solution

Survey on giving and volunteering (continued). Refer to Exercise 10.43. In addition to the 1,072 charitable givers who reported that their charitable contributions were motivated by tax considerations, another 1,693 givers reported no tax motivation, giving a total sample of 2,765 charitable givers. Of the 1,072 who were motivated by tax considerations, 691 itemized deductions on their income tax returns. Of the 1,693 who were not motivated by tax considerations, 794 itemized deductions.

a. Consider the two categorical variables, tax motivation (yes or no) and itemize deductions (yes or no). Form a 2  2 contingency table for these variables.

b. Compute the expected cell counts for the contingency table, part a.

c. Compute the value of x² for a test of independence.

d. At  = .05, what inference can you make about whether the two variables, tax motivation and itemize deductions, are related for charitable givers?

e. Create a bar graph that will visually support your conclusion in part d.

Exercise 10.43

Survey on giving and volunteering. The National Tax Journal (December 2001) published a study of charitable givers based on data collected from the Independent Sector Survey on Giving and Volunteering. A total of 1,072 charitable givers reported that their charitable contributions were motivated by tax considerations. The number of these 1,072 givers in each of 10 household income categories (saved in the accompanying file) is shown in the table below.

a. If the true proportions of charitable givers in each household income group are the same, how many of the 1,072 sampled givers would you expect to find in each income category?

b. Give the null hypothesis for testing whether the true proportions of charitable givers in each household income group are the same.

c. Compute the chi-square test statistic for testing the null hypothesis, part b.

d. Find the rejection region for the test if a = .10.

e. Give the appropriate conclusion for the test in the words of the problem.