# Cross tabulated count data a recent poll surveyed a

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Problem 7 Cross tabulated count data A recent poll surveyed a simple random sample of 100 voters in Washington. Respondents were classified by age group and voting behavior. Use the following results to test the hypothesis that age is independent of voting behavior. OBSERVED Voted Did not vote Total 18 to 28 30 70 29 to 45 50 50 >45 75 25 Total 155 145 7.1 What is the general formula for the expected value of the cell counts under the null hypothesis that voting status is independent of age? Work out the expected values in this table under the null hypothesis that age is independent of voting preference. Show both the formula with plug in values, and solve for the answer. (7.2-7.7) EXPECTED Voted Did not vote Total 18 to 28 7.2 7.5 100 29 to 45 7.3 7.6 100 >45 7.4 7.7 100 Total 150 150 7.8 What is the general formula for the contribution of each cell to the Chi-squared statistic? 100 100 100 300 300
Practice Final 13 Work out the squared standardized residuals (zij2) in this table (7.9-7.14) zij2Voted Did not vote 18 to 28 7.9 7.12 29 to 45 7.10 7.13 >45 7.11 7.14 7.15How many degrees of freedom does the Chi-square statistic for this test have? Show the formula with plug in values and the result. 7.16What is the α=0.05 critical value of the Chi-squared distribution for this test? 7.17Would you accept or reject the null hypothesis if the sample Chi-square statistic = 50?
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