this pursuant to chapter 20 of the acts of 2021 this meeting will be conducted by a remote means. Members of the public who wish to access the meeting may do so in the following manner by emailing steve mccarthy at mccarthy s at amherstma.gov that's m-c-c-a-r-t-h-y-s at amherstma.gov no in-person attendance of members of the public will be permitted but every effort will be made to ensure that the public can adequately access the proceedings in real-time biotechnological means in the event that we are unable to do so for reasons of economic hardship and despite best efforts we will post on the town website an audio or video recording transcript or other comprehensive record of proceedings as soon as possible after the meeting and with that done we'll do a roll call of the attendance uh hallie here cast on here Doug here dylan here and i am here so we're all here um and we'll call the meeting to order at 6 o 2 p.m um public comment if anyone here no we have no attendees okay well um so i know it's been a while so why don't we just launch into our discussion items and steve said we don't have any new licenses this time but perhaps next time yeah we did get a couple applications from umass for one days for uh later in the year i think early april um so those are still going through the review process so those should be ready next time okay great we will look forward to that on the 21st um so the first item for discussion on the agenda is meeting time and we all made this meeting and i think i just wanted to reconfirm that it was mondays from six to eight the second was it the second and first and third first and third monday um until doug doug's tuesday's free up is that correct is that what everyone has that's what i wrote down so we have um the seventh and then the 21st of march and then the fourth and the 18th of april is that correct is the 18th of school holiday it is it is so doug when are you think that the tuesdays are going to be better for you well that 19th would probably be free i don't know what's everyone let me look at my calendar real quick and actually what i should do is look at the school committee calendar so that's what i'm going to do first have you been doing i've been good all things all things considered okay all right good anyone see the uh the black bears are back in town they were like up near our house maybe like three weeks ago i just saw um uh just some on cottage street a little earlier today the cups are almost full size now i really want to see them sometime but is one of them still injured i didn't even i didn't notice um i wasn't looking for it but they all seem to be walking normal but if i was looking a little harder i might have noticed i think it's pretty noticeable so maybe they maybe it healed well on a different note i think that um so school committees meet in april the uh don't always meet on wednesday so that's not an issue um it versus meeting on the fifth and reaches meeting on the 12th and the 26th i would suggest that the uh by the 26th so that would be i don't know if that's the third because if we have to shift off the vacation week because the 18th is a is a um monday's the holiday patrice day i think and then uh so if we want to avoid that week or if that tuesday doesn't work for people then that following tuesday the 26th i think it is i i can do i think okay so we could just do the fourth and then the 26th maybe i mean i'm okay with monday the 25th i i mean monday the 18th what we have now i don't i don't i i mean i don't have to i mean i don't i'm gone i don't have to be at the meeting if everyone else is here and there's a forum for i am here on the 18th but not on the 19th i will be at harry potter world for you fun yeah we're just ripping that fan date off where's harry potter world universal florida okay so fun really you think you can do a meeting the day before you fly yeah i'm only taking two kids okay all right i um i can do tuesdays in general um but if we were to switch to them to consistently because right now i'm doing tuesday nights i'm actually bartending in northampton um and i could do mondays instead but it would just need to be a consistent switch we were to switch to tuesdays i can kind of do one or the other consistently but uh so it's monday the 18th the holiday so is that steve today you don't technically work so maybe we should move to the 26th that then yeah that's fine let me double check that i'm not sure if we actually have that day off or not i don't you mass is closed so i assume that we'd go i would be surprised if you didn't steve yeah as a taxpayer in the town of amherst you're welcome to come in and do extra work for no fat the 26th is fine for me um dylan what bar are you at i'm over at fitz willies right now fitz willies okay no tuesday nights are they uh is it getting getting busy tuesday nights uh no tuesday nights is uh fairly quiet i'm just doing uh just doing some training over there with them but the uh it is getting busy at fitz willies now uh it's quiet for for the pandemic but it's uh looks like it's picking back up to normal so okay pandemic keeps easing so did you say done with the 26th is not good for you but tuesday uh correct yeah tuesdays uh tuesdays aren't good for me um in general unless we wanted to all shift to tuesday then i would change it to do mondays and then could do tuesdays here okay so i think for me that just to speak to that point about the tuesdays you know once we get to that that point in april i think i can go to tuesdays from that point on so if you want to do it you know on that 26th are you going to wait till we go into may i'm open to either or so i think it's just a question of giving filling that up lead time to switch the schedule to tuesdays to mondays so following so just to clarify following that the 26th and following you're fine on tuesdays you're open okay and everyone else is okay with tuesdays except for dylan what i mean is this enough notice for you to make the switch yeah yeah i can make that that that switch so then at that point we'll be tuesdays consistently correct that's the idea yes first and third yes the first and third tuesdays except for the 26th which we're making up from the week before and so then we will do two weeks in a row if if we need or since there's five tuesdays in may does it makes sense to do second and fourth in may i don't know the answer to that question steve you have an opinion do you think steve yeah i think that makes sense to keep alternating um i mean really i can make whatever work it's no it's no no problem for me i do think we will have some applications coming in for the outdoor dining so having just something i can i can count on in the schedule will be helpful but in terms of days it's you know really whatever works for you guys i can accommodate how about we just go to second and fourth starting on the on april 26 second and fourth tuesdays second and fourth tuesdays so instead of the fifth we do the 12th and the 26th oh so i was i was assuming we're going to start this oh you mean what you mean may because you well right so switching the 18th for the 26th and then may forward second and fourth for okay for 10th and then the 24th and then and then we stick with that the 14th and the 28th of june is that all right with everybody that's great okay all right did you get all that steve so we're looking at 326 is the next meeting 320 no the next one is 321 is the monday 321 okay i guess i got a little mix up okay sorry so the next one is march 21st 321 at 6 and then we go to 4th 4th the 4th april 4th at 6 as well at 6 and then we skip to then we move to tuesdays and we go to april 26th 426 at 