Chapter PV, Problem 38RE

(a)

To determine

To explain the statement to the fans.

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, fans who never took statistics can’t understand why the company did not offer this WNBA player an endorsement contract. So, this is because the poll have a margin of error and the $25\%$ or below is still within the margin so this why the company did not offer this WNBA player an endorsement contract.

(b)

To determine

To explain did the company initially commit a Type I error or Type II error in not signing her.

Answer to Problem 38RE

It is Type II error.

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. Suppose that further polling reveals that this WNBA star really is known to about $30\%$ of the target audience. Thus, the company initially commit a Type II error in not signing her because it is rejecting the null hypothesis when it is true.

(c)

To determine

To explain would the power of the company’s test have been higher or lower if the player were more famous.

Answer to Problem 38RE

The power of the company’s test have been higher if the player were more famous.

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, the power of the company’s test would have been higher if the player were more famous because it is more if the null hypothesis was false.