Chapter 8.2, Problem 51E

To determine

To calculate: The sample size of the register voter in the city who plan to vote Chaves when the confidence interval is 95%.

Answer to Problem 51E

The correct option is (c).

Explanation of Solution

Given Information:

Margin of error $E=0.05$

Confidence interval = 95%

Formula Used Sample size $n=\frac{{\left[z_{\raisebox{1ex}{$\alpha $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right]}^2\times 0.25}{E^2}$

Calculation:

Confidence interval = 95%

Convert 95% into decimal.

  $\frac{95}{100}=0.95$

For confidence interval 0.95, use table A.

  $z_{\raisebox{1ex}{$\alpha $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=1.96$

Since, guessed value $\stackrel{⌢}{p}$ is unknown.

Find the sample size. Use the formula $n=\frac{{\left[z_{\raisebox{1ex}{$\alpha $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right]}^2\times 0.25}{E^2}$ .

  $\begin{array}{c}n=\frac{{\left[z_{\raisebox{1ex}{$\alpha $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right]}^2\times 0.25}{E^2}\\ =\frac{{1.96}^2\times 0.25}{{0.05}^2}\\ =385\end{array}$

Hence, the correct option is (c).