Lecture7-1

Lecture7-1 - BUAD 310 Applied Business Statistics 2/22/10...

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BUAD 310 Applied Business Statistics 2/22/10
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Chi Square Tests 1. Goodness of fit test 2. Test for independence 2
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An Example: Microwave Oven 3 Brand Cleveland Market Share Milwaukee Frequency 1 20% 102 2 35% 121 3 30% 120 4 15% 57 Microwave oven wholesaler wishes to compare consumer preferences in Milwaukee with the historical market shares in Cleveland. If the consumer preferences in Milwaukee are substantially different, the wholesaler will consider changing its policies for stocking ovens. The wholesaler examines a random sample of 400 Milwaukee consumers.
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Chi Square Test for Goodness of Fit Consider the outcome of an experiment where each of n randomly selected items is classified into one of k groups . We want to test the hypothesis that p 1 , …, p k are the probabilities of being classified in a particular group. ( note : p 1 + … + p k = 1) Let f i = number of items classified into group i ( i -th observed frequency ) E i = np i = expected number in i -th group if p i is probability of being in group i ( i -th expected frequency ) To check whether the observed frequencies are consistent with the assumed probabilities, we should compare f i ’s to E i ’s 4
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An Example: Microwave Oven 5 Microwave oven wholesaler wishes to compare consumer preferences in Milwaukee with the historical market shares in Cleveland. If the consumer preferences in Milwaukee are substantially different, the wholesaler will consider changing its policies for stocking ovens. The wholesaler examines a random sample of 400 Milwaukee consumers. Cleveland Milwaukee Expected Brand Market Share Frequency Frequency 1 20% 102 80 2 35% 121 140 3 30% 120 120 4 15% 57 60
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Chi Square Goodness of Fit Test H 0 : probabilities are p 1 , p 2 , …, p k vs H a : the null hypothesis is not true Use the chi-square test statistic: Find the p-value using chi-square distribution. Reject H 0 at significance level α if p-value < α Note : Large values of the test statistic provide evidence against H 0 . The larger the test statistics, the more evidence against H 0 . 6 2 2 1 () k ii i i fE = E
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P-Value After you have computed the test statistic use chi-square distribution with k -1 degrees of freedom (df) to find the p-value ( right tail probability ) 7
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Chi-Square Distribution 8 2 Like the t -distributions, the chi-square distribution is described by the degrees of freedom (df) Chi-square distribution is skewed to the right and takes only positive values (≥ 0)
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Some Chi-Square Distributions 9
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Chi-Square Table (p. 651) 10
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Chi-Square Table (continued) 11
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This note was uploaded on 09/05/2010 for the course BUAD 310 taught by Professor Lv during the Spring '07 term at USC.

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Lecture7-1 - BUAD 310 Applied Business Statistics 2/22/10...

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