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=56.5. You would like to be 98% confident that your esimate is within 4 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.

n=

Answer 1

Solution :

Given that,

standard deviation = = 56.5

margin of error = E = 4

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.01 = 2.326

Sample size = n = ((Z_/2 * ) / E)²

= ((2.326 * 56.5) / 4)²

= 1080

Sample size = 1080