Question

A researcher is interested in estimating the average salary of police officers in a large city. She wants to be 99% confident that her estimate is correct. If the standard deviation is $1050, how large a sample is needed to get the desired information and to be accurate within $200?

Answer 1

Given:
σ = $1050, ppulatin standard deviation
99% confidence interval
Accuracy = +/- $200

The accuracy is given by
z*(σ/√n)
where
z* = 2.576 for 99% confidence level (from tables)
n = sample size

Therefore
2.576(1050/√n) = 200
√n = (2.576*1050)/200 = 13.524
n = 182.9

Answer: The sample size is 183