step number two, specify the level of significance and your N and what you are given. For example, whether the population standard deviation is known or not. So yeah, looking at the statement, the population standard deviation is given, so it's known. My alpha value is 0,05. My N is 100, right? Step number three, finding your, or determining what type of a test is this. Based on the information, population standard deviation is given. So therefore I'm going to assume that we're going to be using our Z test because when the population standard deviation is known, we use the Z test. Step number four, determine the critical value. So now with step number four, we do the same. Remember at 95% confidence level, it's 0,05. So our alpha value will be divided by two. So it's 0,05 divided by two, which means it's 0,0250. We go to the table to go look for 0,0250 inside the table and we go out, it's on 1,9 and we go up six. And therefore our critical value is 1,96. And because it is a two-tail test, we're going to find plus or minus because it will be on the negative side and on the positive side. And immediately from here, you can draw your graph and say they will be my regions of rejection. So anything that falls here will be rejected. So this will be 1,96 and this will be minus 1,96. And there are my regions of rejection. Anything that falls here, we're going to reject. The null hypothesis, anything that falls here, we're going to reject the null hypothesis. So now we need to find our Z test. Before we can say we are rejecting the null hypothesis step number five, we compute the Z test statistic. So our Z of the sample mean minus the population mean divided by the population standard deviation divided by the square root of N, which gives me our sample mean is 29.84. And our population mean it's always stated in the hypothesis, so it makes it easier. There it is. It's stated our population standard deviation was 0,8 and our N of 100, square root of 100 and we calculate this and we find that our Z test statistic is minus 2.0. So where is minus 2.0? And we know that here in the middle here, it's zero. So minus two will fall some way inside the shaded area. So it will be some way that side because it's minus two, your numbers increase and you go to the left in terms of negative numbers, in terms of positive numbers, they will increase to the right. So minus two falls in the rejection area and then now we can go and make our decision. So that's step number six, step number six. There is our region of rejection based on our alpha value of 0.05, 0.05, our alpha value of 0.05 because there are two sides, we divide it by two which is 0.025 and then we go and find our critical value of minus 1.96 and positive 1.96 and we create our region of rejection and we found that our test statistic is minus two therefore it falls in the rejection area and we can say our Z test of minus 2.0 is less than minus 1.96. So the test statistics is in the rejection area and we can conclude by saying since the Z test is equals to minus 2.0 which is less than the critical value of Z minus 1.96 we reject the null hypothesis and conclude that there is sufficient evidence that the mean diameter of a manufactured bold is not equals to 32 and that's how we make a decision. Let's look at another scenario when we look at rejecting the or doing the hypothesis testing for Z when the population standard deviation is null now here the catch is that we are going not to use, we are not going to use the critical value and the test statistic like we did here but we're going to use the p-value. Remember what the p-value is? The p-value is your probability value that is the value you find inside the table like your alpha value. You said it's the probability in the table. The p-value will also be the probability we're going to find on the table using our Z test statistics. So it means this answer here which is our Z test statistic value we're going to use it as our Z value on the Z normal distribution table in order for us to find the p-value and this is only applicable for Z hypothesis testing only when we do Z test hypothesis testing. So later on when we do proportions because we also use the Z we can find the p-value or we can make conclusions based on the p-value. So now how do we do that? So when we make a decision using the p-value if your p-value is less than the alpha value we reject the null hypothesis. And if it's greater than or equals to alpha value we do not reject the null hypothesis. So always remember if p-value is lower the H naught must go. The null hypothesis must be rejected. Okay, so how do we do this? Also we have the five steps that you, the four steps you know of and then we edit the step where you just need to go and find the p-value instead of finding the critical value. We remove the critical value step. So you still do, you can still state your null hypothesis and alternative hypothesis. You still need to know what your level of alpha is because we're going to use our alpha value or our level of significance to make a decision and you need to know what your sample size is. You need to know what the test statistic is and how you calculate it. So we only state here that it's a Z test statistic and then you calculate the Z test statistic. And once you have calculated your Z test the answer of your Z you're going to use that to go find the p-value. Now what is very, very, very important as well here there are two things. If our alternative hypothesis says two-tail test how we go find the p-value? There are two of them. So we're going to find the p-value but you're going to add them, multiply that by two. The value you find on the table you're going to multiply it by two. If it's less than or greater than the value you find on the table will just be your p-value, right? Here's the catch. Remember how we dealt with normal distribution questions. If the alternative hypothesis, right? If the answer there is less than then it means your p-value will just be the value you find on the table, right? Maybe that's good, that's great, that's perfect. If it is greater than, always remember will be one minus the value you find on the table because remember that the table values are always the probability of Z less than because our p-value is a probability we always need to keep that in mind. Now coming to the place where it is not equal where you have to take both two p-values and add them together, you need to pay attention. If your Z-value is positive, let's start with negative. If your Z-value is negative, if it's negative, if your Z-value is negative then you can say two times the table value. That will give you your p-value. If your Z-test, if your Z-value is positive you're going to say two times one minus the table value. And that's how complex it is when it comes to the p-value. But if you can get this right, you can get everything correct. So these are the ways that you're going to find your p-value and make a decision based on that, right? Always remember that, always, always. Take a picture, take it, memorize this because when you do your practice examples and you need to be able to know all this, okay? And then the last step, we make a decision and conclude. So we're going to use the same question that we had or the same example. I'm not going to go through each statement again. The same way you state your null hypothesis and alternative, we know that we're doing a two-tail. So therefore it means our p-value. We're doing a two-tail p-value. If it's negative, we're going to just take the value and the table multiplied by two and what is your angle? If it's positive, then we're going to do all these other calculations in between, okay? So we specify alpha value because we need that. We remember in our conclusion, if the p-value, if it's less than alpha, we're going to reject the null hypothesis. So it's going to be very important because our rule states that we need the alpha value, okay? And we assume that the population standard deviation is known because they told us and we're using the Z test and we calculate our Z test and we did find that our Z test is minus 2.0. And then, before I come to that slide, let's wait right here. So because it's 2.0, so what did we say when it is minus, it's minus, right? The value we find on the table, we're going to multiply it by two. So we need to go to the Z table and we'll find minus 2.0. So we come here, minus 2.0 and zero at the top and the answer is 0.00228. So this is only on one side and this must be applied on both side. Remember, our critical value, we say this is, not this, this is minus two, sorry, positive two and minus two on this side and we found that this probability here is 0.0028, right? Oh, 228. Um, 0.228 and 0.0228. So because there are two of them, we just going to say two times 0.0228, which will give us our critical, our p-value. So our p-value, our p-value will be the combination of the two, the multiplication of that. So let's see two times, what these two times? 