I believe that God wants to break fear and anxiety from off of your life once and for all. You're watching this, the anointing is flowing, the power of God is here. And I truly believe that as you hear this word, that anxiety and fear that have gripped your heart, that have gripped your mind, that have gripped your thoughts, that anxiety and fear is going to lose its grip and you're going to walk in the peace of the Holy Spirit. I truly believe this message is prophetic because in this hour I have seen in the spirit that this attack, this demonic assault of anxiety and fear has been launched against the body of Christ and against God's people. But today we're going to get into the word and I truly believe that from this moment on you will find liberty from that attack. No more anxiety, no more fear, it's going to be broken off of your life. Tag your friends, share this video. I truly believe that God is going to use this as a prophetic message. You never know who's struggling in this area, so share it with your friends and let's get this prophetic word out because this program has been anointed and I say that with confidence because the Lord spoke to me very clearly to teach on this topic, to preach on this topic that you might be set free from fear and anxiety and even if that's something that's not necessarily gripped you personally, this is something you need to know so that you can minister freedom to others who struggle in this area. Stephen Moctezuma is here with me as usual. He's going to lead you in worship and then we're going to get right into this prophetic message. And as you watch, as you hear the word, that you're going to be completely set free from anxiety. You're going to be completely set free from the spirit of fear and I truly do believe this is spiritual. Now, for the most part, fear and anxiety come from the flesh, but that doesn't mean that demonic beings cannot agitate, prolong or intensify this battle, this inner struggle with anxiety and with fear. Some of you, you lack the peace of God. Now the truth is that the believer is to be crowned with the peace of God. That is a mark, a spirit filled mark that is to be upon the life of the believer, the peace of God. But sometimes we struggle. There is this inner chaos. There is conflict. There is clutter within the mind, within the heart. We are bombarded with thoughts. We are bombarded with negative ideas. We are bombarded with fears about what the future might hold for us and filled with apprehension, filled with terror. We go through facing life without the peace of God. God wants to give you his peace, his perfect peace that passes all understanding. In other words, it doesn't make any sense why you should have this sort of peace. Even if you're in the middle of chaos, you can have this peace, the apprehension for the future, the fear of what might be, the phobias and the paranoia. All of that needs to come to an end. There are people watching me. In fact, there is somebody watching me. They're in anxiety.  The anxiety and the fear, it plagues your mind and it affects your view of how God sees you. It affects your perception of where you stand with the Lord. And perhaps that anxiety is linked to shame of the past or linked to what might go wrong in the future. Perhaps you are afraid of sickness. Perhaps you are afraid of death. Perhaps you are afraid of interaction with other people. Whatever the case may be, anxiety chokes the life out of you. Fears, whether they are reasonable or unreasonable, stubbornly find their place in our mind and they are difficult to remove. They are difficult to break. These thought patterns are difficult to escape, but we can do it with the power of the Holy Spirit. You were called to live in peace. You were not called to live in paranoia. You were not called to live in torment. You were not called to live in fear and terror and apprehension about the future. You were called to be crowned with peace. God wants to give you peace. If you don't have peace, then something isn't right. Because the Bible makes it very clear that the believer is to walk in peace. Colossians chapter 5 verses 22 and 23 say, But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control. Against such things there is no law. Romans chapter 14 verse 17 says, For the kingdom of God is not meat and drink, but righteousness and peace and joy in the Holy Ghost. Colossians chapter 3 verse 15 says, Let the peace of Christ rule in your hearts to which indeed you were called in one body and be thankful. We must remain in peace. You know, you can be delivered from addiction. You can be delivered from demonic beings. And you can be delivered from spiritual bondage. But for the rest of your life, until you reach glorification, you will battle the flesh. And fear and anxiety, though again, they can be agitated, prolonged or intensified by demonic beings, are primarily found in the flesh. They come from the flesh. They come from self. They come from worry. They come from fear. That is the place of the soul. But God wants to give you breakthrough in this area, and only Jesus can give you this peace. The scripture says in Matthew chapter 11 verses 28 through 30, Jesus says, Come unto me, all ye that labor and are heavy laden, and I will give you rest. Take my yoke upon you and learn of me, for I am meek and lowly in heart, and ye shall find rest unto your souls, for my yoke is easy and my burden is light. Only Jesus can give you peace. Isaiah chapter 9 verse 6 says, For a child is born to us. A son is given to us. The government will rest on his shoulders, and he will be called. Wonderful counselor, mighty God, everlasting Father, prince of peace. The scripture says in Isaiah chapter 53 verse 5, But he was wounded for our transgressions. He was bruised for our iniquities. The chastisement of our peace was upon him, and with his stripes we are healed.  