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 statistics students. Suppose we want to be $92$% confident that our sample mean is within $1.5$ IQ points of the true mean. The mean for this population is clearly greater than $100$ . The standard deviation for this population is probably less than $15$ because it is a group with less variation than a group randomly selected from the general population; therefore, if we use $\sigma = 15,$ we are being conservative by using a value that will make the sample size at least as large as necessary. Assume then that $\sigma = 15$ and determine the required sample size.

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