 I think the problem might be my laptop. It might not be the network, but now I'm now back connected to the Wi-Fi. Let's see if the thing will respond quicker. So, we are now on question 16. A survey of a random sample of 300 grocery shoppers in Kimberley found that the mean value of their grocery purchase was 78 rent. Assume that the population standard deviation of the grocery purchase is 21 rent. The 95 percent confidence interval for the mean grocery purchase is. So, we are looking at confidence interval questions. And because they're talking about the standard deviation, we need to ask ourselves, is the population standard deviation known? Because that will tell us where on the table are we going to find. Oh, sorry, my note. My point button is to refresh because I was disconnected from the internet. So, the first question you need to check or the things that you need to check for is, are you given the population standard deviation or the sample standard deviation? And because you will need to go and find the critical value on the Z table or the T table. So, in this question, they have given us the population standard deviation. So, it means we're going to use the Z table here. So, it's, we are back now, even though we are back, just going to open a new one. So, I don't know what is that anyone, that one. So, because we're given the population standard deviation, let's make it this bigger and a little bit. We need to go find the mean plus or minus the critical value of Z over 2 times the population standard deviation divided by the square root of n, which is the standard error. So, what we are given is the sample size, which is our n of 300. We are told what the mean is from the sample, the mean is 78. We are also told what the population standard deviation is, 21. And we are also given a 95% confidence interval. Therefore, it means our alpha value is 0,05 because a 95% confidence interval is 1 minus alpha of 0 comma 95. Make alpha the subject of the formula, you will see that it is equals to that. By now, you should have that table if I go to this thing that we shared with you now. Let me just double check if they did share that kind of information with you. It might not be there. See what else is on this document. That is useful. These probabilities. This one I scroll until I get to confidence interval. That is if it's included in this document. Normal distribution is great. I'm sure that I am scrolling too fast on my distribution. I don't think there is further more questions on that. This is active, but you need 6 as in F. The confidence interval. I will look for another document. There should be another one as well. But anyway, what I was trying to get to is when we look at this, our critical value for Z of alpha over 2, which will be Z of 0,05 divided by 2, which is the same as Z of 0,0250. It means this probability we go and find on the table. Inside this table, we look for 0,20 and we look for the Z value, which is 1,9 and 6. Our critical value is 1,9,6. That is the value that we're going to substitute onto here. We say 78 plus or minus 1,96 times our standard deviation of 21 divided by the square root of 300. What I was getting to is you need to have your alpha divided by two critical values, especially for the Z, they is on the nodes. There is a table that has the critical values for Z over 2. Use that table to identify your critical values and have it ready in your confidence interval chapter that you would have summarized and use that information because you don't have, in the exam, you will not have the liberty to go and search for the critical values inside the table and go look for the Z values, especially for things that are obvious that you should know. You can minimize on that if you have created that. Let's calculate the confidence interval quickly. If I take my calculator, oh, yeah, I lost my cashier calculator because I lost my, I had to restart my network. So, this one is still works. You can use this, 0. 78 minus 1.96 times 21 divided by the square root of 300. Equals the upper area is 75.62. And I can go and find the plus sign. And the upper area will be on the upper side. The plus sign will be 18.3 services. So the answer is option D, right? So the answer is option D, right? Someone has their points on, and they are not... Hand again. There is a hand or did you lower it? 20.38, 80.38, 80.38. So the answer is option D, right? 80.38. So the answer is option D. Do you agree? Did you all calculate it? Yes. Yes. If you started with the upper area, the plus side, you will get number A. So always be careful. Start with the minus, which is your lower limit and then the plus is your upper limit. So you always start with the lower limit. That is, so the problem is not the network is there because I can see that I am almost, my Wi-Fi is fine. And I don't know what's wrong with this thing. It should be done by 7. Otherwise, I don't know. Come on. The last part is I cannot move next until it's finished. Okay. I don't know. Lizzie, maybe we should postpone this because if you have any problems, it could be a long time. Yeah, the thing is when I close this, then we will have, next time we meet again, we start from the beginning. We can skip through all the questions up until 16. This is very disappointing, right? It's finally, this is not your fault. Yes. Let's see. Confidence interval. So developer confidence interval for A95% confidence for the population proportion if the sample size is 240 success. So this is proportion, right? So with proportions to the side, with proportions, we also still use the Z. But we need to find the P, which is X over N, which will be 40 divided by 200. We just do the calculations. Then the confidence estimate will be given by that formula. So we know that we do in Z alpha divided by 2 and it is at 95% confidence interval. By now, you should know that the critical value is Z of 1,96. So do the calculations. What is 40 divided by 200? 0.2. 0.2. Then just substitute 0.2 plus or minus. You can see that the answer is not you to solve the entire equation. You just need to solve the margin of error 1.96 times the square root of 0.2 times 1 minus 0.2 divided by 200. That's what you need. You just need to solve everything. You just need to solve this sign. Only that part. That's the only thing you need to solve. 0.2 plus or minus. Do the calculations. 1.96 times 0.2 times 1 minus 0.2. What do you get? 0.0554. 0.0554. What do I get? 0.0554, which if I look at the question, it only needs 3 decimal. So that will be option D. And I think after this one, we can take that suggestion off because by the rate that we're going right now, I don't think we will even get to 8 to 7 o'clock. It will go beyond that. Maybe I will need to switch off my machine. So this will be the last one. And then the next time we see each other, we will do 18 up until 25. Okay. I'm going to stop right here. And I want to stop it right with the answer. And that will conclude today's session because I don't think going ahead with this rate. So let's stop right here. I'm going to stop sharing. And I'm going to stop recording.