Exploring the STAT-TEST Menu

A researcher claims that the average cost of men's athletic shoes is less than $80. He selects a random sample of 36 pairs of shoes from a catalog and finds the following costs. Is there enough evidence to support the researcher's claim at alpha=0.10?

$60, 70, 75, 55, 80, 55, 50, 40, 80, 70, 50, 95
120, 90, 75, 85, 80, 60, 110, 65, 80, 85, 85, 45
75, 60, 90, 90, 60, 95, 110, 85, 45, 90, 70, 70

The STAT-TEST menu will allow us to do hypothesis testing on the data, and statistics as well. We will look at the following features of this menu on the next few pages; Z-Test, T-Test, finding a Z-interval and T-interval for a set of data, and we will take a look at an example where we will use the chi-square test. The other tests will be added to these pages at a later date.

In order to access the STAT-TEST menu, Press the STAT button, left arrow once, and your there. Your screen should have the options at the right. Notice this is an extensive menu. We will try to solve the intro problem in the following steps.
Choose Z-TEST from the menu and start by using the data option. In order to get a sigma value, run 1-Var STATS on your data first. To place the sigma value on the screen move your cursor to sigma, press VARS,5, then 3. Set your value for Mu, and use the mu<80 option. Highlight the calculate option and press ENTER. (Keep in mind that this calculator does not find critical values, it only shows p-values.)
Using the draw option, we can see the area under the curve highlighted with a z-value of -1.5657 and a p-value of 0.587. From this information, we should reject the null hypothesis since 0.587 < 0.10. There is enough evidence to support the claim that the average cost of men's shoes is $80.
If you want to use the summary statistics for this problem, then highlight the STATS option on the menu, and then move to calculate, and then press ENTER.

**This problem can be found in the textbook "Elementary Statistics A Step by Step Approach" by Allen Bluman

Go on to T-Tests...