Section 13.1 Chi-square Test for Goodness of Fit (GOF) AP Statistics

AP Statistics, Section What would it have been like to be a crew member on the Titanic? The crew of the Titanic made up 40% of the people on board. But 45% of the deaths were from the crew (685 of 1517 deaths were from the crew) Did the crew pay a heavier cost?

AP Statistics, Section 13.13

4 What is a test statistic? z, t are test statistics In the previous example, z= What if…  z=0?  z=5?  z=-3? We can say that the test statistic is a measure of unusualness. The higher the value, the more unusual the value.

AP Statistics, Section PercentObservedExpected On board Lost O-E(O-E)^2/E First class32915% Second Class28513% Third Class71032% Crew89940% %

AP Statistics, Section 13.16

7 What new for Chi-squared GOF No parameter of interest; rather a model describing the distribution amongst several categories. H0: the model is good. Ha: the model is not good. No normality check; rather no expected counts lower than 1. No more than 20% of the expected counts lower than 5. df=number of categories-1

AP Statistics, Section The statistic for goodness of fit The Chi-square test statistic measures how closely the observed data matches what is expected given a particular model

AP Statistics, Section Step 3: Test Statistic

AP Statistics, Section ObservedExpected CountPercentageCount(O-E)^2/E Blue 24% Brown 13% Green 16% Orange 20% Red 13% Yellow 14%

AP Statistics, Section Exercises odd