Chapter 9.2, Problem 43E

a.

To determine

To discuss: The Type I and Type II errors in this case and explain their results.

Answer to Problem 43E

The sample size is 35.

Explanation of Solution

Given:

Number of trials ( n ) = 200

Number of success ( x ) = 83

The hypotheses are:

  $\begin{array}{l}{H}_0:p=0.37\\ H_a:p>0.37\end{array}$

Type I error happenes if the null hypthesis is rejected even if it is correct.

In this case, the type I error would occur if it is concluded that the proportion of students who got approval for parking is above 0.37 even if it is 0.37.

Type II error happenes if the null hypthesis is not rejected even if it is not correct.

In this case, the type II error would occur if it is concluded that the proportion of students who got approval for parking is equal to 0.37 even if it is above 0.37.

b.

To determine

To explain: The statement that power of the test is 0.75 for p = 0.37

Explanation of Solution

The power of test means the true proportion is 0.45 and the likelihood of not accepting the null hypothesis is 0.75.

c.

To determine

To discuss: The two ways to increase the power.

Explanation of Solution

The power could be increased by following mentioned ways:

(a). Increasing the level of significance.

(b). Increasing the size of the sample.