0.0456. 0.0456 and that is our p-value. You can say two times that or you can say 0.0228 plus two. 0.0228, it will also give you the same 0.046. They will give you the same thing. And that's what we do here. So you can say two times or you can say p-value. It's 0 plus, 0.028 plus 0.028, or you can just take the value you find on the table, multiply it by two and that will give you your p-value. And then we can make our decision. Since the p-value of 0.0456 is less than our alpha value of 0.05, we therefore reject the null hypothesis because there is sufficient evidence to conclude that the mean diameter average, E or the average diameter of a manufactured bold is not equals to 30 millimeters. And the same conclusion that we use or we found when we were using critical value and the Z test is the same as when we're using the p-value and the alpha value. So you can for only for Z only, this is only applicable when we're using the Z test. We can use either the critical value and the Z test to make a decision or we can use the p-value and the alpha or level of significance to make a decision. Now, let's move on, unless if there are any other question. I had an exercise, but based on the time, I'm thinking now, okay, let's take these five minutes to do this exercise and then we will move to the, when the population standard deviation is unknown and then we will do the proportion. So in this exercise, if in a sample of N of equals to 20, selected from the population, so the sample of 20, the sample mean of 58 and the population standard deviation of 12, suppose that the E Twitter wants to test the following hypothesis. The null hypothesis, which states that the mean is equals to 55 versus the alternative, which states that the mean is not equals to 55 at alpha or at the level of significance of 5%. Which one of the following statement is incorrect? To start with, we just need to highlight what we're given so that it makes it easier. So I'm given N, I'm given the sample mean, which means it's my X bar, the population, oh, there we go, that is my sigma, my population standard deviation is known. I can make reference to that right now, is known and my hypothesis testing, in the hypothesis testing, I'm given the population parameter, which makes life easier and my alpha value is 0,05. Okay.  I'm going to the hypothesis testing step by step. So step number one, we state the null hypothesis and the alternative hypothesis. I don't have to state that because they already did that for me right there, right? If they didn't, I would state the null hypothesis and the alternative hypothesis. And looking at my alternative hypothesis, I know that I am doing a two-tail test, right? That's what I know. Number two, step number two says, state what else you're given in terms with relation to your alpha, which is 0,05 and your N of 20. And I know that my population standard deviation is known, right? Step number three, if my population standard deviation is known, then it means I'm doing AZ test statistic, right? Because my population standard deviation is known. Step number four, step number four was finding the critical value. So now let's go find the critical value. So finding the critical value, we go into find the critical value by using Z alpha of two, which means it's Z of 0,05 divided by two, which is Z of 0,025. Zero, and I know that this is 1,96 because we used it previously. I don't have to go and show you again, which is that value, 1,9 and at the top six. So it's the same thing. So that is my critical value. And step number five, and on step number five, then I need you guys to help me to find the answer because I didn't open my calculator today. So we need to find Z equals the mean, sample mean minus the population mean divided by, the population standard deviation divided by the square root of N. Now I'm going to take a detour a little bit because I can see that I'm asked to find the standard error. So I'm going to ask you guys to calculate this manually and give me the answer for the top and the answer for the bottom with this exercise. So at the top, our mean is 58 minus our population mean is always stated in your hypothesis testing, which is 55 divided by our standard deviation is 12 divided by the square root of N is 20. Now I want you to give me the answer for the top patch. 58 minus 55 is three. Then at the bottom, June 12 divide by the square root of 20. 2.68. 12 divide by 20, square root of 20 is 2.68. How many digits? You must not cut off. 6, 8, 3, 2. 3, 2. Does it end there? No, there's quite a lot. Yeah, but you are cutting me. Like I want all the digits. I want to know point 6, 8, 3, 2, 8. Then it means if we leave it, yeah. If we leave it to four decimal, then it will be 3, 6, 8, 3. Because I'm looking at the answer here, it's four decimals. So you need to pay attention to the information given to you to leave your answer at the end relating to the number of decimals that you have, right? Okay, so then let's calculate this and find the actual. So just take three divide by that value. 1 comma 1180 comma 1180. There. Right, so that is step number five. Step number six, we need to make a decision and making a decision we can make, draw our normal distribution graph and we have our critical value, right? It was 1.96. So 1.96 and it will be negative on this side. And on this side, it will be 1.96 positive. Anything that falls this side, we're going to reject anything here. We're going to reject. And otherwise, if it falls in the white area, we do not reject. So now let's go and find out. So based on this information that we have, number five, our critical, our Z test, or maybe I forgot to also put the stat. You can also put stat or you don't have to put stat there. So whether it's 1.114, it falls in on this side, right? And they do not reject area, right? Because this is 1. 1.96 and this side, it's minus. And if I have a zero at the big, here in the middle, then it will fall somewhere on the side of zero, on the right hand side of zero, still in the do not reject area. So to reject the null hypothesis, and we can blah, blah, blah, blah, from then on at the level of significance, blah, blah, blah. So that is based on the critical value, right? Oh, we can also base the decision on the P value. So I'm taking it one step because we don't have the P value there, but I'm just taking it one step. So we have our Z, we can go and find, and because it's positive to go find the P value. So our P value and we're doing a two-tail test, this is positive, then it means we're going to say two times one minus the value we're going to find on the table. So on the table, we need two decimals. So it will be 1.12, right? So we go and find one on the positive side of the table. We're looking for 1.1 and at the top, it should be two because we're looking for 1.1, 1.2, where they both meet, which is 0.86861 minus 0.8686. What is the answer? 0.2628, oh, sorry, I'm multiplied by two already. You already know it's five? 0.2628. 