6 and then then uh second and fourth tuesdays from then on out yes and then perfect and may 24th yeah forgive my loud type and try to uh take minutes on a different computer here so sounds good i've got that down okay perfect thank you so meeting time discussion item b adult use marijuana regulations don't yeah i don't really have any updates for anybody on this i'm sorry i think what i need to do is is give it one more read through make sure it's all set and then i think the second piece is to uh look at the creation of a bylaw which would be a actually that may have to happen first with the council before we adopted the policy and the and the regulations about how to get the license it has to be something that exists so i'll do the review you know sort of final review of those rags if anybody has anything that they thought of or or if they go back through them and have any comments please forward those along um but that would be the i think the next steps on that um thank you does anyone have any questions for dud okay um lunch cart regulations so um i was in touch with many johannaki uh town council and of the tso committee about um where they were at with the um changing the regulating the bylaws granting the port of license commissioners authority to license lunch carts on the sidewalk and on the street and in december the town council passed part of that half of the legislation so it's half done and we now have the authority to grant licenses on sidewalk lunch carts and she's going to bring it up with the town council meeting tonight she couldn't make the meeting because she has another meeting and um see when they will be discussing and granting us authority to license lunch carts on the street so as soon as she lets me know i will pass it on and um send another draft of the lunch cart regulations so that's what that's at that's all okay great um guidelines regulations for liquor license decisions i have it printed and ready to do one final proofread with a pen before i mail it off because i always miss stuff on the computer okay super thank you heli any questions nope all right um license fee comparison jar guest on i'm uh i i haven't made progress since we spoke last um so i need to uh i need to schedule some time for that um thank you all right thanks guest on if i'm we go ahead Doug i was just going to say you know this this begs a question a little bit um thinking about that and our comparison of the towns because what you had gathered today was it was interesting the the breadth of choices towns have made relative to their rates i think that begs a question about what we would think would be an appropriate license fee for adult use and and i think the the other thing to keep in mind regarding adult use i mean there's the the sort of retail sales that we have now and that's what's covered under the regulation but i think what's coming that we want to be thinking about getting cared for is is if the state allows social consumption in you know facilities you know cafes or whatever um sort of i mean i think there's a lot of wrinkles still to go on that but i think thinking in terms of what's the right level of of license fee for all of those is is something that kind of meshes with with what you're looking at on those those rates so i just want to put that in people's minds to think about thank you and um how can we get feedback from from the town about i mean i know that we're not fundamentally a revenue generating commission um but any decisions we have you know would have a uh more or less impact on the town budget and i'm wondering how we can kind of get feedback to inform our judgments about that well guys don't i could certainly much like we did with the um the reductions in rate for liquor licenses last year i can run that up to um the finance director and the town manager and ask for their feedback okay and um i know they've been taking a look at a lot of things recently so i'm sure they'd be able to slot that right in and okay you consider some things i mean it might be be good for us to kind of you know set a um i don't know about you know concrete you know we could we could look at concrete proposals for particular free changes or we say you know we think this should be lower we think this should be higher right you know whatever you feel like um would be appropriate based on the review yeah i was also going to mention earlier i'm actually going to be working on a little project to take a look at some of the point operated device prices around the state too so um you know we could maybe we could we could try to have a little meeting at some point phone meeting and kind of just go over what you found so far and and i'll you know probably find anything else when i'm doing that i can send along to you as well i'm smiling remembering in high school how i i reached out to a coin up guy who'd like just put some machines in the school and i was collecting half for a while okay yeah so do we uh steve the money we do generate through um the licenses does that just go into some general fund or what is um do we know how much we are generating through fees? Doug's nodding so um my impression is yes and he would certainly know better than i would um and we would have um yeah i mean i did have to just do a report for the state on the total liquor license or revenue i don't have that available with me but um i could send that along and everything else i mean i think it would just be um you know multiplication you'd probably probably calculate that figure yeah i i will say this regarding the regular budget you know it is part of a broader group of things if you were to look at the budget look at the revenue sources it's lumped in with all the other sort of miscellaneous income um but you know every little bit helps um and it's you know the thing is if you think about our license i mean it's like 3500 for i mean our liquor licenses generate a fair amount of revenue i'm not sure our you know live entertainment licenses is five bucks a popper really you know generating much but nonetheless uh you know it's it's some money it's not a ton it's part of the general support so it is general fund revenue but it's it's a factor i mean you know if it went to zero or if we decide to slash the rates on a bunch of these things to 100 bucks or something for all of them it would be a significantly and you know significant hit to the to the to the revenue and would be noticed um so we want to be you know we don't want to gouge people at the same time want to kind of factor in what that's helpful in support because it does you know for example you know police are our sort of agents in the town and so you know passively it sort of funds some of the police department and so the fact that they cruise by and do certain things or do ID checks or do some undercover stuff you know that's part of why we charge you know as much as we do for some of those licenses because they kind of pop in and do that work and it's not an explicit sort of one for one but it's just part of how that whole budget gets supported so that's part of i think the thing we want to go through and we're evaluating our revenues on on these and is what are what are the ways in which those funds are supporting you know our our town budgets yeah okay yeah i mean when you know i think we we we were struck by some of the discrepancies on the on the big ticket items on the liquor licenses and so it would be useful when we're actually talking about it to have a simple spreadsheet so we could enter numbers and and you know have a reality check at the budget level okay anything else on license fees if not um oh topics not