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

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# Section 13.1 Chi-square Test for Goodness of Fit (GOF) - PowerPoint PPT Presentation

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

AP Statistics

• 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?
• 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
• 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

Exercises
• 13.1-13.13 odd

AP Statistics, Section 13.1