011+Categorical+data

Brand a b c i 123 ni 61 53 36 probabilities p1 p2 p3

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Unformatted text preview: is observed in the one-way table. Brand A B C i 123 ni 61 53 36 Probabilities p1 , p2 , p3 are unknown. Do these data indicate that a preference exists for any of the brands (use α = 0.05)? Solution. The null hypothesis is 1 H0 = {p1 = p2 = pk = p3 = }. 3 2 A. Zhensykbaev Categorical data analysis The expected values are E (x1 ) = np1 = 150 · 1 = 50, 3 E (x2 ) = E (x3 ) = 50. The est statistic of χ2 -test is χ2 = 1 (61 − 50)2 + (53 − 50)2 + (36 − 50)2 = 6.52. 50 The χ2 = χ2 .05 is chosen using the Table VII for the degrees of freedom α 0 df = k − 1 = 2: χ2 .05 = 5.9915. Since 6.52 > 5.9914 we conclude that the 0 realization contradicts to H0 hypothesis. Two-way (contingency) tables. Before we considered data classified according to a single qualitative criterion. Now consider multinomial experiments in which the data are classified according to two criteria, classification according to two qualitative factors. We make inferences about the true proportions that occur in the k categories based on the sample information i...
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