He died to make you whole. He died to give you peace. He died that even the effects of sin might be removed from you. When you sin, you damage your conscience. When you sin, you cause shame to come about within the soul. When you sin, you disconnect yourself from the Lord and find yourself in chaos and find yourself with concern and find yourself filled with inner clutter. And all of those things torment the mind. Sin torments the mind. Guilt torments the mind. Shame torments the mind. But Jesus died not just to forgive your sins. Jesus died to heal your mind, to bring peace to your mind. So he restores you, completely healing you from even the effects of sin. The chastisement of our peace was upon him. You know, the scripture calls him. In Isaiah chapter 9 verse 6, the Prince of Peace. And it was well I was reading about the crucifixion of Jesus that the Lord spoke to me something that really just moved me. I don't know about you, but there are those moments when I'm reading the scripture and perhaps I've missed something before. But in those moments, God reveals something to you that's precious and maybe even rarely known. And the Lord spoke to me in that moment when I was reading about the crucifixion of Jesus. And the Lord spoke to me in the moment when I was reading about how they placed a crown of thorns upon his head. And I remember when I was reading of that terrible thing they did to the Lord. When they placed the crown of thorns upon his head the Holy Spirit brought to my memory. He's the Prince of Peace. And the Lord told me it was with the crown of thorns that Jesus was crowned the Prince of Peace.  Jesus died to give you peace. If Jesus wanted you to live in torment he would not have paid such a high price for your peace. If Jesus wanted you to live in fear and anxiety he would not have shed his blood for your peace. The chastisement of our peace, the price for our peace was upon him, he paid it. So how do you walk in this peace? Well, number one, you walk in peace by obeying. Number one, you need to obey. First John chapter four verse 18 says, such love has no fear because perfect love expels all fear. If we are afraid it is for fear of punishment and this shows that we have not fully experienced his perfect love. And that's first John chapter four verse 18. Now, the perfect love of God removes from us all fear. However, it is possible that we can disrupt the flow of God's perfect love in our lives through disobedience. So perfect love casts out all fear and if we are living in fear it's because we are afraid of punishment. Why would someone be afraid of punishment? It's because they've done something wrong. So disobedience makes you afraid. Disobedience robs you of peace. When we live in a way to where we do not fully experience the perfect love of God, we invite inner chaos. We invite inner clutter. We invite inner conflict. And really the truth is that lacking peace isn't just about anxiety and fear. It's about just chaos. It's about just clutter. The mind is so filled with so many different things that it cannot focus itself upon the things of God. Now we have fully experienced the love of God when we walk in obedience. And if we are not walking in obedience then we have not fully experienced God's love. Now, let me be very clear. I am not saying that God doesn't love you if you disobey. I am simply saying that you do not receive the fullness of those benefits within yourself such as peace if you are walking in disobedience. The flow of God's love is coming to you but it's very difficult to receive God's love when we are not walking according to God's love. The trouble is not with God offering his love. It's with us receiving it. First John chapter 5 verse 3 says this, Loving God means keeping his commandments and his commandments are not burdensome.  The scripture says in 1 Peter chapter 3 verse 11, Turn away from evil and do good. Search for peace and work to maintain it. Isaiah chapter 48 verse 22 says, But there is no peace for the wicked, says the Lord. Disobedience is a door for anxiety in your life. When you're not walking according to God's will, when you're not walking according to how God told you to walk, you invite anxiety to grab hold of your heart and your mind. And the further you walk into disobedience, the tighter the grip of anxiety comes upon you.  