Chapter 9.2, Problem 52E

a.

To determine

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

Answer to Problem 52E

The confidence interval is $\left(0.59,0.73\right)$ .

Explanation of Solution

Given:

  $\begin{array}{l}\text{Population proportion}\left(p_o\right)=73\%=0.73\\ \text{Number of students involved}\left(n\right)=200\\ \text{Number of students that are in favor of well being}\left(x\right)=132\end{array}$

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 $\left(0.59,0.73\right)$ .

Interpretation:

There is 95% chance that the proportion of students that agree that well being is an important goal lies between 0.59 and 0.73.

b.

To determine

To explain: Whether it could be concluded using the above confidence interval that the national value is being held at this university.

Explanation of Solution

From the confidence interval obtained in above part, it is clear that the value 0.73 lies in the computed interval. Thus, it could be concluded that the national value is being held at this university.