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 = 44.3 . You would like to be 98% confident that your estimate is within 1.5 of the true population mean. How large of a sample size is required?

n =_______

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 = = 44.3

margin of error = E = 1.5

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 * 44.3) / 1.5)²

= 4719

Sample size = n = 4719