Psalm chapter 119 verse number 165 says, Those who love your law have great peace and nothing causes them to stumble. When you love this word, so much that you walk in it. When you love this word so much that you obey it, you walk in perfect peace. Obedience brings peace. Number two, prayer brings peace. Now, specifically, the prayer request brings peace. Now, I know the prayer request is sort of looked down upon in some Christian circles and I've heard people, whenever they're talking about the prayer request or asking God to move in your life concerning the natural things, be accused of preaching the prosperity gospel or believing the prosperity gospel. But let me make something very clear. The Bible teaches that God wants you to prosper. Now, I am not saying that you'll never have any struggles. I'm not saying that you shouldn't pick up your cross and deny yourself and follow Christ. I'm not saying that there will never be any conflict in your life. I'm simply saying that God wants to bless you. God wants to prosper you. God wants to place resource in your hand so that you can fund the gospel further. That's the truth. Look, here's why people like this channel because I do everything within me to hold true to what the Bible says. And some people are offended at some things and some people are offended at other things. But look, you can't be offended when I tell you that the Bible teaches that God wants you to prosper. Now, again, I'm not saying it's all about money. I'm not saying it's all about self. I'm not saying it's all about comfort. But the truth is that God does want to bless you. And in fact, it is the prayer request that opens the door to peace in our lives. This scripture makes it very clear. Philippians chapter 4 verses 6 and 7 say, Don't worry about anything. Instead, pray about everything. Tell God what you need and thank Him for all He has done. Then you will experience God's peace, which exceeds anything we can understand. His peace will guard your hearts and minds as you live in Christ Jesus. Now, this scripture is very popular. We often claim it. I want perfect peace that passes all understanding. And we claim it religiously without understanding it completely. The scripture is talking here about making your request known to God. Now, I want to note something here. First of all, the scripture says, Don't worry about anything. Instead, pray about everything. So substitute your worry with prayer. Secondly, it says, Tell God what you need and thank Him for all He has done. In other words, you can tell Him about your needs while still being thankful for everything He has given you. Asking God for more does not mean that you are ungrateful. Asking God for more does not mean that you are unthankful. You can ask God for things. You can tell Him what you need while thanking Him for what He has done. The scripture makes it very clear that you can do both at the same time. So this scripture is talking about prayer requests. It's talking about unburdening yourself of your concerns and placing them in God's hands. Look, the scripture says in Psalm chapter 103 verse 14, For He knows how weak we are. He remembers we are only dust. In other words, God understands our weaknesses. God understands how we are made. God understands that we need to unburden ourselves through the prayer request by giving Him all of our concerns. So God gives us the prayer request. He says, Come and ask me. Tell me what you need while thanking me for what I've already given you. And as we're asking, as we're telling Him of our needs, as we're giving Him our concerns, we are giving our burdens to God. If you're financially distraught, give it to God. If your relationships are in disarray, give it to God. If your health is an issue, give it to God. If there's trouble in your mind, give it to God. Whatever you are facing, whatever the circumstance, whatever the situation, you can hand it over to God through the prayer request. And this is what the scripture says in verse 7. Then, in other words, this is in sequence after you've made the prayer request. Then you will experience God's peace, which exceeds anything we can understand. When will you experience it? Then. When is this then? It's after you've unburdened yourself of the prayer request. So the prayer request is not evil. It's not selfish. It's not self-centered. It's not worldly. It's not the prosperity gospel. The prayer request is simply you taking all of your burdens, all of your concerns, and saying, Lord, here's what I need from you, and now I give it to you. Now, here's the problem. Most Christians stop here because the prayer request is the gateway to peace. You can take all your concerns, put them in the hands of God, and be free of the burden of those concerns. But then here's the problem. Most believers, they come with their prayer request, they give it to God, they fill the peace of God, flood their heart, and then they say, okay, Lord, I'm done. Thank you. I'm leaving now. That's a problem. That's where it becomes an issue when you stop there. But God gives us the prayer request so that we can experience His peace and therefore enter deeper into His presence, not leave and just experience the shallow things. God has given us the prayer request as