CH11 Notes

CH11 Notes - 1 GOODNESS of FIT & CONTINGENCY TABLES We...

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1 We want to reach conclusions about the proportion of items falling into k categories. Statistical inferences on categorical data are usually based on a sampling distribution called the CHI – SQUARE Distribution. We use a method known as a GOODNESS OF FIT procedure to compare the proportions of items which fall into k categories, that is, it compares the distribution of observed outcomes of a random sample with the distribution of observed outcomes of a random sample with the distribution one would expect to observe if the claim of a Hypothesis (H 0 ) were correct. Note Marketing Strategy Example on page 528. Manufacturing Banking Insurance Government Medical Total Observed 13 7 8 10 12 50 Expected 10 10 10 10 10 50 If all customers are evenly distributed then one would expect the proportion for each of the k categories to be the same, that is, 20%. There are five categories, hence 1/5 of total for each category. H 0 : π 1 = π 2 = … = π 5 = 0.20 H a : At least one π differs from the rest. The test statistic is Pearson’s CHI Square Goodness of Fit Statistic is
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2 ∑ (O i – E i ) 2 / E i If the expected number of occurrences is at least 5 , the sampling distribution of the test statistic is closely approximated by a CHI- SQUARE
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This note was uploaded on 12/07/2009 for the course MGMT 302 taught by Professor Canavos during the Spring '09 term at VCU.

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CH11 Notes - 1 GOODNESS of FIT & CONTINGENCY TABLES We...

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