Question

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ = 45.1 σ = 45.1 . You would like to be 95% confident that your estimate is within 10 of the true population mean.

How large of a sample size is required?

Answer 1

Solution

standard deviation    =45.1

Margin of error = E = 10

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*45.1 /10 )2

n =78.1385

Sample size = n =79