Chapter 9.2, Problem 9.31E

a)

To determine

To perform hypothesis test for one sample proportion $\widehat{p}$ .

Explanation of Solution

Given:

Null and alternative hypothesis:

  $\begin{array}{l}{H}_o:p=0.3\\ H_a:p<0.3\end{array}$

Test statistic = z = -1.77

Calculation:

Test statistic z = -1.77

Using the P-value approach:

P(Z<-1.77) = 0.0384

The p-value is p = 0.0384

Using excel formula, =NORMSDIST(-1.77)

Ifa = 0.05 then p = 0.0384<0.05, the result is significant.

If a = 0.01 then p = 0.0384 >0.01, the result is insignificant.

b)

To determine

To perform hypothesis test for one sample proportion $\widehat{p}$ .

Explanation of Solution

Given:

Null and alternative hypothesis:

  $\begin{array}{l}{H}_o:p=0.3\\ H_a:p\ne 0.3\end{array}$

Test statistic = z = -1.77

Calculation:

Test statistic z = -1.77

Using the P-value approach:

  $2\times P\left(Z<-1.77\right)=2\times 0.0384=0.0768$

Using excel formula, =NORMSDIST(-1.77)

The p-value is p = 0.0768

If a = 0.05 then p = 0.0768>0.05, the result is insignificant.

If a = 0.01 then p = 0.0768>0.01, the result is insignificant.