Question

An IQ test is designed so that the mean is 100 and the standard deviation is 8 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 2 IQ points of the true mean. Assume that sigmaequals8 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 = = 8

Margin of error = E = 2

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

sample size = n = (Z/2* / E) 2

n = (2.576 * 8/ 2)2

n = 106.17

n = 107

Sample size = 107