Question

Two random samples were drawn from members of the U.S. Congress. One sample was taken from members who are Democrats and the other from members who are Republicans. For each sample, the number of dollars spent on federal projects in each congressperson's home district was recorded. Dollars Spent on Federal Projects in Home Districts Party Less than 5 Billion 5 to 10 Billion More than 10 billion Row Total Democratic 6 16 23 45 Republican 11 17 19 47 Column Total 17 33 42 92 (i) Make a cluster bar graph showing the percentages of Congress members from each party who spent each designated amount in their respective home districts. (In the graphs, blue represents Democrats and red represents Republicans.) Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (ii) Use a 1% level of significance to test whether congressional members of each political party spent designated amounts in the same proportions. (a) What is the level of significance? State the null and alternate hypotheses. H0: Different proportion of Democrats and Republicans within each spending level. H1: Different proportion of Democrats and Republicans within each spending level. H0: Same proportion of Democrats and Republicans within each spending level. H1: Same proportion of Democrats and Republicans within each spending level. H0: Different proportion of Democrats and Republicans within each spending level. H1: Same proportion of Democrats and Republicans within each spending level. H0: Same proportion of Democrats and Republicans within each spending level. H1: Different proportion of Democrats and Republicans within each spending level. (b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.) Are all the expected frequencies greater than 5? Yes No What sampling distribution will you use? Student's t binomial chi-square uniform normal What are the degrees of freedom? (c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.005 < p-value < 0.010 p-value < 0.005 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? Since the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis. Since the P-value ≤ α, we reject the null hypothesis. Since the P-value ≤ α, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the 1% level of significance, there is sufficient evidence to conclude that the proportion of spending for Democrats and Republicans within each level of spending is not the same. At the 1% level of significance, there is insufficient evidence to conclude that the proportion of spending for Democrats and Republicans within each level of spending is not the same.

Answer 1