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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 oneway 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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 Spring '13
 ChristopherStocker
 Math, Binomial, Probability

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