011+Categorical+data

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online