Question

A compensation analyst for an investment bank wants to estimate the mean hourly wages of several hundred employees in the first 5 pay bands plus or minus within plus or minus $20. Management wants a 99% confidence level for the analysis. Assume that the population standard deviation is known to be $40 and that hourly wages are normally distributed. Find the minimum sample size required for this analysis.

Answer #1

The provided margin of error is $20, the population standard deviation σ=40, and the significance level is specified at 0.01, we can compute the minimum required sample size by using the following formula:

Since 99% confidence interval, 0.01 level of significance,
therefore **Zc = 2.576**

Hence the minimum sample size required is

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