See the preceding exercise, in which we can assume that = 15 for the IQ scores.

See the preceding exercise, in which we can assume that α = 15 for the IQ scores. Attorneys are a group with IQ scores that vary less than the IQ scores of the general population. Find the sample size needed to estimate the mean IQ of attorneys, given that we want 98% confidence that the sample mean is within 3 IQ points of the population mean. Does the sample size appear to be practical?

The sample size required to estimate the population mean.

Data From Preceding Exercise:

The Wechsler IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of college professors. We want to be 99% confident that our sample mean is within 4 IQ points of the true mean. The mean for this population is clearly greater than 100. The standard deviation for this population is less than 15 because it is a group with less variation than a group randomly selected from the general population; therefore, if we use σ = 15 we are being conservative by using a value that will make the sample size at least as large as necessary. Assume then that σ = 15 and determine the required sample size. Does the sample size appear to be practical?