a tool to unburden ourselves and give them our concerns. So number one, obey. Number two, pray. The prayer request is fine. You can ask Him for things. Number three, and this is probably one of the more difficult ones, is trust. Matthew chapter 6 verses 25 through 34 say, for this reason I say to you, do not be worried about your life as to what you will eat or what you will drink, nor for your body as to what you will put on. Is not life more than food and the body more than clothing? Look at the birds of the air, that they do not sow nor reap nor gather into barns and yet your Heavenly Father feeds them. Are you not worth much more than they? And who of you by being worried can add a single hour to his life? And why are you worried about clothing? Observe how the lilies of the field grow. They do not toil nor do they spin.  But if God so clothes the grass of the field which is alive today and tomorrow is thrown into the furnace, will he not much more clothe you?  Or what will we wear for clothing? For the Gentiles eagerly seek all these things, for your Heavenly Father knows that you need all these things. But seek first his kingdom and his righteousness and all these things will be added to you. So do not worry about tomorrow for tomorrow will take care of itself. Each day has enough trouble of its own. Jesus understood the human condition and man's, I shouldn't say need, but man's desire to control everything. Man has this desire to control everything and that desire to control everything is expressed through worry. Worry is a useless attempt at control. I'm gonna say that again because I want you to get that. Worry is a useless attempt at control. Those of you with anxiety and those of you who struggle with paranoia or fear and phobias and all of these things, really what it is is this deep based fear of pain or death or something that you do not want to experience. And so what you do, here's how the mind works. What we do to try to take control over what we're afraid might harm us is we worry. We imagine that if we can think about something enough if we can obsess about something enough if we can concern ourselves with something enough that we will take control of that situation. But the truth is that we cannot control anything by worry. We cannot add a single hour to the day Jesus said by worrying. Worrying is a useless attempt at control. So what should we do instead? Philippians chapter 4 verse 8 says and now, dear brothers and sisters, one final thing. Fix your thoughts on what is true and honorable and right and pure and lovely and admirable. Think about these things that are excellent and worthy of praise. Whatsoever is true, that's a big one. We must rid ourselves of the lies of the enemy. If what we believe contradicts the Word of God then it is a lie. If what we believe keeps us from approaching God it is a lie. If what we believe keeps us from experiencing the peace and the joy of the Holy Spirit then it is a lie. You identify the lies by finding the beliefs that rob you of peace. If what you are believing is robbing you of peace is robbing you of joy then either it is completely a lie tied to a lie or based on a lie in some way. But deception is so powerful because it is believable. We would not believe unbelievable lies. We believe things like, well maybe God doesn't love me as much as I think he does. We believe things like, well maybe God hasn't forgiven me. Why? Because it's believable that God wouldn't forgive us because of our sin. And we know how wicked we can be. We know how unbelieving we can be. So it makes sense to us God wouldn't forgive me. God wouldn't love me. And it's believable. So we have to compare what we believe to the truth of the Word of God. Whatsoever is true. And this is the difficult part. You have to trust. People analyze things too much. People overthink too many things. You don't know how many messages I get, how many phone calls I get from people who just are overthinking their situation. They know what the Word of God says concerning his forgiveness, concerning his love, concerning his protection, concerning his mercy. Yet they obsess over silly things that they've done. They obsess over sinful things that they've done. They obsess over odd beliefs or odd ideas that they have that make them fearful. I know people who believe that God will never forgive them. I know of people who believe that they were created to live in torment. I know people who believe just the strangest things, but you need to be rid of those thoughts and focus your mind and say, I'm gonna grab hold of the truth and I'm not going to believe anything that's a lie. And that comes to trust. This is the part where you let go. This is the part where you stop obsessing over everything. Stop trying to fix everything by thinking about it.  Stop trying to pinpoint every little problem. Stop trying to find your own solution. Just let it go. That's right. Let it go. Just say, Lord, I give it to you. I trust you. I'm not going to obsess over this. I'm not going to analyze this anymore. And you need to get angry and say, I am done. Righteous indignation needs to rise within you. And you need to say, I am done with the spirit of fear. I break that power off of me in Jesus' name. You've got to come out of that clutter. You've got to come out of that overthinking.  