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AP Statistics Tuesday, 15 April 2014 OBJECTIVE TSW (1) identify the conditions to use a chi-square test; (2) examine the chi-square test for independence; and (3) develop an understanding for a chi-square test for homogeneity. WS Chi-Square #1 is due Thursday, 17 April 2014. Everyone needs a calculator.

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2 Test For Independence

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2 test for independence Used with categorical, bivariate data from ONE sample Used to determine if the two categorical variables are associated (dependent) or not associated (independent)

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Assumptions & formula remain the same!

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Hypotheses – written in words H 0 : are independent H a : are dependent Be sure to write in context! Do NOT just write: “The two variables are independent / The two variables are dependent.”

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Expected Counts Assuming H 0 is true,

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Degrees of freedom Or cover up one row & one column & count the number of cells remaining!

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Example 4 A beef distributor wishes to determine whether there is a relationship between geographic region and cut of meat preferred. If there is no relationship, we will say that beef preference is independent of geographic region. Suppose that, in a random sample of 500 customers, 300 are from the North and 200 are from the South. Also, 150 prefer cut A, 275 prefer cut B, and 75 prefer cut C.

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If beef preference is independent of geographic region, how would we expect this table to be filled in? NorthSouthTotal Cut A150 Cut B275 Cut C75 Total300200500 9060 165110 4530

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Now suppose that in the actual sample of 500 consumers the observed numbers were as follows: (on your paper) Is there sufficient evidence to suggest that geographic regions and beef preference are not independent? (Is there a difference between the expected and observed counts?)

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Assumptions: Have a random sample of people All expected counts are greater than 5. approximately normal distribution H 0 : geographic region and beef preference are independent H a : geographic region and beef preference are dependent P-value = 0.0226df = 2 = 0.05 Since p-value < , I reject H 0. There is sufficient evidence to suggest that geographic region and beef preference are dependent. Expected Counts: N S A90 60 B165110 C45 30

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Assignment WS Chi Square Independence –Due on Thursday, 17 April 2014.

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