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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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what would it have been like to be a crew member on the titanic
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

what is a test statistic
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

what new for chi squared gof
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 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
Step 3: Test Statistic

AP Statistics, Section 13.1

exercises
Exercises
  • 13.1-13.13 odd

AP Statistics, Section 13.1