In the examples you were given the population standard deviation or the sample size was greater than 30. Usually you do not know the population standard deviation and with samples sizes less than approximately 30 you will do a better job testing a mean if you use a t-test.

For example, suppose NASA decides it wants to invest in a new rocket to send into space. When NASA investigates the costs or effectiveness of its rocket ship launches, it needs to figure out how to get reliable data out of only a few past launches.

In cases like this, you must use a test that does not require knowing the population standard deviation but still allows you to calculate statistics such as confidence intervals and margin of error. This is where the t test comes into play.

This week, you’ll learn how to use the t distribution to create confidence intervals and run a hypothesis test on a population mean with a small set of data values and when the population standard deviation is not known. You will also work with qualitative variables and run hypothesis tests on two-way tables.