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

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)

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

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

  2. 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

  3. AP Statistics, Section 13.1

  4. 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

  5. AP Statistics, Section 13.1

  6. AP Statistics, Section 13.1

  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 13.1

  8. 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

  9. Step 3: Test Statistic AP Statistics, Section 13.1

  10. AP Statistics, Section 13.1

  11. Exercises • 13.1-13.13 odd AP Statistics, Section 13.1

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