11.1: Tests for Goodness of Fit By the end of class you will be able to use the chi square test to check for the goodness of fit between a sample and population.

Chi Square Distribution?

Some Uses for Chi Square Test for goodness of fit (if a frequency distribution matches a known distribution) Tests for independence of variables (are results based on two different populations) Tests for homogenity (does the entire population “behave” the same way) **All tests will be right tail**

You are buying a new car! What color do you want? White Black Silver Blue Gray Red Beige/Brown Green/Yellow 20% 17% 13% 12% 11% 5%

You ar What color do you want? Expected Values: White Black Silver Blue Gray Red Beige/Brown Green/Yellow 20% 17% 13% 12% 11% 5%

Chi Squared Goodness of Fit Degrees of Freedom: _________________ Test Value: Ho: There is no difference between the observed values and expected values H1: Our sample shows a preference (difference)

M&M’s: Are the colors really distributed as the Mars company predicts at .05?

Ambulance Calls (.1): Mt. Laurel EMS calls represent those of NJ. Claims (NJ): Saturday: 20% Sunday: 10% Monday:8% Tuesday: 7% Wednesday: 15% Thursday: 20% Friday: 20% Actual out of 147 (mtl) Saturday: 29 Sunday: 11 Monday: 13 Tuesday: 9 Wednesday: 25 Thursday: 29 Friday: 31

A teacher made a multiple choice test with the following distribution of answers. Is the distribution of answers what one would expect at a .05 level of significance? A: 10 B: 6 C: 2 D: 2

Summarizer: Rate it On a scale from 1-5, how well are you able to accomplish today’s mastery objective? Explain.