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=21.2σ=21.2. You would like to be 95% confident that your estimate is within 1 of the true population mean. How large of a sample size is required? Do not round mid-calculation. However, use a critical value accurate to three decimal places — this is important for the system to be able to give hints for incorrect answers.

Answer 1

Solution :

Given that,

standard deviation = = 21.2

margin of error = E = 1

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

Sample size = n = [(Z_/2 * ) / E]²

= [(1.960 * 21.2) /1 ]²

= 1726.569

Sample size = 1726.569 is required