0.2628, okay? So our P value, remember the rule, the rule says P value, if it's less than alpha, we reject. That was the rule. So our P value is 0.2628, which is greater than 0.05, therefore we do not reject. You can see that the same results, we do sign, the same results. So now we can come to the question and answer. Which one of these statements is incorrect? So number one says we're using a Twitter test. That's correct, because we did determine that it's a two-tailed test. Number two says the standard error is 2.836. We did find that standard error. Remember that this is your standard error, right? So our standard error was 26833. Our test statistic is 1.180, we did find that it is 1.118. Zero, number four, H naught is rejected. We say we do not reject. So therefore this is the incorrect statement. The critical value is 1.96, which means that is correct. As you can see, yeah, I'm just demonstrating to you to say all six steps, because we used all of them, we used that step, this step, this step, and this step. So you need to know all the six steps of hypothesis testing in order for you to answer the question, because if this was a question in the exam, then you need to be calculating all six steps in order for you to find which one is incorrect or which one is correct. And that is hypothesis testing for the mean when the population standard deviation is known. I just demonstrated as well how do we find the p-value when we get the answer of a positive, right? Okay, now let's move on to hypothesis testing for the mean when the population standard deviation is unknown. Are there any questions before we continue? Thanks, no questions. Then we can move on to the next one. Thanks, so with that hypothesis testing for the mean when the population standard deviation is unknown, we use the t-test statistic. And it's similar to the z-test statistic. Remember the z-stat, it was the population mean minus, or sample mean minus the population mean divided by the standard error. And because we had the population standard deviation, you can see that since we are not given the population standard deviation, we will be given the sample standard deviation, therefore we're going to be using the sample standard deviation there. So that's the only difference. The formula is the same. The other thing that will be different is how we find the critical value. Okay, so we're also going to follow the same six steps. I'm not going to repeat them, we've touched on them. And this is an example. The average cost of a hotel room in New York is said to be 168 grand per night for to determine if this is true. A random sample of 25 hotels was taken and the result in the mean of the average the sample mean of 172 grand 50 and the standard deviation of 15 grand 40 test the hypothesis at alpha of zero comma zero five. Now, you need to make sure that you know what you are given by reading the question again so that you understand it's there. So yeah, it says the average cost of a hotel in a room is said to be 168. They didn't say it is less than it is greater than those key weights are very important when determining the sign you will put in your alternative hypothesis. And because none of those kind of weights are used we're going to assume that this is a two tail test because then it's an equal and our alternative will be not equal. And this is how we will state our null hypothesis and our alternative hypothesis based on the statement given. So we're going to be doing a two tail test. So the first thing we do so because they also gave us, oh wait, let's go back our N, N of 25, we are given the mean of 172.50 of 172.50, we are given S which is the sample standard deviation S of 1540 and they are asking us to find this at alpha of zero comma zero five. So that is very important information that we have. So now let's do our six steps of hypothesis, step number one stating the null hypothesis and alternative, step number two state what you are given and also calculating the degrees of freedom because we know that we're going to use that in our critical value. So our degrees of freedom, it's N minus one which is 25 minus one, it's state 24. Our population standard deviation is unknown. So we're going to be using T test and this is step number three, step number four we need to go and find the critical value. So finding the critical value remember we use alpha and the degrees of freedom and because we're doing a two-tail test so it will be alpha will be divided by two. So that will be zero comma zero two five zero and that is why the critical value there is zero comma zero two five and 24. Remember to go to your T table, critical values of T and 24 and remember to ignore the top part only the values closer to the table are the values that we are using. So you go to 24 and zero comma zero two five where they both meet and that will be your critical value of two comma zero six 39, which is our critical value and we calculate our test statistic which we substitute the value the mean is 172.50 minus the mean the population mean which is always given in your hypothesis testing which is 168 divided by the standard error of the sample standard deviation divided by the square root of 25 which then the answer gives us one comma four six and because we have our critical value we can create our region of rejection and our 146 will fall within they do not reject area because our critical values are minus 2.06 and minus and plus 2.06. So 1.46 falls in there do not reject area and we can conclude by saying we do not reject the null hypothesis and there is insufficient evidence that the true mean cost of every of different the two mean cost of the hotel is different from 168 and that's how you do a hypothesis testing when the population standard deviation is unknown. I do have for the upper tail. So this one is another example. So phone industry manager thinks that the customer monthly cell phone bills have increased and now average is over has increased and it averages over 52 rent per month. So over it's greater than and that is what the researcher wants to prove. The company wants to test this claim. So now because it says over it cannot be on their null hypothesis it will be in their alternative hypothesis. So then we will create a false null hypothesis and because it is a over it will be greater than. So our null hypothesis we can write it this way or you can just leave it as equal it will still be the same. So your null hypothesis will state that the mean is equals to 52 rent or is not over 52 rent and the alternative will state that the mean is over 52 or it's greater than 52. And we can state what then alpha value of zero comma one zero. Sorry, I've been talking a lot. My throat now is not responding. Just give me a second. Okay, so we are given the alpha value of zero comma one and our end of 25. We know that we can find the degrees of freedom which will be 24. So our degrees of freedom will be 25 minus one which is 24 and because this is a one tail test remember we only have greater than. So it will be in the upper side area. So our alpha of zero comma one zero we go to the critical value table and we're looking for 24 and zero comma one zero where they meet and that will be our critical value is one comma three one seven eight and that is our critical value of T24 and zero comma one zero which is one comma three one eight one seven eight. One seven eight. So which is one seven eight. That's what we found with me, one seven eight. That is our critical value. So from our region of rejection critical value we decide the site will be with our rejection area and anything that falls in the wide area will be do not reject area and we then now can go and calculate our test statistic using the information provided and we calculate our test statistic and we find that it is zero comma five five. Now remember the table, the critical value we found was one comma three one eight from the table and now our test statistic is zero comma zero five and therefore we can determine where it will fall and it falls in the do not reject area and we can conclude we do not reject the null hypothesis since the test statistic is equals to zero comma five five which is less than or equals to the critical value of one comma three one eight. Therefore there is not sufficient evidence that the main bill is over 52 rent and that's how you make a decision. I also have an exercise. My worry is if I do this exercise we won't be able to do the proportions. Let me get your feeling. Do you want us to carry on up until five that my throat now is refusing and it's fighting with me? What are you take? Must we continue until five? No response. So I'm not gonna do the exercise. We'll just move on to the proportions because we only left with 10 minutes. So the hypothesis testing for the proportions. With the proportion we only going to deal with when the your expected mean or your expected mean or your variance is more than five. So in your module you don't have to worry about the others. So you just need to worry about doing hypothesis testing for the proportion you don't even have to test that scenario, the assumption. So we're going to use for every hypothesis testing for the proportion we're going to use the Z test statistic. Also the Z test statistic that you have learned in