The standard IQ test is designed so that the mean is 100 and the standard deviat

Question

The standard IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of all adults. We wish to find the sample size necessary to estimate the mean IQ score of all people who have successfully passed a college statistics course. We want to create a confidence interval that is no wider than 6 IQ points. The standard deviation for this sub-population is certainly less than 15 as it should be a less variable population. Therefore by using = 15 we will obtain a conservative sample size, meaning it will be sufficient large enough. How large a sample should we utilize for a 90% confidence interval? (use the z-score 1.64485 )

Explanation / Answer

for 90% CI; z score =1.64485

for std deviation =15

here margin of error E=6/2 =3

therefore required sample size =(z*std deviaiton/E)2 =~68

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