An IQ test is designed so that the mean is 100 and the standard deviation is 17
ID: 3392553 • Letter: A
Question
An IQ test is designed so that the mean is 100 and the standard deviation is 17 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 95% confidence that the sample mean is within 3 IQ points of the true mean. Assume that =17 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.
The required sample size is ___. (Round up to the nearest integer.)
Is this a reasonable sample size for a real world calculation? ______
Explanation / Answer
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )
Standard Deviation ( S.D) = 17
ME =3
n = ( 1.96*17/3) ^2
= (33.32/3 ) ^2
= 123.358 ~ 124
Is this a reasonable sample size for a real world calculation?
Yes, it is reasonable