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Inference for Catergorial Data Multiple Choice Practice Problems for AP Statistics (page 2)

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By — McGraw-Hill Professional
Updated on Feb 4, 2011

Solutions

1. The correct answer is (c). The expected value for that cell can be found as follows:
2. The correct answer is (d). Since there are 12 months in a year, we have n = 12 and df = 12–1 = 11. Reading from Table C, 0.01 < P-value < 0.02. The exact value is given by the TI-83/84 as Χ2 cdf(23.5,1000,11)= 0.015.
3. The correct answer is (d). Because we have independent random samples of teachers from each of the two levels, this is a test of homogeneity of proportions. It would have been a test of independence if there was only one sample broken into categories (correct answer would be (b) in that case).
4. The correct answer is (b). The expected values for the cells are exactly equal to the observed values (e.g., for the 1st row, 1st column, so X2 must equal 0 the variables are independent, and are not related.
5. The correct answer is (e). The expected values for this two-way table are given by the matrix:
6. Then,

7. The correct answer is (c). In a Χ2 test for independence, we are interested in whether or not two categorical variables, measured on a single population, are related. In a Χ2 test for homogeneity of proportions, we are interested in whether two or more populations have the same proportions for each of the values of a single categorical variable.
8. The correct answer is (e). Using Ethnicity as the row variable, there are five rows (r = 5) and four columns (c = 4). The number of degrees of freedom for an r × c table is (r – 1)(c – 1). In this question, (5 – 1)(4 – 1) = 4 × 3 = 12.
9. The correct answer is (c). In III, the expected count for each category in a goodness-of-fit test is found by multiplying the proportion of the distribution of each category by the sample size. The expected count for a test of independence is found by multiplying the row total by the column total and then dividing by n.

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