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=35.3σ=35.3. 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?

As in the reading, in your calculations:
--Use z = 1.645 for a 90% confidence interval
--Use z = 2 for a 95% confidence interval
--Use z = 2.576 for a 99% confidence interval.

Answer 1

Solution :

Population standard deviation =    = 35.3

margin of error = E = 0.1

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 2

sample size = n = [Z/2* / E] 2

n = [2 * 35.3 / 0.1]2

n = 498436

Sample size = n = 498436