the sampling distribution study unit. We're going to use it here and call it a Z test statistic. So also remember like with the previous ones if you are not given the sample proportion you will be given observation that satisfy that sample and you can calculate the proportion. So you should be able to calculate your P by using your X divided by N. And our standard error we're going to go back. Remember in confidence interval we were using the standard error using the sample proportion to calculate the standard error and going back to sampling distribution study unit seven where we use the population proportion to calculate the standard error. Right. Yes, you get an example. A marketing company claims that it receives 8% response from its mailing. To test this claim a random sample of 500 were surveyed with 25 responses. Because that the alpha is equals to 0,05 level of significance. Now what are we given here? We are given the population proportion and we are told we are given the population proportion because the claim is that they're receiving 8% of responses back and they did their random sample from the 500 which is our N. They had the response of 25 which is the X and the alpha value of 0,05. And to test this claim, the six steps of hypothesis testing. The first one we state the null hypothesis and the alternative hypothesis. Step number two, we're going to state the alpha value and the sample size. We're going to determine the test statistic and the sampling distribution. You're going to find the critical value from the Z normal distribution table and decide where your rejection area and non-rejection areas will be. We're going to compute your Z test statistic and we're going to make a decision and conclude. You can see that all the hypothesis testing that we just did go through, they apply all the same steps. So you need to know all six steps of hypothesis testing. So because yeah, we also dealing with the Z test, you also need to remember that you can be asked questions to also use the P value for making a conclusion and the decision. So now let's test that. The first step, state in the null hypothesis and alternative, the mean, the proportion, population proportion is equals to zero comma zero eight. The alternative population proportion is not equals to zero comma zero eight. Therefore, we're doing a two-tail test. Our alpha was zero comma zero five given and is 500 P. We were told that we have 25 out of 500 and we calculated it was zero comma zero five. Critical value because it's alpha of zero comma zero five and we're doing a two-tail test. Our critical value will be one comma nine six because it's Z alpha over two, which is Z of zero comma zero two five, which is one comma nine six. Our origin of rejections, we identified them. We can then calculate our test statistic. Our P was zero comma zero five. We calculated it because it was 25 divided by 500. Our population proportion was given in the null hypothesis statement is zero comma zero five. Calculating the standard error and the answer we get for the test statistic or substituting the values for your standard error and calculating if I'm there, Z test is minus 2.47. We can then make our decision and conclude whether it's minus 2.47 fall. It falls in the rejection area on the left-hand side and therefore we can state that we are going to reject the null hypothesis at alpha of zero comma zero five and conclude that there is sufficient evidence to reject the company claim of eight percent response rates. And that is how you state your hypothesis testing for the proportion. If we needed to do the rejection, the decision based on the P value, then then we're going to use our Z test statistic of minus 2.47 and go to the Z values and look for minus 2.47 and that we will find zero comma zero zero six eight. And based on that information of zero because it's two side, we can then add them together or we can multiply by two and that will give us zero comma zero one three six and our P value is less than alpha value. Therefore we reject the null hypothesis. Okay, in the last three minutes, we can look at this example. We'll go through each step by step and tell you each question. Mava to randomly select a sample of hundred children with ASD and found that only 70 of them are in special needs school. So our sample N is hundred and our X is 70. But Kali and Mava to are at it once again. This time they want to determine whether the true proportion of ASD children in special needs school in the population is 0.75, which is our population proportion pi. Assume at alpha of zero comma zero five level of significance, which one of the following statement is incorrect. Now, reading the question and the statement, they would just want to determine whether the true proportion of children in special needs because it's just direct, then it means it's an equal. The null hypothesis will state that the proportion is equals to zero comma seven five. Your alternative will state that it is not equals to zero comma zero seven five. Therefore, this statement is correct. Number two, finding the critical value because we're doing a two tail test and this is a two tail test. So it means our alpha divided by two will be zero comma zero five divided by two, which is zero comma zero two five zero. By now, because we have been doing this forever, I know that it is one comma nine six. And therefore the critical value here is correct. Step number three, the value of your test statistic is minus zero comma minus one comma zero nine. So let's find that Z that is equals two. Your small p minus your pi divided by the standard error, which is your pi times one minus your pi divided by n. Our p is 70 divided by 100, what is 70 divided by 100? 0.7. 0.7. 0.7 minus 0.75 divided by the square root of 0.75 times one minus 0.75 divided by divide by our n is 100. You can calculate the whole of it. What do you get? I get minus 1.54. What do you get? Same here. You also get minus 1.54. Yes, I also get minus one. Therefore that one is equal to minus 1.54. So that one is equal to minus 1.54. So that one is equal to minus 1. Therefore that one is incorrect. And they say the p-value is zero comma 25. We can double check that as well. So let's go and look for the p-value. And the p-value we use, the value we found. What do you get? One point? Sorry, I think I'm writing it all wrong. Minus 1.154, right? 1.54. Yes. It's equal. Minus 1. So we can leave it as minus 1.15. So we go to the table and look for, remove all this. Minus 1.15. Minus 1.1. And at the top, we're looking for five as our last digit. And that is 0.125. 0.125. So our p-value, because it's a two-tail, our p-value is equals to two times, forgot, from 51. 0.1251, which is equals to? 0.2502. 0.2502, which means that is correct. And that's how you will find your p-value. And the last one says we do not reject the null hypothesis. So we can assume that the rule says, if the p-value, so because this is the rule, right? That is the rule. It says if the p-value is less than the critical value, we reject the null hypothesis. Our p-value is 0.2502. Our alpha-value is 0.050. So it is greater than, therefore we do not reject because the rule says we reject the null hypothesis if the p-value is less than that. So we do not reject the null hypothesis that is true. Otherwise, we could have used the critical value. And our critical value is 1.96. 1.96 and 1.96, this side is negative. And we look at our z-value is minus 1. It falls in the do not reject area as well. And that's how you do the hypothesis testing. Likewise, on the notes, I did include some extra additional questions for you to practice and go through the same content. So we do have exercise one where you can look at some of the information from there. And exercise two, you can take a screenshot of them and exercise three, I think they're about six exercises. Exercise four, exercise five. You can always, if you are using the video, you can always pause and do the exercise and then move on to the next one. And then the last exercise was exercise three. So we must exercise six, which deals with proportions. And that concludes today's session. Let me go rest my throat. Thank you for coming through. Are there any questions or comments? If there are none, then... Thank you, thank you, Lizzie, thank you. I have a lovely weekend. There we go, have a lovely weekend. Oh, evening. That's harder, like that. Thank you, bye.


