Question

How large a sample should be selected to provide a 95% confidence interval with a margin of error of 10? Assume that the population standard deviation is 20.

Answer 1

Given that, population standard deviation $(\sigma)$ = 20

margin of error ( E ) = 10

confidence level = 95%

A 95% confidence level has significance level $(\alpha)$ = 0.05 and critical value is, $Z_{\alpha/2}= 1.96$

We want to find the sample size ( n ),

$n = (Z_{\alpha/2} * \frac { \sigma}{E })^2 = (1.96 * \frac { 20}{10})^2 = 15.3664$

$n \approx 15$

Required sample size is 15

Note: if you want sample size is nearest to next integer then it is equal to 16