A company wants to (cheaply) test the effects of a weight loss drug they're developing. They claim that the drug will help any person who is overweight lose 5 pounds in a week. They decide to conduct a hypothesis test at the 99% significance level to further strengthen their claim. Thus they decide to compensate a group of 40 people who are overweight to take this drug for a week and come back for a weight in.

They decided to proceed with a hypothesis test and they want to disprove the null hypothesis that their drug does not help people who are overweight with weight loss (that is, m=0)

Part A: State the null hypothesis and alternative hypotheses for this particular test.

Part B: Use the data given to determine the following statistical measures and find the confidence interval at 99% for the average weight loss in one week. Is a 5 pounds loss contained within this confidence interval? If so, does that mean that customers can expect to lose 5 pounds on this drug?

Part C: Perform a hypothesis test! Which type of tailed-test will you use? Find the t-statistic for the data and determine whether to reject the null hypothesis. Hint: the critical value of the t-distribution with 39 degrees of freedom is approximately 2.426. If you have two critical values, separate them with commas and list your positive value first in the T-Critical Value(s) cell.

Part D: Were you able to reject the null hypothesis at 99% significance? If so, interpret the significance of this rejection. Does it provide sufficient evidence to prove that their drug helps their customers lose 5 pounds in one week? If you think this is insufficient evidence, describe how you would change the experiment to make it more meaningful.

Data