You've probably seen this on TikTok, but this is what the girlies are all using to give themselves a fake blowout, and it looks amazing, so I literally straightened my hair for this for the first time in years because I want to try the blowout with this heated round brush. This is the Wavy Talk 5-in-1 ceramic curling wand set, and I mostly just bought it for the heated round brush, but there are other attachments in there. It comes with the base, a skinny one, a tapered one, a beaded one, a thick one. The reason I bought it, the heated round brush, a glove, and some clips. So let's put this together.  Now it's attached. So let's plug this baby in, and it has different settings. I think I'm going to put it on one. I'm going to a Valentine's Day party today, so that's what's up with all of the pink, but I want to have the bouncy wavy curls, and I am really scared of this because I've never successfully used a round brush before. That's partially because I don't use heat on my hair, so I don't really have a need to use a round brush, but my sister got one caught in her hair once, and I was so terrified of them ever since, so I'm still really scared right now. Let's section out my hair. So I have the top pieces out of the way, and I'm going to start with the bottom, and the brush is heated up for a few minutes now, so it's probably warm enough, but let's find out. I'm just going to comb this one last time in case that brush tries to get stuck. Now I'm going to brush the bottom pieces inwards and the top pieces out. Okay, this is not that bad. I don't want to speak too quickly, but this is not that bad, and I'm like wrapping and curling the end piece, and it is sliding very easily. I'm going to hold it at the top and then unroll a little bit, and then brush through the ends. And let's see. Okay, that did something. I'm going to brush this one like diagonally just so that they don't combine into each other so I can get a little bit more volume. I'm going to hold it up here for like four seconds, and then start to unwind, and then brush through just the end. Okay, this is cute. Brushing from the top is nice to start so that everything is even, and then by the time you curl into it, it's just a flat little curl that will easily wrap around. And the goal of this is pretty much to have the ends just like have a floofy little airy light curl so it looks like a blowout, so that's why I'm really focusing on the ends. And then I have seen the girly's twist to the end, and then they just pull down. I think I'm going to just twist them a little bit and let it do its thing. I can't wait to get to the top sections and curl it outwards, and to the layers, oh my goodness. So this works best with layers, and I have some face framing layers, and then it kind of goes out like that. And the more layers you have in your hair, the more it will look like just like a layered blowout that's kind of like, I don't know, like a waterfall or something. Let me know if there's a term for that, but that's what I've been really seeing very layered people doing this, and well, layered hair people doing this, and it just looks so good. So let's do the rest of the bottom and get that base layer going and make it as wispy as possible. And by the way, I do have heat protected in my hair from before when I straightened it. Also, I'm pulling outwards away from my head now to build up some volume. Bottom is finished, so let's do the top. And look at how beautiful and bouncy this looks. I'm so excited to see the final product. So at the top, I'm going to start by curling upwards, so it gives at least a little volume. And I'm curling this away from my face. So far, this doesn't seem to be snagging at all, and that's what I was so scared of, but it's going really smoothly. And I think as long as you uncurl it the right amount, then it won't get stuck. And maybe that's because it's a ceramic barrel, so it's easier to slide on. I'm also alternating curling away from my face and towards my face, just so the different sections don't kind of clump together. But for face framing pieces, I'm curling away from my face. Okay, this is insane. Look at the volume, look at the ends, the blowout, oh my goodness. I've literally never had my hair like this before. I've never done a blowout look before. I usually do tighter curls, but this is giving exactly why it's been giving the other girlies on TikTok. I'm really surprised and very relieved because I bought this thing at full price, like four minutes before it went on sale. Look at how stunning these layers are. I'm so glad I got a layered haircut. And by that I mean I gave myself layers. And I think my face framing pieces just look so good. And now the last thing people would do would probably be hairspray, but I just don't really feel like that. And I have to leave now if I'm going to be on time. So I want to keep my friends waiting. This is the final look. I'm so happy with it. I definitely recommend trying out the heated round brush. Do it on low and it still works very well. So yeah, I'm kind of in love with this brush. I'm so glad I got it. TikTok shop, you did not let me down on this one. So let me know in the comments what you think and what I should try next.


When you do low carb right, binge eating is not in your life. Hey there enjoy root22.com on another low carb keto carnivore chat. And today it's the faint memory we have called binge eating. We're going to share some of our wild memories of what binge eating was like before we understood for real what sugar and carbs does to our body. You may want to read the book sugar blues. It was written way before even high fructose corn syrup, but it'll help you understand sugar a little bit. Not as much as the science end of it, but it's more in the history of sugar and how really awful and evil it is. God, man, we would drink beer after beer after beer, 12 packs, sometimes more. I had hunger pangs all day long every day of the year. Our go-to foods back in the day were pizza, bread, sandwiches. Everything we ate was carb based. God, dips, sauces, burgers, fries, pizza, of course, ketchup, anything. It was just all sugar based. The texture had a lot to do with it, too, like chips, crunchy chips and stuff like that.  That's sort of like a eating and a betting you're eating. But they're gone now. They're absolutely gone. By the way, drinks, too. Any sugary drinks, ice teas or whatever, sugar in your coffee and artificial sweeteners. I guess the senior versions of the artificial sweeteners like Aspartame and all those others, they made us hungry. We know that for a fact they made us hungry, even though they had no calories. They made you hungry and you just made up five times more of calories in the food that you ate because of those diet drinks. Today, it's just 100% low carb foods and we're never, ever, ever hungry. Unless it's I've gone a day without eating and then you slowly get this a level of hunger, which is your body saying, please feed me fuel so I can keep your body strong and fit. We also try to do, you know, we generally follow like the 18 six or 16 eight rule where you only have like a six or eight hour window of eating during the day. That's natural because we don't wake up hungry. And oftentimes we just don't eat breakfast or we skip it entirely or I make breakfast for the family. I don't I try not to eat. I'll say, I'll just have a burger or so or two at dinner. And a lot of times it automatically just becomes an OMAD. OMAD, one meal a day because it's just very easy when food isn't on your minds and your body isn't having this, you know, roller coaster of blood sugar levels. So that's it binge eating, not a problem. Have a good day. Click the bell and subscribe.


