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 10 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. Assume that sigma = 10 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

Solution

Solution:

In order to find the sample size such that one can be 99% confident that the sample mean is within 8IQ points of the true mean,

P(100 - Z(1 - 0.01/2)*10/sqrt(n) < ? < 100 + Z(1 - 0.01/2)*10/sqrt(n)) = 0.99

P(100 - 2.58 *10/sqrt(n) < ? < 100 + 2.58*10/sqrt(n)) = 0.99

2.58*10/sqrt(n) = 8

Thus, n= 10 (ans)