Question

A researcher wants to estimate the mean IQ score for a population of high school students. How many students will she have to select for the IQ tests if she wants 95% confidence the sample mean is within 3 IQ points of the population mean? Assume the population standard deviation is 15.

Answer 1

Solution :

Given that,

Population standard deviation = $\sigma$ = 15

Margin of error = E = 3

At 95% confidence level the z is,

$\alpha$ = 1 - 95%

$\alpha$ = 1 - 0.95 = 0.05

$\alpha$ /2 = 0.025

Z _{$\alpha$ /2} = Z_0.025 = 1.96  

sample size = n = [Z _{$\alpha$ /2}* $\sigma$ / E] ²

n = [ 1.96 * 15 / 3 ]²

n = 96.04

Sample size = n = 97