The Romance of the Ranchos Monterey, 1818 Privateer's Sacks Capital of California Santa Barbara, 1818 Privateer's captured at Ortega Rancho Santa Barbara, 1822 American Wynn's Senorator who saved his life The Title Insurance and Trust Company of Los Angeles presents the Romance of the Ranchos a program dramatizing the colorful characters and the historic events in the building of our Southern California Each week our wandering vocero Frank Graham returns with another fascinating tale of the days of the dawn The business of the Title Insurance and Trust Company of Los Angeles is to protect owners and investors in real estate against the risks of defective titles Today our country, and each of us individually face far greater risks through the treacherous assaults of the desperate enemies of democracy America has the resources to crush these threats once and for all Let us mobilize these resources at once, all of us by buying more and more United States defense bonds and stamps Only by such united effort can we win the war The sooner we do it, the more American lives we can save And now here's Frank Graham to tell us the story Buenos noches, señoras y señores Our story tonight is concerned with a man who many historians credit with being the first American to settle in California and with one of the most romantic incidents in all the history of early California It's a story which has been colored by many retellings until, in its many versions, it has become almost legendary with the authenticity of many details obscured by time But the essential facts concerning the life of the young adventurer Joseph Chapman are unquestionably correct And the colorful and romantic tale is worth the telling for it is filled with the romance of the ranchos Joseph Chapman was born in New England Little else is known about his early life until his ship before the mast on a New England whaling ship bound around the horn for China It was a long, rough voyage before they finally reached port in the Hawaiian islands then called the Sandwich Islands And it was there that late one night Chapman talked to a chance acquaintance But, monsieur, you are young, adventurous, ma'am You will not care too much how it was done if you could earn a nice spot first Well, what are you driving at?  Well, no, I don't Monsieur, have you ever heard of look-up-it-then Bouchard? Not the privateers, ma'am Yes, listen Oh, no, monsieur, I'll have no part in that crew I'm well satisfied with what I have Monsieur, surely you would like much gold? Well, I'll get it some other way You need not waste any more breath, monsieur, I'm not interested But wait! Good night, monsieur Very well, monsieur Ici, vite, mes marins Au fort, d'accord Bien, good work, monsieur So, you will have no part in that crew like ours, hein? Bien, we shall see I'm bored with him, I'm quick And so Joseph Chapman was carried aboard the Argentina flagship of the much-feared privateer the Palatou Bouchard A few hours later, when he awoke he was confronted by the master of the ship Eh, monsieur Chapman You are awake What hit me? Just a bling pin, my lad Just a bump on the head, nothing to worry about You're Bouchard? Oui, je suis Bouchard And you, monsieur You are my new first mate First mate? Oui, do not be surprised I know you, you are an handyman, monsieur A navigator, a carpenter, a good fighter, perhaps? Hmm, I can use you Is that so? Well, you've got another guest coming, Bouchard Oh, take a look over there, eh What?   It was burnt, by a torch No, it was not entirely his fault Not his fault? If I could only catch the rich I would kill him with my own two hands Papa, forget that, now there is no time to lose they come this way Take everything of value to the mission, santi See, see, you are right That is all we can do That and pray that the soldiers will get here in time Sergeant Lugo's detachment arrived just in time Don Jose Maria Ortega had moved all his valuables to the nearby mission and the soldiers hid themselves in the bushes on the shore just as Bouchard shipped home to the outside of the surf On board Well, Mrs Chapman, I see no sign of life for the glass, the buildings are deserted not a deep stares Perhaps it's an abandoned ranch house See, abandoned for fear of Bouchard Look at the well-kept fields, the corals They run away, and not many hours ago This will be easy We can take our own time to ransack each building Captain, this will not be like the last time No, Monsieur, much easier I mean, it will not be necessary to burn and destroy Of course, after we have what we want burn everything Where's Chapman? Those are my orders They are not a bed I have a way of dealing with mutiny and not just a little bump on the edge Now, you're in charge of the landing party Over you go, go away In toward the surf came the boat bearing Chapman's landing party, waiting in the bushes with the men of Sergeant Antonio Maria Lugo And then I'm not going to try to learn through that surf, surely? It looks like it See, he's bringing it on in What's in your?     See, he's either climbing up the tree to fix them now We'll be ready in a moment Now you'll see, my buffalo It does not take to go sailing around the world Robbing people, burning, killing Someday, sooner or later You meet somebody just a little bit smarter And you are finished, swinging at the end of Europe Well, it has to come sometime It may as well be now Oh, but no, senor You are so young, so handsome So, why, you have everything to live for But I'm not going to No, it is too bad I'm sorry, senor I like you Thank you, senor I've never been hanged by such a gentleman as you Gratis, senor See, senor Otega I am glad that I got back in time I have brought my family back from the mission To see the men who have robbed and plundered Maybe even killed them You are just in time, senor The robes are ready And now you shall be able to see your men Wait, wait There is one thing I must do first Guadalupe, come here Look Are any of these men the one who struck you? Oh, but the father, he did not exactly strike me Oh, so he is here, eh? Man, which one is it? I did not say he was the father Which one is it, I say? Let me get my hand on him Why not tell him, senorita What is this? Oh, senorita You know him?    Guadalupe, I cannot understand you I should not want the blood of any man On the sole of my father Guadalupe, I do not understand this But, well, if that is the way you feel See, see, that is the way I feel Papa, you must not kill him Very well, sergeant You must not kill him But, senor, what am I to do with him? How should I know? Take him back to Los Angeles Los Angeles? Oh, but, Papa, I... See, what is it? Do, do not think Perhaps they should be kept here They might escape Oh, no, senorita, they should not escape I shall see to that But you will not harm them, senor You must promise me that Oh, senorita, of course not I must have enough to have to hand them I do not know what I should do with them in Los Angeles But perhaps the governor will tell me Perhaps, perhaps if you were to give assurance Of their safe appearance, they could That is, some of them could stay And help you with the work Guadalupe, I do not know what you are thinking of I will have none of them Oh, see, but I will, senorita That's a very good idea I, myself, will go shorty for this one This great buffalo, I like it Oh, gracias See, senorita What do you think of that, senor buffalo? Can you be trusted? Go watch, I go Yes, I think you can trust me, senor You're very kind Oh, wait, senorita You too are kind I don't deserve such treatment from you But I thank you I would have done the same for any man, senor Oh, well, thanks anyway I hope that someday perhaps You'll forgive me Perhaps, someday I will, senor Today's war efforts are resulting in Necessary curtailments Priorities and restrictions on sales Of certain essential materials Along with some other factors Which are only psychological Have seriously affected some lines of business It is important for all of us To remember, however, and to point out To others that the general picture In Southern California is relatively bright For one basic example Let us compare the volume of real-estate Transactions in Los Angeles County For December 1941, most of which Occurred after the beginning of the war Were those of the same month the year ago We find that in 1941 The transfers of ownership of real-estate Actually increased almost 12% At the number of investments in real-estate Actually increased over 8% At the same time, foreclosures on real-estate Decreased 39% And we find further, despite alarming An exaggerated eastern newspaper Stories about the Pacific Coast That the large eastern insurance companies Are still actively seeking and making loans On Southern California real-estate New people needing homes And new money financing these needs Are still pouring into the Southland To the benefit of all of us So title insurance and trust company Urges you to remember that in most fields Southern California is still The white spot of the nation Still the land of opportunity And still the best of all places To work and to live I'm Don Antonio Maria Lugo Sergeant in the armies of Spain And true to his word He gave Joseph Chapman his liberty Trusting in the young man's honesty In fact, staking his place in the community on it And he was not mistaken For given a chance Chapman endeared himself to the population He was put to work supervising The building of the first church of Los Angeles The old plaza church still standing And in use And it was on this job that he won the admiration