Chapter 8.2, Problem 3.2CYU

To determine

To find: The sample size. Also, explain the effect of increase in confidence level on the sample size.

Answer to Problem 3.2CYU

The sample size is 1180.

Explanation of Solution

Given:

Population proportion $\left(\widehat{p}\right)=80\%=0.80$

Margin of error ( E ) = 3% = 0.03

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 2.579

The sample size is calculated as:

  $\begin{array}{c}n=\left(\widehat{p}\right)\left(1-\widehat{p}\right){\left(\frac{z}{E}\right)}^2\\ =0.80\left(1-0.80\right){\left(\frac{2.576}{0.03}\right)}^2\\ =1179.537\\ \approx 1180\end{array}$

Thus, the required sample size is 1180.

Conclusion:

From the above calculations, it is clear that the increase in confidence level is leading increase in the sample size.