Expected values of x x1 xk are e x1 np1

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Unformatted text preview: ibution. Expected values of x = (x1 , ..., xk ) are E (x1 ) = np1 , . . . , E (xk ) = npk . We want to make inferences about the true proportions that occur in the k categories based on the sample information in the one-way table. Test of a hypothesis about multinomial probabilities. 1 A. Zhensykbaev Categorical data analysis We assume that the sample size n is large (this is satisfied if for every i the expected value E (xi ) will be not less than 5. The null hypothesis is H0 = {p1 = p∗ , ..., pk = p∗ }. 1 k Alternative hypothesis is Ha = {at least one of the multinomial probabilities does not equal its hypothesized value}. Test statistic is k 2 χ= i=1 (ni − E (xi ))2 , E (xi ) E (xi ) = np∗ . i Rejected region is RR = {χ2 > χ2 }, α where χ2 is chosen using the Table VII of McClave and Benson for the α degrees of freedom df = k − 1. Example. A supermarket conducts a consumer preference survey by recording the brand of bread purchased by customers in its stores. There are three brands of bread A, B and C. A random sample of 150 buyers...
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