 Hi, this is Dr. Don. I have a problem out of Chapter 7 on inference and single sample hypothesis tests. A lot of students struggle over making a decision which kind of test to run, a Z test or a T test. The key in Business 233 is whether or not you know the population standard deviation sigma. If you do not know sigma, you should always use the Z test. I should note that in some textbooks they use a discriminator of the sample size and if you have a sample size greater than 30, you can use the Z test. But in Business 233, if you don't know sigma, use the T test. In this particular problem, we're given a claim that the population mean mu is greater than 76, alpha is .05, and we're given summary sample statistics. The sample mean X bar 76.6, the sample standard deviation S, not the population standard deviation sigma, but it's equal to 3.1 and a sample size of 26. The first thing we have to do is come up with a null and an alternative and that's important. Here we're given the claim is the mean is greater than 76 because that is an inequality greater than is an inequality that makes the claim the alternative and the null has to be the complement the opposite which would be less than or equal 76 which is that answer there. So they want the test statistic, the p-value, and then a decision. We're going to do it using stat crunch and we go over here to question help and then we open stat crunch by clicking there. Okay, I have stat crunch open for most of our problems. We start by clicking the stat button here, we're doing a T test so we go to T stats. We have one sample and then we have the summary statistic so I'm going to click that. I'm going to go here to the dialog box. We enter x bar 76.6. We enter the standard deviation of the sample 3.1, sample size n is equal to 26. We're going to do the hypothesis test for the population mean. The assumed value is 76 and we're doing a greater than right tail test so we select that drop down for our alternative. I'm going to click on get the p-value plot because I think that can be useful and we click on compute and here we get our answers. I always like to double check here in the summary. Yes, we were doing a single sample T test for the population mean. The claim was the mean was greater than 76 and the null then becomes equal or less than or equal 76. We look down here, there's our sample mean which is correct, degrees or freedom, n minus 1 is 25. Our T statistic, our standardized test statistic is 0.986 and that gives us a p-value of 0.167 rounding the 3 and those are the answers that they want over here, the standardized test statistic of 0.99 and the p-value of 0.167. Down at the bottom, if we click on this greater than symbol, we will get the probability sketch and you can see that the area under the curve to the right because we got a right tail test is 0.1666. Now one of the things that the T distribution hypothesis does not give you is the critical value of T and sometimes you need that so I'm going to show you that real quickly here. All we need to do to get the critical value of T is go to stat calculators T and we bring up this calculator. We need to enter the degrees of freedom which is n minus 1 or 25. This is a right tail test. I click on that and then I enter the alpha which is 0.05 and click compute and it gives me a critical value of 1.71 rounding 2 and if we look over here, if we find 1.71 it's somewhere in there so that agrees that the test value is not in the rejection region and again that explains why the p-value is not less than alpha and that is our final part. We fail to reject the null because the p-value is greater than alpha.167 is greater than 0.05 and if the question asks, we also fail to reject because the standardized test statistic of 0.99 is not greater than the critical value of 1.71 so I hope this helps. And if it does help, please consider subscribing to my YouTube channel, the stats files. Just click the big red subscribe button.