Suppose that a weight loss company advertises that people using its program lose an average of 8 pounds the first month and that the Federal Trade Commission (the main government agency responsible for truth in advertising) is gathering evidence to see if this advertising claim is accurate. If the FTC finds evidence that the average is less than 8 pounds, the agency will file a lawsuit against the company for false advertising.

(a) What are the null and alternative hypotheses the FTC should use?

(b) Suppose that the FTC gathers information from a very large random sample of patrons and finds that the average weight loss during the first month in the program is x̅ = 7.9 pounds with a p-value for this result of 0.006. What is the conclusion of the test? Are the results statistically significant?

(c) Do you think the results of the test are practically significant? In other words, do you think patrons of the weight loss program will care that the average is 7.9 pounds lost rather than 8.0 pounds lost? Discuss the difference between practical significance and statistical significance in this context.