Question

4.162 Weight Loss Program Suppose that a weight loss company advertises that people using its pro- gram lose an average of 8 pounds the first month and that the Federal Trade Commission (the main government agency responsible for truth in adver- tising) 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 first with a that the average weight loss during month in the program is x 7.9 pounds pounds itn p-value for this result of 0.006. What is the con clusion of the test? Are the results statistica significant?

Answer 1

Answer

Part a

Here claim is average is less than 8

$H_0: \mu=8 vs H_1:\mu<8$

Part b

Now here for large sample p value is 0.006<alpha hence we reject the null hypothesis.

Hence the result is significant as pvalue<alpha

Part c

Practically this is not significant as difference is very minute. But statistically it is significant as p value is too small.