An IQ test is designed so that the mean is 100 and the standard deviation is 16

Question

An IQ test is designed so that the mean is 100 and the standard deviation is 16 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 6 IQ points of the true mean. Assume that sigmaequals=16 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 nothing. (Round up to the nearest integer.)

Explanation / Answer

Margin of error = 6

z*sigma/sqrt(n) = 6

for 95% confidence level is known to be 1.96

1.96* 16/sqrt(n) = 6

solving for n, [ 1.96*16/6 ] ^2 = 27.32

Hence, the sample size should be 28 .

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