reasonably anticipated 48 hours prior to the meeting is there anything i have nothing no steve no nobody all right review of minutes we do not have review of minutes this time so we move on if there's nothing else to adjournment is that a quick question for steve any uh any update on if we're going back in person anytime soon are we still doing remote i have heard nothing on that front um as of now we're still full masks in town hall and everything so i don't know if the town's making any any kind of moves on that anytime soon i have a small bit of info on that so the board of health meets on thursday this week the 10th uh and then they'll you know and they'll review the current you know um indoor public spaces mask mandate um so they'll probably my guess is like everybody else they'll make some decision about ending it changing it that sort of thing but um until they do anything we're kind of if we wanted to meet in person we'd have to be masked so and and we're still allowed by this by the state to to meet remotely until did that get extended through the summer or is that it was an april deadline for that but i think they've extended that haven't they steve i believe so yeah till so we have i think we may have the option but i think the board of health meets thursday and i think that'll be helpful as far as understanding what the direction is that that they're going that'll be good to hear my my understanding i think from reading the news is that the the town council itself is divided on the on the question i guess we'll find out right i mean if the board of health says we're going to continue with the mask mandate doesn't matter what the council because it's sorry i mean i mean the on the on whether the council wants to meet in person or not oh oh oh i would understand that yeah yeah on that question i'll see all right okay um anything else at all is there a motion to adjourn second second thanks dylan um i guess with no further discussion we'll take a roll call out of here uh doug hi dylan hi kelly hi cast on hi that i vote i um were adjourned at six six twenty two p.m. thanks everybody let us see you all thank you very much look with your more tremendous brackets thank you so much all right i'll see you on the 23rd


Welcome to the 2021 BDT year in review. It's been a very challenging year for so many of our members, our partners, and our stakeholders. And there may be many new challenges ahead. But despite all that, I believe BDT has much to be proud of. Over the past year, our project portfolio continued to grow, following the positive trend achieved over the past two years. Our new Youth Initiative Generating Connect goes from strength to strain, with Generation Connect youth groups now working actively in every corner of the world. Our partner to connect digital coalition launched on the sidelines of the UN General Assembly is gearing up to mobilize new resources, partnerships, and commitments to bring the unconnected online. I invite you all to join us in this coalition so that we can leverage our shared resources to bring the vital power of digital to everyone, fast. Closing the digital divide has never been more critical. With the pandemic accentuating and accelerating our dependence on technology, we urgently need to bring the transformational power of the internet to billions of people still offline. New ITU data estimate that while 4.9 billion people have connected, the gap between the digital rich and the digital poor remains a stark reflection of global inequality. Over 90% of the 2.9 billion still offline live in the developing world. And the reality is that hundreds of millions of those that we count as connected actually struggle with infrequent, unreliable connectivity that's too expensive, too hard to access, or too slow to play any meaningful role in improving their lives. That means that ITU's mission to connect the world has never mattered more than it does today. ITU's next World Telecommunications Development Conference in June 2022 comes at a crucial time. At that global conference, we have a unique opportunity to use digital to totally rewrite the global development paradigm. We absolutely must not miss our moment.


Lou mountains, Australia Let nature be your therapist Too much time in big cities. It's called evolutionary mismatch.


As Salaamu Alaikum. Welcome to lecture number 36 of the course on statistics and probability. Students you will recall that in the last lecture I discussed with you in detail the confidence interval for mu and the confidence interval for mu 1 minus mu 2. In today's lecture I will begin where the confidence intervals for p and p 1 minus p 2 and then we will go on to a very interesting and important topic, determination of sample size. So, let us begin with a confidence interval for p, the proportion of successes in a binomial population. As you now see on the screen, for a large sample drawn from a binomial population the confidence interval for p is given by p hat plus minus z alpha by 2 into square root of p hat into 1 minus p hat over n. In this formula as in the case of the confidence interval for mu z alpha by 2 will be equal to 1.96 for 95 percent confidence and it will be 2.58 for 99 percent confidence. Of course, if we want only 90 percent confidence then z alpha by 2 comes out to be 1.645. Students, it is p hat plus minus z alpha by 2 into the square root of a certain quantity and according to what I explained in the last lecture, this is the statistic plus minus z alpha by 2 into the standard error of our statistic. Shai dhaap ku yaadhu, when I discussed with you the sampling distribution of p hat, I did convey to you that the standard error of p hat. In other words, the standard deviation of the sampling distribution of p hat was equal to the square root of p hat into q hat over n and this is exactly what we have in the expression that I just presented. So, apne dekhaha ke uska jo overall format hai that is very similar to what we were discussing in the last lecture. Let us now apply this formula to an example. As you now see on the slide, let us look at a survey of teenagers who have appeared in a juvenile court three times or more. A survey of 634 of these shows that 291 of them are orphans one or both parents dead. What proportion of all teenagers with three or more appearances in court are orphans? The estimate is to be made with 99 percent confidence. In order to solve this problem, the first thing to note is that n is 634 and that is a large sample size, so that the formula that we are discussing is valid in this particular situation. Next, we talk about p hat and considering being an orphan as success, p hat comes out to be 291 over 634 and that is equal to 0.459. As such, q hat which is the proportion of failures in the sample comes out to be 1 minus p hat and that is 1 minus 0.459 which is equal to 0.541. Now, substituting all these values in the formula of the confidence interval, we obtain 0.459 plus minus 2.58 into the square root of 0.459 into 0.541 over 634. Of course, we put the value 2.58 in place of z alpha by 2 because of the fact that we want 99 percent confidence. Now, solving this expression, we obtain 0.408 as the lower limit and 0.510 as the upper limit of our 99 percent confidence interval for p. Students, let us try to interpret this result. This is the problem in which we are talking about teenagers who have appeared in the juvenile court three times or more and we are trying to see what proportion of them are orphans. Our result is 41 percent to 51 percent. This is the 99 percent confidence interval for p. The true proportion of orphans among teenagers of this type. Now, note