finding sample size statistic

Question

The Oxford IQ test is designed to have a mean of 100 pts and a standard deviation of 15 for normal adults. Find the sample size necessary to estimate the mean IQ score of college professors. We want to have 90% certainty that our sample mean is within 4 IQ pts of the true mean. For the population that we are dealing with, the mean IQ score is greater than 100. The standard deviation is less than 15 pts because it is a group with less variation than a randomly selected sample from the general population because of the amount of education that college professors have. So by using σ = 15, we are being mathematically strategic that will give us a sample size at least as large as necessary. Is this a practical sample size?

Answer 1

Hello Emily,

The general sample size formula that you want to use in this situation is

n = (Z^2 * o^2) / E^2

so it’s just a matter of identifying what those values would be for this question

from the values given we see that the tolerable error is 4 IQ pts, so that means E = 4. then Z = 1.645 since it’s a 90% level. finally o = 15.

putting that all together yields

n = (1.645^2 * 15^2) / 4^2

n = 608.855 / 16

n = 38.05

rounding up to the nearest whole number means that you would need to sample 39 professors in order to maintain these parameters, which seems like a reasonable amount! :)