Question

A researcher is interested in estimating the mean salary of firefighters in a certain area.She wants to be 95% sure her estimate is correct.If the standard deviation is $5500,how large a sample is needed to get the desired informationand to be accurate within $2500?

Answer 1

To calculate the sample size to determine a mean we use the following formula:

$n=(\frac{Z\sigma}{E})^2$

n is the population size. Z is the Z value for the confidence level (for a confidence level of 95%, Z = 1.96)

σ is the standard deviation ($5500 in this case) and E is the margin of error. ($2500 in this case). Replacing values in the formula:

$n=(\frac{1.96\cdot5500}{2500})^2\approx18.59$

Then, the sample size should be 19 to estimate the mean with 95% confidence.