that this interval has a particular width 41 percent to 51 percent or a very high level of confidence for p. The sample size was 634 which is a quite a large sample size. If we want the width to be lower, we can reduce the level of confidence and that will make it a little narrower because 99 percent is a very high level. Even 95 percent is alright and if we do that, then of course, our Z alpha by 2 will become 1.96 and in that case, when we compute, we will get a relatively narrower confidence interval. Let us now look at another point important point. It is 634 sample size. Generally, we can apply this formula. Students, you may remember that when I told you that the binomial distribution can be approximated by the normal distribution, I presented a rule of thumb in it and that was that if both Np and Nq are greater than or equal to 5, then we can apply the normal approximation to the binomial. In this case, both Np hat and Nq hat will be much larger than 5 and so this particular formula can be applied. Let us now consider another example. After a long career as a member of the city council, Mr. Scott decided to run for mayor of the city. The campaign against the present mayor has been very strong with large sums of money spent by each candidate on advertisements. In the final weeks, Mr. Scott has pulled ahead according to the polls published in a leading daily newspaper. But in order to check the results, Mr. Scott's staff conducts their own poll over the weekend prior to the election. The results show that for a random sample of 500 voters, 290 will vote for Mr. Scott. Develop a 95% confidence interval for the population proportion that will vote for Mr. Scott. Can Mr. Scott conclude that he will win the election? You have seen that this is a very interesting problem and quite a real life problem. First of all, let us see what is success. In the previous problem, of course, success was the first thing that we had to realize and in that one, the fact that the teenager is an orphan that was being regarded as success because I have already explained to you that success is a technical term. Here voting for Mr. Scott is success and voting against Mr. Scott is failure. If this is the definition of success, then of course it is very easy for us to compute P hat, the proportion of successes in our sample. And as you now see on the screen, since 290 people have favored Mr. Scott out of 500, hence P hat is equal to 290 over 500 and that is equal to 0.58. Of course, 0.58 is a point estimate of P, the true proportion of people in the population who will be voting for Mr. Scott. Now, as far as the 95% confidence interval for P is concerned, we have the formula P hat plus minus z alpha by 2 into the square root of P hat into 1 minus P hat into 1 minus P hat over n and substituting all the values, our interval comes out to be 0.537 to 0.623. In other words, the 95% confidence interval for P is 54% to 62%. Students, you remember that Mr. Scott thinks that he will win the election? Now, the point estimate that is 58% or the 95% confidence interval that is from 54% to 62%. Now, these figures are higher than 50% or agar 50% se zada log vote karenge to zahir hai ke he will be winning the election. To iska matlab yeh hua ke on the basis of this survey that his staff has conducted on their own, he can reasonably conclude that he will be winning this election. Let us now consider another example. As you now see on the screen, a group of statistical researchers surveyed 210 chief executives of fast growing small companies. Only 51% of these executives had a management succession plan in place. A spokesman for the group made the statement that many companies do not worry about the management succession unless it is an immediate problem. However, the unexpected exit of a corporate leader can disrupt and unfocus a company for long enough to cause it to lose its momentum. Use the survey figure to compute a 92% confidence interval to estimate the proportion of all fast growing small companies that do have a management succession plan. Students, iski andar, we are interested in computing the proportion of companies that do have this plan in place or have 92% confidence interval construct kar na chate. So the first thing to note is that if in our diagrammatic version of this situation we are putting 92% area in the middle, it means that we have to place 4% area to the left and 4% to the right. So in this case may zki value, as you now see on the slide, according to the area table of the standard normal distribution, z alpha by 2 comes out to be 1.75. Hence we can use this value to compute our confidence interval. The formula of course is p hat plus minus z alpha by 2 into the square root of 1.75. p hat into q hat over n. Now we have n equal to 210 and p hat equal to 0.51 as we noticed a short while ago. Hence substituting all these values in our formula, the 92% confidence interval comes out to be 45% to 57%. Now that we have discussed how to construct the confidence interval for p, let us proceed to the confidence interval for p1 minus p2. In this situation we may be interested in determining the difference between the proportion of successes in one particular population and a similar proportion in another population. Suppose we are interested in determining the difference between the proportion of smokers in Karachi and the proportion of smokers in Lahore. So we will be talking about p1 minus p2 where one stands for Karachi and two stands for Lahore or kai or interesting situations where we are interested in the difference between proportions in two populations. So as you now see on the screen for large samples drawn independently from two binomial populations, the confidence interval for p1 minus p2 is given by p1 hat minus p2 hat plus minus z alpha by 2 into the square root of p1 hat q1 hat over n1 plus p2 hat q2 hat over n2. The point estimate plus minus z alpha by 2 into the standard error of the point estimate p1 minus p2 hat minus p2 hat plus minus z alpha by 2 into the square root of sum big quantity and this sum big quantity square root is the standard error of p1 hat minus p2 hat. Of course I could have started deriving all of them for you but I would not want to do that. I would like you to develop a sense of the basic pattern without necessarily having to go into the lengthy mathematical derivation. Let us now apply this particular formula to an example. As you now see on the slide in a poll of students in a large university 300 of 400 students living in students' residences that is hostels approved a certain course of action whereas 200 of 300 students not living in students' residences approved that particular course of action. Estimate the difference in the proportions favoring the course of action and compute the 90 percent confidence interval for this difference. Now in order to solve this problem first of all let us denote by p1 hat the proportion of students favoring the course of action in the first sample that is the sample of residence students. Also let p2 hat be the proportion of students favoring this particular course of action in the second sample that is the sample of students who are not residing in students' residences. Then according to the data that we have available to us p1 hat is equal to 300 over 400 and that is 0.75. Also p2 hat which is 200 over 300 comes out to be 0.67. Therefore the difference in the two sample proportions is 0.67. Therefore 0.75 minus 0.67 and that is 0.08. Now the required level of confidence is 90 percent. Therefore Z alpha by 2 is 1.645 and hence our 90 percent confidence interval for p1 minus p2 is 0.08 plus minus 1.645 into