And earned an unusual nickname All right, swing that theme across the top We'll brace it here Who is he, my son? What brings you here? He was for another laborer I bring you this man, one of my best Indians From the mission Pedro, come Pedro Don't hang around, come here No, please, do not make me work here Take me back to the mission Pedro, what is the matter? I cannot understand you Well, this is not such hard work, Pedro No, no, I want to go back But Pedro, why are you acting like this? He looks scared to death Yes, Pedro, what is it? What are you afraid of? Him, El Diablo I did not want to work with him Me? El Diablo? Pedro, why do you course in your Chapman such a name? Because he worked with the black art in magic And we chopped down a tree He make it fall whichever way he want He's El Diablo Oh, I see now Why, Pedro, that's just a trick I learned In the woods of New England Anybody can chop down a tree and make it fall the way he wants You can do it yourself, want to learn how? No, no, I will not Never mind, Jose, I shall talk to him He will make a good worker Me, El Diablo That's good I can hardly blame him, senor For you have done more work here in a year Than we have been able to do in three before you came It may not be black magic But your ingenious ways of doing things Have certainly speeded up our work enormously I'm glad you're satisfied, Padre Satisfied, oh, my dear Jose I don't know what we would do without you Just this morning, Father Sanchez And I had the rather heated words over you Over me, Padre? But why? He wanted you down at the mission to help with the grist meal He's in need of repair And I would not let him have you For I need you here Well, Padre, I hope I don't cause you trouble Oh, but you do, a great deal Just trying to keep you for my own purpose You may cause a great split in the ranks Of the Padres yet El Senor Diablo Joseph Chapman won the affection of the Padres But he became almost a son To old Don Antonio Maria Lugo He visited his spiritual godfather often What troubled you? You have been sitting out here alone For hours staring at the moon I'm sorry, Don Antonio I've just been dreaming Ah, dreaming And when a young man dreams It is usually of a young lady And it is right you should dream that way, my son You You would not dream of the sea Of going off again back home to New England Oh, no, no, nothing was further from my thoughts This This is my home now My boy, I have hoped to hear you say that That is wonderful Wonderful The Padres and I have talked many times We all want you here to stay You see, we are feared There is no need to fear my running away Don Antonio I'm still your prisoner, remember And I give my word Oh, no, no, I did not mean anything like that That means nothing anymore I have already asked the governor to grant you a pardon Wipe out your score Really, sir? I shall be glad for that And you shall have it soon I should have replied from the governor any day now But that is why I was afraid I was afraid that once you were free You go back Sit away from here No, I don't think I'll ever want to leave here again No, you will write the first time About my dreams Ah, senorita That is good I was hoping that too, my son Before you should marry and settle down Raise your family of Californianos You're getting ahead of me, senor I haven't even found the girl But you were dreaming I was thinking of a girl I Saw just twice A beautiful girl With her lovely hair, burnt Ah, my son, senorita Guadalupe Don José Ortega's daughter See I wonder if she's forgiven me yet My son, she did not risk her life And save yours for nothing I wish I could believe that Perhaps you will have a chance To find out soon Senor José, my son Ah, don Antonio Lugo What brings you to the challenge? Oh, padre, I'm looking for Senor Chapman Oh, I'm sorry, he's not here Not here? Not working? He's gone, left this morning Gone? You mean he ran away? No padre, that's impossible He's a good honest man Oh, of course I know I did not mean that, senor He did not run away He was sent away and mort by the order of the governor The two were sorry to lose him But he was needed to build a flower For the mission of Santé Inés Ah, that's his battery What? Santé Inés? Well, that is, that is Don José Ortega Oh, this is wonderful, wonderful The governor sends me news That senor Chapman will soon be found Now he is sent to Santé Inés Where he will see This is wonderful, wonderful Senor Chapman, come in You sent for me, Padre? Yes, I have a job for you You mean you want me to stop work on the flower mill? Oh, no, this will take only a few minutes I understand that you know something Of the art of medicine Not a little Well, the senorita From a neighboring ranch So has suffered a broken arm She is here now You will help us fix it perhaps, no? Of course, where is she? Right this way, go Yeah, my dear, we shall have you where in no time Senor Chapman, this is... Senorita Oh You know each other?  Not too much You ought to fix it See, in just a moment I've been hoping to see you, senorita I'm almost glad this happened Senor, you must enjoy my being hurt First, my hair Oh, senorita, haven't you forgiven me yet? See, I have And I have heard much about you What you have done in Los Angeles I am glad that you were not as bad as my father thought Oh, that's forgotten now You see, even your hair has grown out See, nothing remained to recall that day Nothing but this Senor, what is it? A little pouch of leather See, that I always keep close to my heart Always But why? Because in it is this Oh, this round of hair See, your hair I've kept it ever since that day Oh, senor, you kept it See, so that I might always have something to remind me of you I didn't know then that I might ever meet you again But I thought of you, a great deal And I of you, senor Senorita, you mean then You really did save my life because See, because I... Even in my anger, that day when you held me so roughly in your arms And burnt my hair I knew that I could never Never forget you I never will Oh, querida mía You never have a chance to now One of the many feats of Joseph Chapman Was the building of the first field vehicle in California An ox-drawn curator Which had two large wooden wheels Hand-hewn from native timber Brought down from the mountains For some time it was the only vehicle in this area Which today leads the nation In per capita ownership of swift modern automobiles Since that time Southern California Has also become a leader in many other fields Including the volume of real estate transactions For nearly 50 years the service of the title insurance And trust company of Los Angeles In verifying and ensuring land titles Has been an important factor in making this volume possible The company has grown to be a national leader too And the number of policies of title insurance issued In the speed and completeness of its service And in the efficiency by which it is able to render This service at minimum cost to its customers Now Frank, what's the story for next week? Next week we'll take you to the great rancho Which once stood on the present site of Azusa And tell you the story of a town that was raffled on It's a tale you're going to enjoy, I know And so until then this is your wandering vaquero Frank Graham saying Hasta la vista, señoras y señores The romance of the rancho Is a presentation of the title insurance And trust company of Los Angeles Featuring Frank Graham as the wandering vaquero Is dramatized by John Donkel And produced by Ted Bliss With special music arranged by Erwin Yeo Bob LeMond speaking This is the Columbia Broadcasting System


So medieval Oxford students had a wide reputation for misbehaviour, some of which was brutal and bloody, some of which was extremely quirky and humorous. So the university itself was keen to articulate its role as a keeper of peace. And in 1429, they wrote, we work to assure peace and tranquility and neither we nor any of our members disturb our neighbouring townspeople or foreigners, but our whole university thrives in the beauty of peace for studying. Well, that might have been the goal, but plenty of students get up to lots of naughty things. We have evidence from Merton College about a student being expelled for, amongst other things, playing tennis in public, which was deemed extremely shocking. Several students were disciplined for calling their masters too out of them, which is sort of the informal version of you in Latin. It's like saying, hey, you to your tutor, rather than yes, sir. We have evidence about humorous but also quite brutal inception ceremonies for students when they started university, kind of like hazing ceremonies. So in New College, we know that freshers were sometimes subjected to a weird ritual where imaginary beards would be shaved off them, given they're only about 14 at the time. I can imagine that would be pretty distressing. And sometimes student misbehaviour was really theatrical. It's a sense that they put in a lot of effort and took a lot of time to organising the props and setting everything up and even dressing up. So in 1417, a group of students decide to march off to Ifley Village, there's a dispute over some land there. And they dress themselves up in full suits of armour. We learn from the documents that they were armed with breastplates, pairs of poltered gloves, van braces, rarer braces, pricking pallets with three ostrich feathers, lance gaze and a Carlisle axe. So there's a real sense of spectacle of these students giddling and jostling their way towards Ifley Village with these magnificent costumes.


