 This is a one-sample Z test for the population mean. We know it's a Z test because the population standard deviation sigma is known and we're going to do it in excel using one of the Calculators in your package a weight loss program claims that program Participants have a mean weight loss of at least 12 pounds after one month you are asked to test this claim You collect a random sample of 30 program participants and their weight losses after one month Assume the population standard deviation is three pounds use alpha equal point zero two Do you have enough evidence to reject the program's claims? The claim was that the mean weight loss was at least 12 pounds at least Implies you use the greater than or equal math operator That means that the null will have to be the claim Because the null is always a form of equality the alternative is The complement of the null which in this case would be a less than Because we've got a less than symbol in the alternative. We know this is a left tail test Here's the data you're given we've got 30 values of weight loss and I'm going to Copy that control copy I've opened up the one sample Z test for the mean calculator and we want to paste our data into the Decolon the blue areas, so I'm going to select that first cell and I'm going to right-click and I'm going to paste just the values in And you can see the calculator starts to calculate. I've already entered in the null hypothesis that the mean was 12 pounds loss The alpha of point zero two and the sigma the population standard deviation of three The calculator Counts the number of data points, which is 30 as we expected Calculates the mean of that data and then calculates the standard error remember that we need to take the population standard deviation and Divide it by the square root of the sample size then to get the standard error of the mean from that we can Calculate the standardized Test statistic for Z in this case it's four point one two six We calculate our critical values based on our alpha This test is a left tail test the lower tail test and so the critical value would be found by putting all of that point zero two in the left tail and then Calculating that and that comes out to be a lower critical value of minus 2.05 if we compare the Test statistic with the lower critical value. We would see that it exceeds It's to the left of that lower critical value Therefore it's in the rejection region that would tell us to reject the null also We've calculated the p-value and we've done that using the norm s-diss distribution Which just requires the alpha and the true tells us that it's we want it from the left tail the left infinity To the z-value so we know to reject the null hypothesis