Question

An IQ test is designed so that the mean is 100 and the standard deviation is 16 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 8 IQ points of the true mean. Show your correct formula with the numbers substituted for the variables.

Answer 1

Solution :

Given that,

standard deviation    = 16

Margin of error = E = 8

At 99% confidence level the z is,

= 1 - 99%

= 1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576

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

n = ( 2.576*16 / 8 )2

n =26.54

Sample size = n =27 rounded