contingency_table - Testing categorical probability:...

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Testing categorical probability: one-way table Consider a multinomial experiment with k outcomes that corresponds to a single qualitative variable. The experiment would consist of n identical trials. There are k outcomes for each trial. The probability of the k outcomes remains the same from trail to trail. And k p p p ,..., , 2 1 1 ... 2 1 k p p p The results are the random variables that fall in each of the k class. Sum of them equals n. k n n n ,..., , 2 1 Now, we can use the observed counts to test about the proportions.
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Hypothesis (Goodness of Fit) Test for Proportions of a Multinomial Population Set up the null and alternative hypotheses. H0: all the proportions are the same and equals 1/k. H1: At least one of the proportions exceeds 1/k. Select a random sample and record the observed frequency, f i , for each of the k categories. Assuming H 0 is true, compute the expected frequency e i in each category by multiplying the category probability by the sample size.
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Hypothesis (Goodness of Fit) Test for Proportions of a Multinomial Population 2 2 1 ( ) f e e i i i i k Compute the value of the test statistic. Note: The test statistic has a chi-square distribution with k 1 df provided that the expected frequencies are 5 or more for all categories. f i = observed frequency for category i e i = expected frequency for category i k = number of categories where:
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Hypothesis (Goodness of Fit) Test for Proportions of a Multinomial Population where is the significance level and there are k - 1 degrees of freedom p -value approach: Critical value approach: Reject H 0 if p -value < Rejection rule: 22  Reject H 0 if Note: This is a one sided test, since when null is true, the test statistics should equal zero.
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Example Example: Lakes Homes Lakes Homes manufactures four models of prefabricated homes, a two-story colonial, a log cabin, a split-level, and an A-frame. To help in production planning, management would like to determine if previous customer purchases indicate that there is a preference in the style selected.
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This note was uploaded on 09/28/2011 for the course STAT METHO 33:623:385 taught by Professor Faridalizadeh during the Spring '11 term at Rutgers.

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contingency_table - Testing categorical probability:...

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