Question

When designing a study to determine the population mean, what is the minimum number you would need to survey to be 95% confident that the population mean is estimated to within 3 participants? Take the population standard deviation σ = 15. Will your project sample size n = 100 be enough? [10 points]

Answer 1

Solution

standard deviation =s =   =15

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*15 /3 )2

n =96.04

Will your project sample size n = 100 be enough yes