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 90% confidence that the sample mean is within 7 IO points of the true mean. Assume that sigma = 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 _________. (Round up to the nearest integer.)

Explanation / Answer

Margin if error = 1.645 * (16/sqrt(N))

7 = 1.645 * (16/sqrt(N))

N = (1.645*16/7)^2 = 14.1376

Sample size = 14 as nearest integer

Larger sample sizes result in smaller margin of error, so we should use a larger sample size.

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