 standard deviation when it's unknown. Do you have any questions? Okay, if there are no questions. So when the population standard deviation is unknown, then we use the T test, which means we're going to go to the T table, go find the critical value there and we use the test statistic T and since we are given the sample standard deviation, therefore we are given the S, not the sigma. The average cost of your hotel room in New York is said to be 168.9, depending on the true random sample of the new five is taken and resulted in the mean of 172.50. And S of, which is the sample standard deviation of 15, which has the appropriate hypothesis at alpha zero comma zero five. Yeah, they give us the sample standard deviation, therefore population standard deviation is unknown. Stating the non-hypothesis, we can see that from here, the average cost of a hotel is said to be 168. It means it is an equal. That's what the researcher wants to prove. The six steps state what you will remember there. The non-hypothesis alternatives, the level of significance and sample size. One test with the T test, find the critical value, depending on your alternative hypothesis, whether we're going to find the critical value for two tail or for one tail. Compute the test statistic and make a decision. Same, same, same, same steps. We're doing a two tail test. We know that the mean is equals to 168. So the alternative will say the mean is not equals to 168. State what we are given and since we're going to be doing the T test, then it's good that we can calculate also the degrees of freedom because our N is 25, our degrees of freedom will be 25 minus one, which is 24. Then we can go find, are we doing a T test because our population standard deviation is unknown. Then we go find the critical value. Remember finding the critical value two tail test, critical value T alpha divided by two with the degrees of freedom, T of zero comma, it was zero comma zero five divided by two and the degrees of freedom of 25 minus one, which then gives us our T zero comma zero two, five, zero and 24 and 24. We go to the T table. To the T table, we look for zero comma zero two, zero and top go down. We look for the degrees of freedom of 24, go down, degrees of freedom of 24, where they both meet. Two comma zero six, three, nine is our critical value. Okay, so now we have our critical value. We can also define where our region of rejections will be and you already defined them in the two tail test so we have two regions of rejection. Calculate the test statistic and we find that the test statistic is 1.46. So we need to locate this 1.46 on the graph. So that we can determine whether are we rejecting or we not rejecting. And it falls in the do not reject area. Therefore, we do not reject because there is sufficient evidence that the true mean cost is different from 1.68. And that's how you do your hypothesis testing. Let's look at when we do a one tail test. A phone industry manager thinks that the customer monthly cell phone bills have increased and now it averages over. There is our key weight. Over means greater than over 52 run per month. The company wishes to cause the same. A human normal population and N is equals to 24. So since this is what the researcher wants to prove, we cannot put it in the non hypothesis. We can only put it in the alternatives. Therefore, in my non hypothesis, the mean is less than or equals to 52. And my alternative states, the mean is greater than 52 over average is not 52. Which is what the, my false hypothesis will state. And to my alternative will state that the average is greater than 52 now. Okay, step number one. Remember I told you in the null hypothesis, it doesn't really matter. We can put the greater than or the less than the equal. It doesn't, it's always going to contain the equal sign. So we can just put the equal sign on there. So still mean exactly the same. The alternative will state that it's greater than. Then we state what we are given our alpha of zero comma one zero, our N which is 25 and our degrees of freedom are 24. We do, our population standard deviation is unknown, therefore we do a G test. The critical value, we find it by using alpha divided by two. Nope, we don't do alpha divided by two because it's a one test. We say T alpha and the degrees of freedom. And we know that our degrees of freedom is 24. Our alpha is zero comma one zero and go to the table and go find that. Then we go to the table. We look for degrees of freedom T alpha of zero comma one zero, this column. And we look for degrees of freedom. And the answer is one comma three, one seven eight. One comma three one eight create our original rejection. We know where our rejection area will be. We go and we calculate the test statistic and we find that our test statistic is zero comma five five. Let's substitute it into the full moon. Now we go back to our original rejection and go check whether our test statistics fall in the do not reject area. And we can see that it clearly falls on there which is our rejection, do not reject area. And we do not reject the null hypothesis since the test statistic is less than or equals to one comma three, one eight and there is not sufficient evidence that the building is over 52. And that's how you make a decision. With that, there is your exercise. Actually, but you don't have in your assignment. Utali and Mabato are collecting or collaborating to test the hypothesis that the mean reading time of adults is less than 100. And the standard deviation, this question is not a sample standard deviation. I'm going to go back to my original one. Let's do this one. We'll do it together, don't worry. You will have to do the calculations and tell me. So yeah, let's take our hypothesis and null hypothesis is stated on our behalf. Number one, we know that we're doing a greater than. So it's a one test and it's a greater than. Step number two, you state what we are given. We're given N of 24. We are given alpha of zero comma zero five, zero comma zero five. Our degrees of freedom is 24 minus one, which is equals to 23. Step