Chapter 21, Problem 33E

(a)

To determine

To find out what is the probability he can hit at least $9\text{ of the 10}$ shots anyway.

Answer to Problem 33E

  $4.64\%$ .

Explanation of Solution

It is given in the question that 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 $60\%\text{ to 80\%}$ . Thus, the probability he can hit at least $9\text{ of the 10}$ shots anyway is calculated by the calculator $\text{TI}-89$ using the Binomcdf command as,

  $\begin{array}{l}binomcdf(10,0.4,1)=0.0464\\ =4.64\%\end{array}$

(b)

To determine

To explain which type of error is that.

Answer to Problem 33E

It is a Type I error.

Explanation of Solution

It is given in the question that 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 $60\%\text{ to 80\%}$ . Thus, it is a Type I error because it is given that the coach thinks the player has improved when he is not. So, when we think that is true but it is actually not true it is a Type I error.

(c)

To determine

To find out what is the power of the test.

Answer to Problem 33E

  $37.6\%$ .

Explanation of Solution

It is given in the question that 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 $60\%\text{ to 80\%}$ . As we know that $8$ is supposed to be new shot percentage so power can be found out by:

  $\begin{array}{l}=8^9\times 2+8^{10}\times 2^0\\ =0.376\\ =37.6\%\end{array}$

(d)

To determine

To list two ways the coach and player could increase the power to detect any improvement.

Explanation of Solution

It is given in the question that 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 $60\%\text{ to 80\%}$ . Thus, the two ways the coach and player could increase the power to detect any improvement are that we would increase the number of shots or lower the standard set by the coach to measure improvement.