Question

3. To estimate the mean hourly pay for employees of a large supermarket chain, how many employees must be sampled if we wish to estimate the mean hourly pay to within $1.50 with a confidence level of 90%?   Assume a population standard deviation of $6.25.   

Answer 1

Solution :

The sample size required to estimate population mean with a 95% confidence level and E margin of error is given by,

Where, E is margin of error, σ is population standard deviation, E is margin of error and Z(0.10/2) is critical z-value at 90% confidence level.

Since, we wish to estimate the mean hourly pay to within $1.50, therefore the margin of error E = 1.50.

σ = $6.25

Using Z-table we get, Z(0.10/2) = 1.645

Hence, the required sample size is,

On rounding to nearest whole number we get,

n = 47

Hence, 47 employees must be sampled.