Question

Q48

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately σ=29.8σ=29.8. 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? Round up to nearest whole number.

Answer 1

Solution :

Given that,

Population standard deviation = = 29.8

Margin of error = E = 10

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

Z/2 = Z_{0.025 = 1.960}

Z/2 = 1.960

sample size = n = [Z_/2* / E] ²

n = [1.96 *29.8 / 10 ]²

n = 34

Sample size = n = 34