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 = 32.5 . 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? Use a z* value accurate to TWO places for this problem. (Not z = 2)

Answer 1

Solution :

Given that,

standard deviation = = 32.5

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 = Z_0.025 = 1.960

Z_/2 = 1.96

Sample size = n = ((Z_/2 * ) / E)²

= ((1.96 * 32.5) / 10)²

= 41

Sample size = 41