Chapter 6.4, Problem 24E

Solution

To describe: The error that has been done to calculate the sample size and correct it.

The sample size is 625.

Given:

Probability of playing basketball regularly = 13% = 0.13

Margin of error $=\pm 4\%$

Calculation:

The sample size is calculated as:

  $\begin{array}{c}\text{Margin of error}=\frac{1}{\sqrt{\text{Sample size}}}\\ \pm 0.04=\frac{1}{\sqrt{\text{Sample size}}}\\ \frac{1}{\text{Sample size}}=0.0016\\ \text{Sample size}=625\end{array}$

The required sample size is 625.

Explanation:

In this case, while calculating the sample size the probability of playing basketball regularly had been considered instead of margin of error that made the calculation incorrect.