Chapter 8.2, Problem 41E

To determine

To construct: The 95% confidence interval for the proportion of adult that play video games and interpret it.

Answer to Problem 41E

The confidence interval is (0.468, 0.512)

Explanation of Solution

Given:

Sample proportion $\left(\widehat{p}\right)=49\%=0.49$

Sample size ( n ) = 2001

Formula used:

The formula to compute 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:

From the standard normal table, the z-score at 95% confidence level is 1.96.

The 95% confidence interval for the proportion of adult that play video games can be calculated as:

  $\begin{array}{c}CI=\widehat{p}\pm z_{\alpha /2}\times \sqrt{\frac{\widehat{p}\left(1-\widehat{p}\right)}{n}}\\ =0.49\pm 1.96\times \sqrt{\frac{0.49\left(1-0.49\right)}{2001}}\\ =\left(0.468,0.512\right)\end{array}$

Thus, the confidence interval is (0.468, 0.512)

Interpretation:

There is 95% probability that the proportion of adult that play video games lies between 0.468 and 0.512.