A basketball player with a poor foul-shot record practices intensively during the off-season. He tells the coach that he has raised his proficiency from 70% to 80%. Dubious, the coach asks him to take 10

shots, and is surprised when the player hits 9 out of 10.

Complete parts a) through d) below.

a. Suppose the player really is no better than beforel ong dashstill

a 70% shooter. What's the probability he could hit at least 9 of 10

shots anyway? (Hint: Use a binomial model.)

(Round to four decimal places as needed.)

b. If that is what happened, now the coach thinks the player has improved, when he has not. Which type of error is that?

A.

This is a Type II error because the coach has mistakenly rejected a true null hypothesis.

B.

This is a Type I error because the coach has mistakenly failed to reject a false null hypothesis.

C.

This is a Type II error because the coach has mistakenly failed to reject a false null hypothesis.

D.

This is a Type I error because the coach has mistakenly rejected a true null hypothesis.

c. If the player really can hit 80% now, and it takes at least 9 out of 10

successful shots to convince the coach, what's the power of the test?

(Round to one decimal place as needed.)