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

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 13.1

AP Statistics, Section 13.1

What is a test statistic? z, t are test statistics In the previous example, z=3.975. 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 13.1

Percent Observed Expected On board Lost O-E (O-E)^2/E First class 329 15% 130 227.55 -94.51 41.81 Second Class 285 13% 166 197.21 -28.49 4.93 Third Class 710 32% 536 485.44 51.49 5.26 Crew 899 40% 685 606.80 71.51 10.07 2223 100% 1517 0.00 61.02 AP Statistics, Section 13.1

AP Statistics, Section 13.1

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 13.1

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 13.1

Step 3: Test Statistic AP Statistics, Section 13.1

Observed Expected Count Percentage (O-E)^2/E Blue 24% Brown 13% Green   Observed Expected Count Percentage (O-E)^2/E Blue 24%  Brown 13%  Green 16%  Orange 20%  Red Yellow 14%  AP Statistics, Section 13.1

Exercises 13.1-13.13 odd AP Statistics, Section 13.1