Question

We would like to estimate the mean salary for a given population. In order to do that, we would like to take a sample. We want a 95% confidence interval with a margin of error of 400. To estimate the standard deviation of the population, we took a pilot sample, the size of 30, and found the standard deviation of their salaries to be 5000.

How many people do we have to ask to create our desired confidence interval (total sample size)?

Answer 1

Solution

standard deviation =   =5000

Margin of error = E = 400

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96

sample size = n = [Z/2* / E] 2

n = ( 1.96*5000 /400 )2

n =600.25

Sample size = n =600