Two random samples were drawn from members of US. Congress. One sample was taken

Question

Two random samples were drawn from members of US. 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. (See table below)

(a) Make a cluster bar graph showing the percentages of Congress members from each party who spent the designated amount in their respective home districts.

(b) Use a 1% level of significance to test whether congressional members of each political party spent designated amounts in the same proportions.

Dollars Spent on Federal Projects in Home Districts

Party Less than 5 billion 5-10 Billion More than 10 Billion Row Total Democratic 8 15 22 45 Republican 12 19 16 47 Column Total 20 34 38 92

Explanation / Answer

Use chi square test to check the hypohtesis.

H0: congressional members of each political party spent designated amounts in the same proportions.

Ha: They were not the same

Two tailed chi square test.

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The chi-square statistic is 2.1755. The P-Value is 0.336973. The result is not significant at p < 0.05.

Hence accept null hypothesis.

Results < 5 billion 5-10 billion >15 billion Row Totals Democratic 8  (9.78)  [0.32] 15  (16.63)  [0.16] 22  (18.59)  [0.63] 45 Republician 12  (10.22)  [0.31] 19  (17.37)  [0.15] 16  (19.41)  [0.60] 47 Column Totals 20 34 38 92  (Grand Total)

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