Question

A new IQ test is designed so that the mean is 100 and the standard deviation is 12 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of residents of a state. We want to be​ 95% confident that our sample mean is within 4 IQ points of the true mean. Assume that sigmaσ =12 and determine the required sample size.

Answer 1

Solution

standard deviation =   =12

Margin of error = E = 4

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

sample size = n = [Z/2* / E] 2

n = ( 1.96* 12 / 4 )2

n =34.57

Sample size = n =35