An IQ test is designed so that the mean is 100 and the stand

An IQ test is designed so that the mean is 100 and the standard deviation is 19 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 90 % confidence that the sample mean is within 8 IQ points of the true mean. Assume that =19 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 to the nearest integer)

What would the critical value be?

What is the required sample size?

Solution

a)
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.1% LOS is = 1.645 ( From Standard Normal Table )
Standard Deviation ( S.D) = 19
ME =8
n = ( 1.645*19/8) ^2
= (31.255/8 ) ^2
= 15.264 ~ 16      
b)
it is 1.645