Assume that you don't know what the population standard deviation is. You draw a sample of 30 screws and calculate their mean length. The mean for your sample is 4.8, and the standard deviation of your sample (s) is 0.4 centimeters.
Not only will we see how to conduct a hypothesis test about the difference between two population means, we will also construct a confidence interval for this difference. The methods that we use are sometimes called a two sample t test and a two sample t confidence interval.