Chapter 9, Problem 95CP

a.

To determine

Verify that the standard error is 0.061 when $H_0$ is true.

b.

To determine

Verify that the rejection region consists of the $\widehat{p}$ above 0.433.

c.

To determine

Verify that the probability that $\widehat{p}$ falls below 0.433 is the left-tail probability is below -1.03 standard deviations, when $p=0.5$.

Explain the reason for expecting the large $P\left(\text{Type II error}\right)$ for the smaller sample size n.