Chapter PV, Problem 37RE

(a)

To determine

To explain why does the company use upper tail tests in this situation.

Explanation of Solution

It is given in the question that an advertising company would not sign an athlete to do product endorsements unless it is sure the person is known to more than $25\%$ of its target audience. Thus, we can say that the company use upper tail tests in this situation because the company wants to see if more than $25\%$ of its target audience knows the athlete and he or she is well known.

(b)

To determine

To explain what type I and Type II errors would represents in this context and describe the risk that each error poses to the company.

Explanation of Solution

It is given in the question that an advertising company would not sign an athlete to do product endorsements unless it is sure the person is known to more than $25\%$ of its target audience. Thus, Type I error represents that the company concludes that the athlete is well-known but that is not true. It offers an endorsement contract to someone who lacks name recognition. But the Type II error represents that the company overlooks a well-known athlete, missing the opportunity to sign a potentially effective spokesperson. So, in Type I error the contract would make the company lose money and in Type II error would make the company lost out on a beneficial contract.

(c)

To determine

To explain how would this change the company’s exposure to each type of risk.

Explanation of Solution

It is given in the question that an advertising company would not sign an athlete to do product endorsements unless it is sure the person is known to more than $25\%$ of its target audience. Thus, if the company is thinking of changing its test to use a $10\%$ level of significance then the chance to falsely reject the null hypothesis increases and the chance to miss rejecting the null hypothesis when it is false will decrease.