Question

Assume standard IQ test scores follow a normal distribution with a population standard deviation of 14 points. In estimating the mean score of a sample group, we want to be 98% certain that we are within 4 IQ points of the true mean. Determine the required sample size.  

Answer 1

Solution :

Given that,

standard deviation = =14

Margin of error = E = 4

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

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

n = ( 2.326*14 / 4 )2

n =66.27

Sample size = n =66