Question

Weight Loss Program 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. What are the null and alternative hypotheses the FTC should use

Answer 1

The null hypothesis is
`H_(0): \mu = 8`, and the alternative hypothesis is
`H_(a): \mu < 8`

Explanation:

At the null hypothesis, we test if the mean is equal to a certain value.

At the alternate hypothesis, we test if the mean is less than, more than, or different of the value tested at the null hypothesis.

Claims to lose an average of 8 pounds the first month

This means that the null hypothesis is
`H_(0): \mu = 8`

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.

FTC tests if the mean is less than 8, so the alternate hypothesis is
`H_(a): \mu < 8`