The National Tax Journal (Dec. 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 ac-companying 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 α = .10.
e. Give the appropriate conclusion for the test in the words of the problem.

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Household Income Group Number of Charitable Givers Under $10,000 $10,000-$20.000 $20,000-$30,000 $30,000-$40.000 $40,000-$50.000 $50,000-$60.000 $60,000-$70,000 $70,000-$80,000 $80,000-$100,000 Over $100,000 42 93 153 91 114 157 101 95 127