Sample Size Calculation

Question

An 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 statistics students such that it can be said with 90​% confidence that the sample mean is within 5 IQ points of the true mean. Assume that σ=15 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

Answer 1

sample size = (z-critical * S/E)**2

z-critical for 90% CI is 1.645

S is given as 15

E is given as 5

sample size = (1.645 * 15/5)**2 = 24.35 ~ 25

a good maximum sample size is 10% of the population as long as it doesn't exceed 1000.