An IQ test is designed so that the mean is 100 and the standard deviation is 25

Question

An IQ test is designed so that the mean is 100 and the standard deviation is 25 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 8 IQ points of the true mean. Assume that =25 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. Would it be reasonable to sample this number of students? A. No. This number of IQ test scores is a fairly small number. B. Yes. This number of IQ test scores is a fairly large number. C. No. This number of IQ test scores is a fairly large number. D. Yes. This number of IQ test scores is a fairly small number.

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) = 25
ME =8
n = ( 1.96*25/8) ^2
= (49/8 ) ^2
= 37.52 ~ 38      

D. Yes. This number of IQ test scores is a fairly small number.

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