the square root of 0.75 into 0.25 over 400 plus 0.67 into 0.33 over 300. Solving this expression we obtain the lower limit of our confidence interval as 0.023 and the upper limit is 0.137. Rounding these we can say that the lower limit is 2 percent and the upper limit is 14 percent. Let us interpret this result. We are saying that the difference between the two categories of students, this difference in the proportions lies somewhere between 2 percent and 14 percent and this statement is being made on the basis of 90 percent confidence. Now you have seen that this is a very wide interval. You have one edge which is 2 percent which means the difference is very small and the other edge is 14 percent and that is not very small. So now you have seen students that our level of confidence was not that high. It was not 99 percent or 95 percent. It was only 90 percent and our interval is slightly wide. This means that the sample sizes are 400 and 300 although they are so large but still they are not large enough for us to have a narrow interval as narrow as we would have liked in this particular problem. So this is the kind of situation that we are dealing with all the time when we are doing interval estimation. See, different formulas are developed on the basis of scientific reasoning, mathematical reasoning. But this cannot be said that we will cover every kind of thing in it and there will be no problem or encounter in it. Obviously all these procedures that you are studying, it is very useful in many situations but the limitations in this problem should be recognized as well. Only then you will be able to apply these mathematical formulae and many other mathematical formulae in a proper way, in a real life situation. Alright, let us now start another very interesting concept and that is the concept of the determination of sample size. See, students, we have been talking for so long regarding estimation and we are saying that the sample size was so much and so on. If you have to conduct a study of this type, the first question will arise that how large a sample should I take from this particular population? This is the first question and all other things have been discussed. So, I will now present to you a method of determining the sample size. If we want to achieve a desired level of precision with a desired level of confidence and I will present it to you first with reference to the estimation of mu. As you now see on the screen, in deriving the confidence interval for mu, we have the expression the probability that x bar minus mu lies between minus z alpha by 2 into sigma over square root of n and z alpha by 2 into sigma over square root of n. This probability is equal to 1 minus alpha. Now, this statement implies that the maximum allowable difference between x bar and mu is z alpha by 2 into sigma over square root of n. Students, I am sure, but there is no need for that. We are saying that the probability that this t is lying between these two limits is probability 1 minus alpha. Now, these two limits between which this quantity x bar minus mu lies, these are the extremes where we can allow this x bar minus mu to this extreme or this extreme. So, we can give this statement which I have given and I would like to request you to have another look at the same slide that you just saw. Now, the maximum allowable difference between x bar and mu represented by the modulus of x bar minus mu and it is equal to z alpha by 2 into sigma over square root of n. Now, the quantity modulus of x bar minus mu is also called the error of the estimator x bar and it can be denoted by small e. Thus, the error bound for estimating mu is given by z alpha by 2 into sigma over square root of n. In other words, if our level of confidence is 1 minus alpha and we want that the error in estimating mu by using x bar, this error should be less than e, then we need n in such a way that the following equation is satisfied. The equation e is equal to z alpha by 2 sigma over square root of n. Now, if I bring square root of n to the left hand side and take e to the right hand side, I obtain square root of n is equal to z alpha by 2 into sigma over e and if I take the square of both sides of this equation, I obtain n is equal to z alpha by 2 sigma over e whole square. Students, this formula we have developed, let us try to understand it. It is n equal to z alpha by 2 sigma over e whole square. In this, the components on the right hand side, look at z line, sigma, the population standard deviation and at the moment we are assuming that it is known. In addition, z alpha by 2 and denominator e. Now, note that z alpha by 2 and e are both in your own control. The question is that z alpha by 2 will denote that number which will be according to your desired level of confidence and e is the maximum error that you are wanting in your estimation process. You will determine this yourself. And this is the way we can determine the required sample size in such a situation. But what if sigma is unknown and obviously most of the time the population standard deviation is not known. Students, in such a case we will estimate sigma by s and this s will be computed from a pilot sample. A study which is prior to the actual study. We will replace sigma by s in this formula and find n. So, let us now apply this concept of determination of sample size to an example. As you now see on the screen, a research worker wishes to estimate the mean of a population using a sample sufficiently large that the probability will be 95 percent that the sample mean will not differ from the true mean by more than 25 percent of the standard deviation. How large a sample should be taken? In order to solve this problem the first thing to note is that the error bound e which is also the modulus of x bar minus mu this is equal to 25 percent of the standard deviation that is 25 sigma over 100 and this is equal to sigma over 4. Also because we want 95 percent level of confidence therefore, Z alpha by 2 is equal to 1.96. Hence substituting these values in the formula for n that we derived a short while ago we find that sigma cancels with sigma in the denominator and we are left with 1.96 into 4 whole square and this comes out to be 61.4656. Hence the required sample size is 62 and it is important to note that 61.4656 will be rounded upward because obviously the sample size cannot be fractional. Students you note that here 61.46 which is the answer was a little less than 61.5 so you could say that according to the ordinary rules of rounding it should have been rounded and turned into 61. But please remember that whenever we are determining the sample size by this process we will always be rounding upward. We should not have rounded it down we should have rounded it upward. So we would like to play safe and it is the processes that we should be rounding upward. All right with reference to mu of course a similar process can be applied with reference to the estimation of p the proportion of successes in a binomial population. So as you now see on the slide the large sample confidence interval for p is given by p hat is equal to Z alpha by 2 into the square root of p hat into q hat over n. This implies according to a logic similar to what was presented a short while ago that the error bound e is equal to Z alpha by 2 into the square root of p hat into q hat over n. Therefore solving for n as before we obtain n is equal to Z alpha by 2 whole square into p hat q hat over e square and it should be noted that the values of p hat and q hat are not known because the sample of course has not yet been selected. Therefore we use an estimated p hat which we obtain from