Question

You are getting ready to take a sample from a large population, and need to determine the appropriate sample size. You are estimating sales at a large chain of department stores. A previous survey from the same population found a standard deviation of $18. What sample size is needed to have a 95% confidence of estimating the population mean within plus/minus $5? Show your work.

Answer 1

The minimum required sample size for a confidence interval estimate of the population mean is given by

where,

n: the minimum sample size

   : the critical value corresponding to a level of confidence

E: the desired margin of error

Given: , ( the population standard deviation for the previous survey)

Critical value: For 95% confidence,

Therefore, the minimum required sample size is 50.