Sample Size Confidence Intervals

Question

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately . You would like to be 90% confident that your estimate is within 1 of the true population mean. How large of a sample size is required?

Answer 1

n = (z* * s/E)^2

where n = sample size

z* is critical z value computed as follows

first find critical probability = (1 + CL in decimal)/2 = (1 + 0.9)/2 = 0.95

then look up z* from table or by using statistical calculator = 1.645

E given as 1 and s given as 66.2 so:

n = (1.645 * 66.2/1)^2 = 11858.99 ~ 11859