You want to grab hold of it, but all of these thoughts are coming into your mind, stopping you from receiving what I'm saying. But I'm telling you, that is the flesh. Let go and trust. Just be at peace. Stop worrying. You know, worry and hurry is a two-headed monster. Worry and hurry come together. Everything is chaotic. Everything is cluttered. Everything has conflict because of worry, because of fear, because of paranoia, because of anxiety. Just let it go. Stop trying to control the outcome by thinking about it. Stop trying to add to the day. You cannot add an hour to the day by worrying about anything. Just trust. So number one, obey. Number two, pray, specifically the prayer request. Number three, you've got to learn to trust. Just let go. Stop trying to control everything. And finally, number four, I have one verse for this, and this is the most helpful, is worship. Isaiah chapter 26 verse 3 says, that will keep him in perfect peace, whose mind has stayed on thee, because he trusted in thee. When your mind is on the Lord, and your mind is focused on Jesus, you experience perfect peace. But here's the thing. Here's the thing about worship. Worship is only worship when God is the only object. Worship is only worship when your focus is on the Lord. If you're focusing on your worries, if you're focusing on your problems, if you're focusing on your situation while you're worshiping, you're not really in worship. Just let go. Forget about your troubles. Forget about your concerns. Stop obsessing. Just relax and worship the Lord. I'm going to pray with you in a moment. The first Stephen Mock-A-Zoom is going to lead you in another worship song. And I want you to worship with him. We have the words up there on the screen for you. It will be a real simple song. But I want you to worship with him. And I want you in this moment now, just to love the Lord. Just worship with him, whose mind has stayed on thee. You see what happens when you just forget about self and troubles and focus on the Lord. Let me pray with you now. Let's break this spirit of fear. And from now on, once the spiritual bondage is broken, it's up to you to subject the flesh and maintain the discipline of not allowing your thoughts to run over the peace of God. So Father in Jesus' name, I pray for that one. I feel the anointing. That one watching now. I pray the spirit of fear from this day forward, the spirit of anxiety, be broken off of their lives in Jesus' name. I break every power of the enemy. I bind every spirit. Lord, I pray right now, complete and total freedom. I break the spirit of anxiety. I break that spirit of fear. And I command total peace to come upon them. Lord, we thank you for newfound freedom. We thank you that where the spirit of the Lord is, there is liberty. I pray the anointing would break every yoke of bondage. I pray the anointing would deliver that one who is receiving this prayer from fear. In Jesus' name, we pray. I want you to say it. If you believe it, say amen. Look at this day forward, it's broken. Now walk in that freedom.  From this day forward, I pray it's a changing day in your life. Well, that is it for the lesson and the prayer. I want to welcome now the new members of Spirit Church. There you are up on the screen. We love you, we are praying for you. I always say that because I always mean it. If you'd like information on how you could join the spirit family, go ahead and use the information at the bottom of the screen, DavidHernanisMinisteries.com slash Spirit Church. Become a member today. We'll send you a weekly email. I want to get to the comments now, but before I get to the comments, remember I have a special message for you in just a few minutes after the comments. So stick around for that. These are comments from last week's teaching, which was on living in the Spirit. That was a teaching on overcoming the power of the flesh and living in the fruit of the Holy Spirit. All right, here we have a comment from Pezman Paran. And they write, This teaching just saved my life tonight in the Spirit. Thank you, brother. And Marie Clark writes, Thank you, brother David. I love how you bring across the messages. I know it as God that you are able to speak as you do. My spiritual eyes are now more open since I was led to your YouTube channel. I am in Jamaica, man of God. I love you with the love of the Lord. As I watch more of your message, I know I will be the richer through the word of God. Well, God bless you. We thank you for watching all the way from Jamaica. And we're glad that the ministry and the content is blessing your life. Another comment to write. Thank you so much. I am a medical student from India. Your videos have actually helped me right now in my situations. Thank you, Lord. Another comment to write. Thank God for Pastor David. Your videos have made a great impact and influence in my Christian life. May God bless your family and ministry. Elizabeth Harwell writes, This message has really spoken to the struggles I have been feeling. I was baptized yesterday and was filled with such joy. Yet today, I feel such sadness. Romans 7, 15 through 25 was exactly what I needed to hear. I know my battle has begun and your message has helped remind me to keep my focus on the Lord.  