Chapter 8, Problem 9CRE

To determine

To find: The sample size.

Answer to Problem 9CRE

The sample size is 35.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Margin of error }\left(E\right)=1000\\ \text{Standard}\text{deviation}\left(\sigma \right)=3000\\ \text{Confidence level }=95\%\end{array}$

Formula used:

  $\text{Sample size}\left(n\right)={\left(\frac{z_{\frac{\alpha }{2}}\times \sigma }{E}\right)}^2$

Calculation:

The value of $z_{\frac{\alpha }{2}}$ corresponding to $95\%$ confidence level is 1.96, which is obtained from the standard normal table.

The sample size can be calculated as:

  $\begin{array}{c}\text{Sample size}\left(n\right)={\left(\frac{z_{\frac{\alpha }{2}}\times \sigma }{E}\right)}^2\\ ={\left(\frac{1.96\times 3000}{1000}\right)}^2\\ \approx 35\end{array}$

Thus, the sample size is 35.