Question

A population is estimated to have a standard deviation of 9. We want to estimate the population mean within 3, with a 95% level of confidence

How large a sample is required?

Answer 1

Solution

standard deviation =   =9

Margin of error = E = 3

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* 9/ 3)2

n =34.57

Sample size = n =35 rounded