Chapter 8.2, Problem 2.3CYU

To determine

To find: The critical value for 99% confidence interval. Also, compute the confidence interval.

Answer to Problem 2.3CYU

The confidence interval is (0.21764, 0.23834).

Explanation of Solution

Given:

Number of students ( n ) = 10904

Number of binger drivers ( x ) = 2486

Confidence level = 99%

Formula used:

The formula to compute the confidence interval for population proportion is:

  $\begin{array}{l}CI=\widehat{p}\pm z_{\alpha /2}\times \sqrt{\frac{\widehat{p}\left(1-\widehat{p}\right)}{n}}\\ Where,\\ \widehat{p}=\frac{x}{n}\end{array}$

Calculation:

From the standard normal table, the z-score at 99% confidence level is calculated as:

  $\begin{array}{c}{z}_{\alpha /2}=z_{0.10/2}\\ =2.576\end{array}$

The confidence interval using Ti-83 plus calculator is calculated as:

  

Thus, the 99% confidence interval is (0.21764, 0.23834).