Question

IQ tests are designed so that the mean is 100 points and the standard deviation is 15 points for the entire adult population. What is the minimum sample size needed to estimate the average IQ of all Stat 200 students to within 3 points with 97% confidence?

Answer 1

Solution :

Given that,

standard deviation =  $\sigma$ =15

Margin of error = E = 3

At 97% confidence level the z is ,

$\alpha$ = 1 - 97% = 1 - 0.97 = 0.03

$\alpha$ / 2 = 0.03 / 2 = 0.015

Z_$\alpha$/2 = Z_0.015 = 2.170

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = ( 2.17*15 / 3 )²

n =117.7225

Sample size = n =118