And Elizabeth is writing from Los Angeles, California. Well, it is the Lord's anointing and this is his program and we give all the glory to God. And I am so glad that you were blessed by the content. Ursula writes, Thank you so much for your teachings. They are crystal clear and understandable.  Terrence Joseph writes, I'm not sure if this will be the same for babes versus matured believers walking out their salvation. It will take time. You must not set unrealistic expectations though. I agree Terrence that we shouldn't set unrealistic expectations. However, I don't think it's unrealistic to say that both mature and new believers can receive the freedom of the Spirit by trusting in the Holy Spirit. That is for every believer. Justin Levy writes, I feel the presence of God manifesting in every way. Thank you for this video David. I also watched the three keys to overcoming sin. Very powerful. I was tempted two days ago but the Holy Spirit has led me to your video. He is so good that I'm able to overcome it.  God bless. Well, I'm very happy to hear about your newfound victory and I believe that if you watch that teaching it will help you to overcome the flesh. I'm telling you we're getting all sorts of testimonies from people who've watched that video, watched that teaching and found breakthrough overcoming the flesh in their life. Another commenter writes, I'm struggling in my own flesh but by this message all the questions in my mind were answered. Thank you God for using this man. God bless you. And our final comment. Thank you for this teaching and all of the others. God has really ministered to my husband and I through your ministry. And he has worked tremendously in each of our walks of faith and in our marriage since my husband stumbled upon your YouTube channel a few weeks ago. Your ministry has revived a passion for Jesus and ignited a desire to spread the gospel which is a miracle in itself. If you knew how introverted my husband and I tend to be. Well, I'm so glad that the Lord is transforming lives through his ministry and you can be a part of that. Listen. You know what we're doing. We're in the middle of a ministry expansion. We want to grow this thing above and beyond as the Lord leads. So, we are expanding our ministry efforts. We want to win more souls than ever before. We want to build more believers than ever before. Help us get to the next level by becoming a $30 a month partner. Here's where we are in the campaign. Now, as you can see we're trying to get 1,000 new $30 a month partners and when we reach that amount that means we're going to be able to move into our new facility which will help us to reach more people through media. We'll be able to do regular meetings at that facility so you can actually come down, have a place, take a vacation in Southern California if you're not from here. Come in and receive from the ministry and we're going to have a prayer center there. We'll be able to produce more content. As I said, we'll be able to go live. It's going to be awesome. In addition to that when we reach that goal we'll also be able to do more events in more locations more often. So, I can come to places like Texas. I can come to places like Florida and New York and New Jersey and Alabama and Georgia and the Philippine Islands and South Africa and Canada and I can go on naming. I know there are several places. We get invites from all over the place and I want to say yes to the nations. I want to say yes to the churches that invite us. So, help us get there. Help us expand our ministry. That's a goal. We're setting 1,000 new $30 a month partners and once you reach that goal it's more expansion from there. Listen, I believe we're going to reach millions. I want you to think big now. Stop thinking small. We need to think big. When you and I together partnered with all the believers that partner with us from all around the world come together. There's no limit to what we can do. I truly believe that you're going to see the day and we are filling up stadiums with people who will give their hearts to Jesus by the thousands. Can you see it? I can. You can be a part of that. You can say I was there from the beginning. I was there when it was first getting started. Don't hesitate. Become a $30 a month partner today. There's going to be a link that appears at the end of this video.  Well, I sure do love you and I thank you for those who have signed up to become our partner. Thank you partners. You help make all of this possible. That is it for this edition of Spirit Church. Until next time, remember nothing is impossible with God. Make a one-time donation or become a monthly supporter by clicking on the donate link now.


