Chapter 8, Problem 6CRE

To determine

To find: The sample size.

Answer to Problem 6CRE

The sample size is 16577.

Explanation of Solution

Given:

Margin of error ( E ) = 1% = 0.01

Confidence level = 99%

Formula used:

The formula to compute the sample size is:

  $n=\left(\widehat{p}\right)\left(1-\widehat{p}\right){\left(\frac{z}{E}\right)}^2$

Calculation:

From the standard normal table, the z-score at 99% confidence level is 2.576.

Consider, sample proportion to be 0.05.

The sample size is calculated as:

  $\begin{array}{c}n=\left(\widehat{p}\right)\left(1-\widehat{p}\right){\left(\frac{z}{E}\right)}^2\\ =0.50\left(1-0.50\right){\left(\frac{2.576}{0.01}\right)}^2\\ =16577\end{array}$

Thus, the sample size is 16577.