a pilot sample. Let us now apply this concept to an example. In a random sample of 75 axel shafts 12 have a surface finish that is rougher than the specifications will allow. How large a sample is required if we want to be 95 percent confident that the error in using p hat to estimate p is less than 0.05 students. Perhaps you are thinking that this seems to be a very complicated situation. Again if we analyze it step by step then the first thing is that we are talking about p and p hat. This means that we are talking about success and failure. So success is what we call which we are interested in. Here we are saying that there are some axel shafts whose surface finish is rougher than what is acceptable. This is success. If it is rougher then this is success and if it is alright then that is failure. Do remember success and failure are technical terms. Now we are talking about the sample of 75 axel shafts we have selected. There are 12 of them which can be classified as success i.e. the finish that is rough. But we are saying that if we want to be 95 percent confident that the error in estimating the true proportion of the shafts which are rougher than the allowed limit that is less than or equal to 0.05. If we want this then what should be our sample size. You will say that this explanation is too long but it is alright. Everything is according to what we are wanting to do. First note that we have already drawn the 75 axel shafts sample. This is why we will look at the pilot sample and the actual sample, the actual study which we want to talk about now, we want to determine the sample size with 95 percent confidence and an error bound of 0.05. Hence as you now see on the screen the p hat that we have obtained from our pilot sample is 12 over 75 and that is 0.16. Also the error bound e which is the modulus of p hat minus p that has been specified as 0.05. Also because we want to be 95 percent confident therefore z alpha by 2 is equal to 1.96 substituting all these values in the formula that was presented a short while ago. We obtain n is equal to 1.96 over 0.05 whole square multiplied by 0.16 into 0.84 and solving this expression n comes out to be 206.52 which upon rounding upward yields n is equal to 207. Students, you saw that the first sample was 75 but that was the pilot sample that we drew in order to have an estimated value of p hat and when we put that in this formula then our required sample size for the actual study that has come out to be 207. So we will draw at least 207 sample size and then we will get error bound 0.05 or level of confidence 95 percent. At least I said that if you keep it bigger than this then it is even better. Your level of confidence might increase or your error bound might decrease so it will be even better. But you can say that the minimal required sample size to have this much confidence at least and to have this much error bound at the most that minimum desired required sample size is 207. Students, you saw that inferential statistics are interesting. You are able to draw inferences and conclusions about real life phenomena and about populations on the basis of sample data. In a scientific and proper way of course, you can draw conclusions about entire populations. As I said in lecture number 31, inferential statistics can be done in two main ways. One is estimation and the other is hypothesis testing. Under the category of estimation, we talked about point estimation, one single value that estimates the parameter and next we have talked about interval estimation. Now students, we are going to start the other very interesting and important area of statistical inference and that is hypothesis testing. What do I mean by hypothesis testing? I mean that I would like to test a certain hypothesis that I already have in my mind. Estimation is the situation in which you assume that we have no idea about that phenomenon and we are trying to estimate mu or p or whatever it may be. We are wanting to do that with an open mind based on the information that we have in the sample that we have drawn. We are wanting to estimate an unknown quantity that we don't have any information about. Students, hypothesis testing on the other hand is this situation where we already have an idea, let me say a hunch about that particular phenomenon. For example, suppose that we are talking about African people who I think we all would agree that they are generally very tall. We might have this assumption in our mind that the mean height of the adult males of this particular African country must be at least so much. Now this is an idea in our mind that at least that is the mean height. In this situation, we would like to test this hypothesis based on sample data. We draw a random sample from that country and we measure the heights of those people who are in the sample and we find x bar. Now our x bar will either support our hypothesis or it will fail to support our hypothesis. If our x bar is close to the hypothesized value of mu, then of course we would like to accept our hypothesized value. But if there is a lot of difference between our x bar and the hypothesized value of mu, then obviously we would not be inclined to accept our hypothesis. So students, this is the crux of the matter. We will see whether our sample data supports our hypothesis or provides evidence against it. But this procedure is a very mathematical and a very sound procedure. But it involves a lot of steps. It involves a few steps and I would like you to concentrate on various points one by one. It is possible that you will not be able to clear all the points in the first attempt. But if you carefully look at each point, then this concept will become clear to you. Now that I have talked about the hypothesis, let us express it in a formal way. As you now see on the screen, we first of all define the null and the alternative hypothesis. A null hypothesis generally denoted by the symbol H naught is any hypothesis which is to be tested for possible rejection or nullification. Examples of null hypothesis are the given coin is a drug is ineffective in curing a particular disease. There is no difference between the two teaching methods. Students, you have noted that the three examples I have presented, they pertain to situations that we may be interested in in real life. But these three statements were not presented in a very mathematical way. Generally, when we write null hypothesis, then we express it in a mathematical way. For example, this first example that this particular coin is unbiased, if we want to express it mathematically, then we will write it this way that H naught is that P is equal to half. So, probability of head is going to be half and if we are regarding head as success, then of course, this probability is to be called P and so we say P is equal to half. Similarly, as you now see on the screen, other examples of null hypothesis expressed in a numerical way are H naught mu is equal to 62 inches and H naught mu is equal to 130 pounds. In both the examples, the first example is that mu is equal to 62 inches. This hypothesis pertain to a population of women and we are saying that our hypothesis is that their mean height that is 62 inches. Similarly, the second one that would pertain to a population of women again I can say and we are saying that their mean weight that is 130 pounds. This is our null hypothesis that is the hypothesis that we want to test. Students, against this we have the other hypothesis that we will accept in that situation if we reject null hypothesis and that other hypothesis is called the alternative hypothesis. As you now see on the slide, an alternative