Confidence Interval Sample Size

Question

We want to obtain a sample to estimate a population mean. Based on previous evidence, researchers believe the population standard deviation is approximately s=56.5. We would like to be 95% confident that the estimate is within 2.5 of the true population mean. How large of a sample size is required?

Answer 1

Hi Bailey,

We have known population standard deviation, so we can use z. Formula for sample size based on the z confidence interval is:

n=[(z_a/2)*sigma²]/E²

Let's break this down.

n=sample size, what we're looking for

z_a/2=z-critical value

sigma=population standard deviation

E=error

Now, let's identify our variables specifically for this problem:

z_a/2=1.96 You can get this from the z-table, but it's probably easier to remember that when we are dealing with two-sided z confidence intervals, z-critical value is always 1.96.

sigma=56.5

E=2.5

Substituting:

n=(1.96*56.5²)/2.5²

n=1001