{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

contingency_table

# contingency_table - Testing categorical probability one-way...

This preview shows pages 1–6. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
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:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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: 2 2 Reject H 0 if Note: This is a one sided test, since when null is true, the test statistics should equal zero.
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.

This preview has intentionally blurred sections. Sign up to view the full version.

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

{[ snackBarMessage ]}