# 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;

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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.

 2 Test For Independence

 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)

Assumptions & formula remain the same!

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.”

Expected Counts Assuming H 0 is true,

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

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.

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

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?)

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

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

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