Offensive will not be stopped by blowing up hydroelectric power station. The armed forces of Ukraine have stated that the Russians blowing up of the Karkovka hydroelectric power plant will not prevent the defence forces from continuing to liberate the occupied territories. Ukraine has all the necessary watercraft and pontoon bridge crossings to cross water obstacles. The enemies in Sidious actions which are creating a social and economic crisis will not stop the defence forces of Ukraine which are ready to liberate the occupied territories of Ukraine. Strategic Communications Department of the Armed Forces of Ukraine said The department noted that the Russian military leadership destroyed the dam because of its fear of the Ukrainian army and the success of the Ukrainian defence forces in carrying out offensive actions. On the morning of the 6th of June, the Russian occupation forces had blown up the Karkovka hydroelectric power plant. The Karkovka dam is part of the Karkovka hydroelectric power plant built in the 1950s and 1960s in Kursyn Oblast. This is the last and lowest rung of the Nipro cascade of power plants.


Hello, good afternoon, everyone. Yeah, as Andrew already introduced, it's about the EcoCloud or EcoScience Research Data Cloud here. It's basically kind of a big project not just technical development. So we have a department of environmental and energy. They are developing the essential environmental measures, which we want to make available, that there is a whole lot of work streams around species trade data, making those away little, getting access to the daily spatial weather grids, and other existing data streams. Then there's a whole work bundle around standardized modeling and analysis capability, which came out of PCCVL, basically, to have a robust set of well-defined and reliable models. The most technical side for us is to develop a platform which gives you access to compute and research and makes it easy to access your data. Log in, go on and start working without caring about where the data comes from and what else is otherwise set up between those every level as possible. Another big part is about training and skills development. This will be part of the EcoEd and EcoPathways programs that will develop a whole lot of training, material, cost, material, run for workshops, and similar things, and also engage its industry. And the last stream is about trusted data. So I'm not too familiar with that bit. My book is more about the technical side, but it's more about knowledge about reliable data, where it gets from, who is using it, and which data can it use to do proper decision-making. A bit of history about it. So with Relate PCCVL about three to four years ago, it's been very well received. It gives easy access to data and modeling and reduced technical barrier to access data and use it. What we have found, though, is that there's an increased demand on customizing the work and having an interactive workflow to work with models and data. Another big use case is users want to use sensitive data, which can't be released publicly anywhere. Many more users are coming on, and they want to use their own data, which they have compiled or retrieved from somewhere, which is publicly inaccessible. Another big thing will be that we try to increase the interoperability with our systems. And all of these we took together and all the lessons we have learned through PCCVL, and we're trying to put into the EcoCloud platform. So the biggest challenges with the EcoSciences is that it's a very diverse community, and with a very diverse set of data we are going to integrate our users want to use. So it's about space data, climate data, marine data. All described in different ways and often doesn't make sense to an early career researcher who comes out from an apology background. Another big thing is portability. If you develop something, share your code, should be able to run anywhere, not just within the EcoCloud platforms. It's said we want to provide the ability to work with sensitive data, so security is a big thing here. And data discovery, data access, and data usage is still a very big challenge. While the work with data description and data portals has been moved forward very well over the last couple of years, accessing actually the data and using it is still a bit of a challenge. Then we want to provide some way to work with large data sets, which are impossible to download or require some HPC environment, and some way to get easy access and integrate projects. And as our users are using their own private data often, we need to integrate cloud storage, so for the next cloud, Anet, Cloud Store, or Dropbox, and similar things. The users we are targeting, researchers, academics, undergraduates, post-graduates, all the high-end users who know how to code and use HPC environments, but still want to share their work. Big data users will be included as well. And of course, to help with collaboration, there should be some useful opportunities to collaborate with proper software engineers as well, to optimize their code, help with coding, or even produce new third party products on top of EcoCloud. The opportunities there, of course, research, science, the ability to publish your code on models you're developing, along with your data you've used, various workshops, software carpentry, data carpentry, provide resources to run curriculums, and all the research community. So on the technical side, there are being three components developed, so the EcoCloud Drive, that's here. Easy, cloud-managed, online storage for code, script, small data sets that will always be there. So even if everything crashes, next time you come in, the last piece of work is still available. The EcoCloud Explorer, which we hope will increase our help with data discovery and access, will mostly be part of CSRO Knowledge Network. And our work there will be to provide help with using the actual data through, for instance, providing code snippets. And of course, there will be the compute side of it. So at the moment, we have opted for providing two-bit notebooks, which are a Python and RStudio, are already available, and also access to virtual desktop tools, at the moment, provided by CSRO, which is a term project. Three minutes, Gerhardt. Sorry? Yeah? So our big architecture is sort of a user comes in. There will be a dashboard from which you can access everything. There's a separate centralized user management. So all services are independent. They don't know about the users, but they use this user management service to identify access to various things. From there on, you can publish clone scripts from other users, find other scripts, notebooks, browse through examples, how to use various data stores or use certain processing. You can explore data, try to get the data in in an easy way, start a new project that essentially gives you a compute environment to pick whatever you want, R, Python, virtual desktop, and use the tools that are available there. And these tools, these environments are usually also customizable, so you can install your own software there as well. And our tech stack, it's a fully, it's a microservice architecture, fully OpenID connected and over to enabled. So all APIs that will be offered and are available will also be accessible through third party systems. Our development itself is mostly in Python and JavaScript. It's been designed to be horizontally scale-able because it's just easier. Vertical scale ability is still there, but there are challenges with resource allocations sometimes. And the whole system also allows to go multi-node, multi-cloud with the work. And the way we have built it up is at the bottom, there's, of course, OpenStack provided by the Nectar Cloud with all its services we are using. The gray box, Sahara, Nokia and Trove, we are currently not using, but certainly looking into it, how we can make an instance for our users. On top of that, the whole OpenStack infrastructure is managed by Kubernetes, which takes care of orchestration, security, all sorts of monitoring, and due to that, we can do wire Kubernetes, we can autoscale everything. Kubernetes itself orchestrates everything that runs within EcoCloud. So there's our attributed notebooks. There will be web processing services, plus the Web UI, but there are still three developed that provide APIs. And Fuzera Virtual Desktop sits a bit outside of it, but will seamlessly integrate with EcoCloud. And all the work we are deploying here, and it's running within EcoCloud, it allows you also to access external services at the moment where we are providing tight integration with knowledge network, various data services, like data.gov.au and other things. Cloud Stories, as mentioned before, your Google Drive, your Dropbox, and external web processing services that would be of high interest for us, just to offload data transfer and compute services. And that's pretty much it for me. Thank you very much. Okay, thank you guys.