Chapter 9.2, Problem 61E

To determine

To find: The test statistics values at which test is significant.

Answer to Problem 61E

The test is significant at $\alpha =0.05$ not $\alpha =0.01$

Explanation of Solution

Given:

  $\begin{array}{l}z=2.43\\ \text{Level of significance}\left(\alpha \right)=0.05/0.01\end{array}$

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:p=0.4\\ H_a:p\ne 0.4\end{array}$

Calculation:

The p -value can be computed as:

  $\begin{array}{c}p-\text{value}=2\times P\left(Z>\left|z\right|\right)\\ =2\times P\left(Z>\left|2.43\right|\right)\\ =2\times 0.0075\\ =0.0150\end{array}$

The test will be significant if null hypothesis rejects.

The null hypothesis will be rejected, if $p-\text{value}>\alpha$

Here,

  $\begin{array}{l}p-value\left(0.0150\right)<\alpha \left(0.05\right)=\text{ Reject the null hypothesis}\\ p-value\left(0.0150\right)>\alpha \left(0.01\right)=\text{ Fail to reject the null hypothesis}\end{array}$

Thus, it could be said that the test is significant at $\alpha =0.05$ .

Hence, the correct option is (b).