number three, to state what we're doing. Because we are told that here is the other thing. How will I know which one am I given? In a random sample, the ninth watch average mean or the mean is that with a standard deviation of this. Since the whole sentence is talking about the sample, then I must assume that I am not given the population standard deviation, but this standard deviation comes from the sample because of that whole line. If the whole line stopped somewhere and started another and talked about population, then I will know that that is the population standard deviation, but because the whole sentence talks about the sample, the random sample of 24 with the average of 12 and the standard deviation of this. Therefore, that is our population, that was sample standard deviation. So population standard deviation is unknown. Therefore, we're going to use a T test. Step number four, you go find the critical value T alpha because it's a one tail test, T alpha and the degrees of freedom, therefore our T is zero comma zero five and our degrees of freedom, we calculate the T plus 23. So we go to the table, on the table, we look for 23, T 23 and alpha zero comma zero where they meet at one comma seven, one, three, nine. And this is our critical value and I'm going to draw our critical value of region of rejection because it's in the greater than sign. So it makes it easier. So we write the one comma seven, one, three, nine. That's where, that's where we are. Okay, so now we can go calculate step number five. T is equals to the mean T minus the mean divided by the standard error, which is our sample standard deviation divided by the square root of N. Our mean sample mean is 12 comma, 12 comma five seven minus our population is always in the hypothesis testing, which is 12 divided by our standard deviation of one comma two, three divided by the square root of 24. I'm going to go to the calculator. Let's open the calculator, makes it easy. Okay, 12.57. Minus 12 divided by 1.23 divided by the square root of 24. E equals two comma, two comma two, seven, zero, two. This we calculated it, we get two comma two, seven, zero, two. If we go back to number six, I'm going to use this also as number six to go find where it is, our two comma some number falls some way in here. So it falls in there, reject area. So if this is my 2.2702, therefore it means I'm going to reject the null hypothesis. And if I had options, I can quickly go around and check if those statements are correct or wrong. I just want to check something from your assignment as well because I haven't given you time to do a lot of exercises. Okay, so in terms of your assignment so far. Okay, so this is your assignment too. So far you should be able to answer. We're going to do this now, just now. So you should be able to answer this just now, not now. So you should be able to answer this because this is based on the introduction I just made earlier in the beginning where we were doing the introduction, the basic concepts of hypothesis testing we touched on this, how you make decisions. And you should be able to answer this question because this is just how you state your null hypothesis and your alternative based on the question that you have. Remember the keywords are always inside your table. So you need to pay attention. So you need to select the correct hypothesis testing. And remember when we state the hypothesis testing we use the population parameter as we can see from here we have the accents and the population parameter. You will need to choose the correct one. You will have to be able to answer this based on the statement that you just read there at the top, here is the statement because it's population standard deviation, what test you are you doing? So you should be able to select the appropriate test. In terms of your test statistic, remember depending on what you're doing, depending also on the null hypothesis and the alternative hypothesis that you go into test. And then this will tell you how your critical value should be. And remember if it's a one-tail, your critical value, if it's a one-tail your critical value find using Z, Z, Z, Z, Z. If it's a two-tail it will say alpha and two. So you need to make sure that you understand that. And that is to answer this. So you calculate the test statistic. So depending when you answer that question, if it's a Z that will be your mean minus your population mean divided by the standard deviation, the standard error. For your critical value remember it will be your Z. Or it's like alpha divided by two. So you will have to know how to calculate all this. So once you have calculated them based on the information then you can come and answer the question. Then number 16, once you have answered your Z the answer for Z you can go to find the PV. And because it says it's more than, remember that it's more than. So the value you find on the table you're going to subtract your PV will be the value you find on one minus from the table. That's what we need to do on this question into 15. Question 16, it's based on making a decision. Here now you need to say how you will make decision based on your PV or your PV or your critical value. Remember you can use two, you have two options. Option one is to use your critical values because it's on the one side. You will use your critical value. So this is option critical value. Your critical value and your Z statistic, your Z state. So you make use of that. Option number two, you've calculated the PV now. You just found what the PV is. You can use your PV. If your PV is less than your alpha if your PV is less than alpha you can make a decision and reject. You reject the null hypothesis. The same way as here is the rejection area. So then you can make a decision. Are you rejecting or are you not rejecting based on the information that you have? And that will be today's session. But before we close off, I need to show you how to do the hypothesis testing for the proportion equipped, which will be question number 15 and the other, the first two questions from your assignment.