Question

An 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 statistics students such that it can be said with 99​% confidence that the sample mean is within 5 IQ points of the true mean. Assume that σ =12 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

Answer 1

Solution :

Given that,

Population standard deviation = = 12

Margin of error = E = 5

At the 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z_/2 = Z 0.005 = 2.576

sample size = n = [Z_/2* / E] ²

n = [ 2.576* 12 / 5 ]²

n = 38.22

Sample size = n = 39.