hypothesis is any other hypothesis which we are willing to accept when the null hypothesis H naught is rejected. The alternative hypothesis is customarily denoted by H 1 or H a. For example, if our null hypothesis is H naught mu is equal to 62 inches then our alternative hypothesis may be H 1 mu is unequal to 62 inches or H 1 mu is less than 62 inches. Students, these two examples I have just presented to you, of alternative hypothesis. There is a big difference which is very important. The first time I said that our alternative hypothesis may be that mu is not equal to 62 inches. It is a simple thing that null is saying that mu is 62 and alternative is saying that no it is not 62 inches. The second time I said something different and I said that null is saying that mu is 62 inches but alternative is that the mean height of this particular population of women that mean height is less than 62 inches. The difference between these two alternative hypotheses may be students. This we have to relate with this thing that this tells us whether we are going to do what is called a two-tailed test or are we going to do what is called a one-tailed test. I had told you that there are many concepts or steps involved in this. Now gradually look at each and every thing and just do not panic or worry that you cannot understand this. Just go along slowly but surely and inshallah you will understand this very interesting concept. Now I will go to the next important concept and that is the level of significance. As you now see on the slide the probability of committing type one error can also be called the level of significance of a test. Students, now the question arises that what is the meaning of type one error? The probability of which we are talking about is the level of significance. For this I would like to draw your attention to all possible situations that you can have in a hypothesis testing procedure. As you now see on the slide there are two situations as far as the actual truth is concerned and there are two situations as far as the decision that we are going to adopt is concerned. See the table in front of you has a box head on the top that gives the two decisions one of which will be made. Either you will accept H naught or you will reject H naught. But the stub of the table is that the actual truth that can be that the null hypothesis that you have hypothesized it is actually true or the null hypothesis that you have hypothesized is actually false. Now the two situations you are seeing on the right side or the two situations you are seeing on the top when you gather them together you have four possible situations. Either H naught is actually true and you also accept H naught. This means that you are taking a correct decision and there is no error. In other words there is no mistake. Now if you look at the bottom right hand corner of the table you find this situation when H naught is actually false and based on your sample data you also decide to reject H naught. So, if H naught was really false and you also decide to reject H naught then it is obvious that once again you are taking a correct decision and there is no error. But students the other two cells of this table present situations where you are taking wrong decisions. If H naught is actually not actually such. But you say that I have to reject H naught because my sample value does not tell you what has been hypothesized then you are rejecting such a hypothesis which is actually true. And this is a wrong decision and this particular error is called type one error. If H naught is actually false but you decide to accept H naught based on your data then once again students you are taking a wrong decision. This kind of an error is called type two error and students the probability of committing type one error is denoted by alpha whereas the probability of committing type two error is denoted by beta. The first one alpha is also called the level of significance of the test. Students hypothesis testing. The formulation of the null and the alternative hypothesis and the concept of the level of significance. Next time we will be continuing with the concept of hypothesis testing and we will discuss various other concepts. In the meantime I would like to encourage you to attempt quite a few questions pertaining to interval estimation. My best wishes to you and until next time Allah Hafiz.


Hello everyone, this is Ahmed Dan of AhmedDan.com. Today I'll have another episode of Safety Razor review and unboxing video and I'll be opening the Edwin Jacker double-edged safety razor black, which I have it right here. If this is your first time or if you visit Thank you for your support on this channel. I was trying different ideas. If you're into thinking outside the box This is the channel to subscribe. If you're looking for more Razor videos, there will be links in the description box below So this is Edwin Jacker Classic So this is the Edwin Jacker rubber coated handle. So it comes in different variations For example, they have a chrome handle or chrome lined or ivory rubber handle But I chose to you know, try the rubber black rubber handle because I have other chrome handles so I wanted to see how it feels and This is a very lightweight razor. It's only 55 gram and the handle length is expected to be Three and a half inch So it's like, you know less than four inch We're going to open this up take a look at it and then I'll share with the razor and give you my opinion Now this is not too expensive razor. This is only about 40 dollars 42 dollars Canadian and This is from Made in England and this is a very old family owned company. They established in 1988 and They have, you know, lots of quality shaving razors and accessories So I wanted to you know, give it a try. This is not in an affiliated or paid review All my reviews are non-affiliated I'm best and honest so that way you can get, you know, the actual and real review nothing Affiliated or unbiased so the Packaging looks like this and this is in an old black and on the back of the box there's some information about Edwin Jacker and On the front it just mentioned the classic shaving accessories. We're going to open this box and see what we have So I can see that there's a quality check, you know, kind of a stamp or sticker So it looks like you know, they put everything a quality control sticker on the product I'm going to just remove everything we have in here So you can see that the box is empty except just a packaging, you know Paper, so I'll just leave this here and we have Looks like a small brochure and it's just giving you Introduction to the other products so you can see that they have Lots of other shaving products and accessories But I haven't tried anything else by them And you can see that, you know, they have shaving brush and other razors and bowl and various shaving accessories, so I'll just put it aside and here we have It looks like a guarantee card it mentioned that, you know after sales care So you can reach out to them if you have any issues or any Questions so they have all the contact information right here So I see that they have even a phone number to call which is a good thing because these days, you know Everyone is moving to electronic chat or email getting difficult to find real people to talk to and They touched five pieces of Darby extra blades So that's a good thing It gives an opportunity to try the Darby blade as well. And here we have the razor So Check it out Okay, so here is what we have the first thing I'm noticing that, you know, I bought the short handle and This is really short. You can tell that it looks like kind of mini razor But I feel