How large of a sample size is required?

Question

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately =59.3. You would like to be 99% confident that your estimate is within 0.2 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

Hi Kaitlyn,

The formula for this type of sample size calculation---where you are given population standard deviation--is:

n=[(z_a/2)*sigma²]/E²

Breaking this down:

n=sample size we are looking for

z_a/2=z-score for p 0.995--since we have a 99% confidence interval here

sigma=population standard deviation

E=acceptable error

Here:

z_a/2=2.575

sigma=59

E=0.2

Therefore:

n=[(2.575)²59²]/0.2²

n=577031

This is very large because of your standard deviation and error level--std. deviation was a high number in numerator; confidence level a low number (0.04) in denominator. I hope this helps.