Please see the attached file.

Follow this flow chart to decide whether to use a z-test or a t-test. The assumptions for each test are under the name of the test. Use the first flow chart if you are comparing means and the second if you are comparing proportions.

"One sample" means that you are comparing a sample mean (or proportion) to a number. "Two samples" means that you are comparing the means (or proportions) of two different samples. "Matched pairs" means that you are comparing samples that are not independent. Usually you are comparing the values from a sample before you do an experiment to the values from the same sample after you do an experiment. In the case of matched pairs, you perform a one sample test on the differences of the paired values.

In all cases, use a two-sided test when you are testing the hypothesis that two means (or two proportions) are not equal, and use a one-sided test when you are testing the hypothesis that one mean is greater than or less than the other.

You can also use this chart if you want to use the t or z statistic for something other than a test, such as a confidence interval or finding a critical value. In this case, if the chart says to use a z-test, you know you'll have to use a z-statistic, and if it says to use a t-test, you'll have to use a t-statistic. The assumptions about the sample and population remain the same.