like it's okay to hold but I'm going to see more when I shave And this is the razor so I Have a feeling this is going to be Three-piece, let me just see Yes, so this is a three-piece razor so what it means that you know all the pieces come separately and you have to attach them And you have to install the blade so basically You're going to put your blade in here Put back the plate and then you're going to just you know screw this or tight tighten this so They're actually metal I you know, it has some weight but not excessive weight I can feel that there's a little bit weight here. So I'll just put it aside and this is our razor So the black rubberized grip is very nice to handle very nice to hold it feels like it is not going to sleep and I'm just going to you know put them together and see how it feels here. So this is How it looks I can hold it but I think I should have bought the Medium version this is a short and the handle feels a little bit too short But you know, I couldn't tell you more unless I go through the shaving process It could be just fine the short handle. So The next part of the video is going to be you know, I'm going to shave with this and give you my opinion So I'll start the shaving with the Edwin Jagger short handle rubber coated razor So this is a three-piece razor and I have everything right here So I'm going to be using the blade which came with the razor and this is Darby extra and then I'm just going to you know place the blade first. So you have to be very careful when you are inserting blade into a three-piece razor. So I'm just going to hold it like this and I remove the blade from the blade packaging so I'll just you know, put it here this way and then I'll put the plate and then I'll gently Twist the handle to lock it. So it looks like perfectly aligned and the blade Exposure is perfectly correct. And actually there's a very little tab on the on the both sides The tab exposure, but it's not a lot, but there is very little with I don't know if you can see it So it it's a non-issue for me But some people like the tab all the way covered and this is the rubber coated handle So I'll just you know, prepare my face and for that. I'll just put some warm water on my face and today we're going to be using the poroso shaving cream with a Synthetic Wilkinson sword brush. I don't use any animal or any Badger brushes. So this is a synthetic brush and the Wilkinson shaving soap So I'm just going to put this soap into my bowl and I have a review of the shaving soap bowl This is only one dollar and fifty cents ball from IKEA. So I'll just put it Lather shaving cream this way and I'll with the brush So let's you know, try to create a leather. So you can see that The process creating a very good leather right away with the shaving ball and I might want to add just a little bit of water not too lot a little more water So this is what I got and I'm happy with what I have. So I'm just going to apply a Leather on my face classic barbershop smell, which I like and I think this is a the blue poroso, which is me eucalyptus Mental so you can see that I have good leather. I'll just like, you know, put a few drops of water and just Leather and I just had a haircut. So you can see that, you know, my sideburn is a little bit up So I have to just, you know, find a point where I should start shaving. So I'll just put it away And I'll wipe my face and I'll just, you know Make little space to see where I should start my shaving Everything should looks okay. So I'm just going to Wash this razor or with this with hot water And you can see here and the way it looks like I think it's going to give me a very smooth shave, but we'll see If there's like some nicks and cuts, that's okay You just learn as you go through. So I'm going to start my sideburn kind of like right here on the both Sides. So I'll just start this way From here and this is the Derby extra blade Feels a very smooth and Very comfortable Hopefully I'm not gonna have any cuts or not too many cuts and let's start here. So you're going to kind of start here And Try to make it even with this side. I think that should be good enough so so far so good It's gliding very smoothly and The advantage of having a sharp razor is that you have more maneuver and this has rubberized grip So it's not going to slip out of your hands So I'm just going to clean this up. So I'm going to start here right under lips Now let's start here in this area to wash It again looks like I have a little cut right here. So I'm just going to apply Little bit pressure on the cut with the tissue paper. I'll just you know, I apply a little bit more foam Upper on the upper lip part and just clean this up a little bit here so I can see So I'm going to stop with one pass I'm not going to reapply shaving cream and shave again because you know I don't want to make this video Too long. So let's just watch this little bit more So I like the razor. I like the blade and I like the fact that it has rubberized handle It gives you very good grip and although it's very small or very short But I find it, you know, it's easier to shave with a short handle than long handle I'm kind of liking it, you know using a short handle and in terms of blade exposure This is just perfectly smooth. You're not going to cut yourself a lot For example, you can see that I just had a one little cut And once you get used to using it a few times, definitely, you know, it's going to get the smoother and better So I'm liking the Edwin Jagger short handle rubberized grip razor and also I'm liking the derby extra blade which we have Right here. So it came with five blades and this blade for me I feel like it's a very mild blade and but that's what I like. I don't like too sharp and rough blade So this blade would be good for like, you know, if you're starting to shave with a de razor and or if you are New but, you know, I think I this is going to be one of my favorite blades once I finished testing All other blades and in terms of the razor, definitely This is going to be my one of my favorite razors, but I have to, you know, test a lot more I have done so far like five to seven razor reviews and they will be more coming up So my overall experience is I'm happy with the product. Thank you for watching. I'll see you shortly


There are women in rural India who do not have the same access as I do, who do not even have families which are supportive of them and these are young girls. Can you imagine those women who as it is are a part of a very patriarchal setup and when if you imagine if a pornography video was morphed with their image, their families would have just stopped them from doing what they are doing and they would not have had the courage to go to a police station and report because in our country also there is a great deal of patriarchity. One thing that the U.N. thing helped me really substantially is it kind of amplified my voice and it got the attention of India. Online trolling is never considered a big deal. They are not coming to the room, it's all virtual. What this has kind of helped make people understand this is not a virtual problem. When you dox me, when you put my image, when you put my phone number, when you put my address on social media, when you send me burnt copies of my book and my resume, it's no longer virtual, it's a virtual lynch form. So what the U.N. and other agencies and such are which are really done if there is one within this come out of it is that it has addressed the issue. I hope the U.N. and other agencies actually keep the pressure on these social media and other platforms and governments to stop this hate against journalists and free speech.