Hi, this is Dr. Don. I have a problem out of Chapter 8, Section 2, on a two-sample test of the mean difference. And we are to get both the confidence interval around the mean difference as well as do some hypothesis tests. We're given some sample data here, but we're told that we have independent random samples of 400 observations each. Unlike 233 and the Larson's text, where the determinant, whether or not you use a z-test or a t-test, is knowledge of the population's sigmas. Here we don't know the sigmas, therefore we would use the t-test and the Larson 233 course. But in McClave and 503, the discriminator we have to use is whether or not the m is greater than 30. And here it's much greater, it's 400, so we use the z-test. Just remember that. In McClave and 503, you look at the sample size, and if it's greater than 30, then you use the z-test unless you're told otherwise. Okay, we're going to do this using stat crunch. Remember, you can go to question help and then open up stat crunch. I already have stat crunch open over here to have a little bit of time. And what we need to do here is go to stat, z-stats, because we've had z-stats, we have two samples with summary. And we bring up the dialog box. We need to put the mean in there, 5312, the standard deviation of the first one, 160, the sample size 400, and then again 5276, 190, and 400. The first question is about the 95% confidence interval. So we go down here and we click on that radio button to say we want the confidence interval for the mean difference, mu1 minus mu2, 95%. And we click compute and we bring up a answer box. We've got our sample mean. This is the difference. That's 36 mu1 minus mu2. We've got a lower limit of 11.65. I think they want just to one decimal point, so that would round to 11.7. And then the upper of 60.3. And that gives us the answer we need there. Okay. And of course, the interpretation of that is we are 95% confident that the difference, this 36, falls in that confidence interval. So that's pretty straightforward. Part B says, test the null hypothesis, mu1 minus mu2 equals zero versus the alternative, mu1 minus mu2 equals zero. So all we need to do, we don't have to reenter the data. We just click on options, edit, and it brings up our dialog box. This time we check we want the hypothesis test for the mean difference. The difference for the null is zero. And the alternative has a not equal operator. So we select the not equal operator. And we click compute. And we get our answers here. We get that the z statistic, which is also known as the standardized test statistic by most authors. Over here in the homework, though, it asks what is the test statistic. And since they give you the z, that's a clue. They want the z statistic, or the standardized test statistic. We have 2.898, which rounds to 2.90, which is the answer they want there. They want the p value given here 0.0037, which would round to three decimal places to 0.004. So that is pretty straightforward. We interpret the results because the p value 0.003 is less than alpha of 0.05. That means we reject the null. And that tells us that there is sufficient evidence that the population means our difference. Remember, if we reject the null, we accept the alternative. And here the alternative is that the means are different, that the difference is not equal to zero. So that's how we answer that problem. Let's go to part c. Suppose the test in part b was conducted with the alternative mu 1 minus mu 2 greater than zero. All we need to do again is go to options, edit. And then we change our operator to greater than to match that. And we click compute. And we get our answer box again here. Our test statistic didn't change, but our p value did. And it is 0.002 rounded to three places. So, and again, we would say reject the null because the p value is less than alpha 0.05. And we would accept the alternative that mu 1 minus mu 2, that difference is greater than zero, which it is sample mean here the difference 36 is greater than zero. Okay, D test the null hypothesis mu 1 minus mu 2 equal 22 versus the alternative not equal to 22. And again, all we need to do is go to edit because our data doesn't change. And we change our operator here to not equal. And we change our null hypothesis to 22. And we click compute. And so we've got our answers up here that the test statistic now has changed because we changed the null value to 22. It's 1.13, which is the answer they want over here. And the p value is 0.260 rounding the three decimal places. And we go down to the bottom there again because the p value is greater than alpha this time, we do not reject the null. And therefore, we say there's not sufficient evidence to conclude that the mean difference is not equal to 22. In other words, the alternative was that it was not equal. And we can't support that with the evidence. Okay, the last part is compare your answer to test conducted in part B, choose the correct answers. And if you go through those one by one, you'll see the test in part B supported the hypothesis because we rejected the null and the test in part D supported the hypothesis that the difference is 22. It's we fail to reject the null that the difference was 22. And again, the final part is the assumptions is that the two samples are independent random samples, which is what we've got up here. So I hope this helps.