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=36.3σ=36.3. You would like to be 95% confident that your estimate is within 0.1 of the true population mean. How large of a sample size is required?

[Do not round mid-calculation. However, use a critical value rounded to three decimal places — this is important for the system to check answers correctly.]

n =

Answer 1

Solution :

Given that,

standard deviation = = 36.3

margin of error = E = 0.1

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 * 36.3) / 0.1)2

= 506204

Sample size = n = 506204