Question

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 45​% to 55​%. ​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 beforelong dashstill a 45​% shooter.​ What's the probability he could hit at least 9 of 10 shots​ anyway? (Hint: Use a binomial​ model.)

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 failed to reject a false null hypothesis.
B.
This is a Type II error because the coach has mistakenly rejected a true null hypothesis.
C.
This is a Type I 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 55​% ​now, and it takes at least 9 out of 10 successful shots to convince the​ coach, what's the power of the​ test?

D) List two ways the coach and player could increase the power to detect any improvement. Select all that apply.
A.
They could increase the number of shots.
B.
They could bring in a sanctioned referee to watch the player shoot free throws.
C.
They could increase the size of the basket.
D.
They could move the player closer to the basket.
E.
They could keep the number of shots at 10 and declare that​ 8, 9, or 10 made free throws will be deemed as having improved.

Answer 1