Testing a Population Mean

This is a straightforward hypothesis test for sample means. We just give the value to test and the sample statistic with no interpretation so you see how the method works.

Notice we use a t-score and t-distribution in this case. We always do this when the hypothesis test is about a population mean.

Problem adapted from Triola’s Elementary Statistics

Height of Women

This is a problem involving the -distribution and involves finding out how likely a certain size sample mean will be.

Here the idea is to change areas in the -distribution into areas for the standard normal curve and look them up in the table.

The is the population mean and it corresponds to z=0 as a z-score. The is a sample mean and it corresponds to a data value in the left graph above. You change it into a z-value in the right graph by using the formula for the z-score:

Notice that the standard deviation this time on the bottom is

This comes from the Central Limit Theorem and is the form you use when you are working with the -distribution.

Problem adapted from Larson/Farber’s Elementary Statistics