Chapter 9.2, Problem 49E

To determine

To check: Whether at 5% significance level it could be concluded that the claim of DMV is incorrect.

Answer to Problem 49E

Yes, it could be concluded that the claim of DMV is incorrect.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Population proportion}\left(p_o\right)=60\%=0.60\\ \text{Number of teens}\left(n\right)=125\\ \text{Number of teens that passed the test}\left(x\right)=86\end{array}$

Formula used:

The formula to compute the test statistic is:

  $z=\frac{\widehat{p}-p_0}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}}$

Calculation:

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:p=0.60\\ H_0:p\ne 0.60\end{array}$

The obtained Excel output is:

From the above output, the p-value is 0.0446. Here, p-value < level of significance. Thus, the decision is to reject the null hypothesis.

Conclusion:

Thus, at 5% significance level there are enough evidence to conclude that the claim of DMV is incorrect.