Chapter 9.2, Problem 51E

a.

To determine

To construct: The 95% confidence interval using the provided information.

Answer to Problem 51E

The confidence interval is $\left(0.607,0.769\right)$ .

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 construct the confidence interval for population proportion is:

  $CI=\widehat{p}\pm z_{\alpha /2}\times \sqrt{\frac{\widehat{p}\left(1-\widehat{p}\right)}{n}}$

Calculation:

The obtained Excel output is:

From the above output, the confidence interval is $\left(0.607,0.769\right)$ .

b.

To determine

To explain: The claim of DMV using the result of above part.

Explanation of Solution

From the confidence interval obtained in above part, it is clear that the value 0.60 does not lie in the computed interval. Thus, it could be said that claim of DMV is incorrect.