Once you have determined that the values are independent, another factor must be determined:
Question no.2: Are the variances of both populations known?
Approximate with s if BOTH sample sizes n 1 , n 2 happen to exceed 30.
Because we know the population variance, or the sample size is greater than 30, we can conduct a test involving the standard normal distribution (the z-test). You can see the similarity between tests of the mean involving one variable and those involving two.
If the sample size does not permit us to approximate the population variance, we must perform an F-test on the sample variances to determine how to proceed.