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 Less than 5 to 10 More than 5 Billion 10 12 23 12 22 Party Row Total 10 billion Democratic Republican Column Total 17 29 18 41 45 47 92 (1) 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.) 40 Pte Prtage 10 10 Papending Pay pendng Pertage Perntage -1blan Pay endng Pay endng () 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. O Hạ: Different proportion of Democrats and Republicans within each spending level. H: Same proportion of Democrats and Republicans within each spending level. O Ho: Same proportion of Democrats and Republicans within each spending level. H: Same proportion of Democrats and Republicans within each spending level. O Ho: Different proportion of Democrats and Republicans within each spending level. H: Different proportion of Democrats and Republicans within each spending level. O Ho: Same proportion of Democrats and Republicans within each spending level. H: 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 57 O Yes O No What sampling distribution will you use? O binomial O chi-square O uniform O normal O Student's t 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.) (d) Based on your answers in parts (a) to (c), will you reject ar fail to reject the null hypothesis of independence? O since the Pvalue > a, we fail to reject the nul hypothesis. O Since the p.value > a, we reject the null hypothesis. O Since the Pvalue s a, we reject the null hypothesis. O Since the Pvalue s a, we fail to reject the nul hypothesis.

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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
Less than S to 10 More than
5 Billion Billion 10 billion
Party
Row Total
Democratic T 10 T 12 23 T
Republican
45
12
17
18
47
Column Total
22
29
41
92
(1) 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.)
50
40
Perntage
Perertage
20
10
10
Party Bpending
Party Spending
Perentage
Perentage
10
e
ban
bilan
Pary Bpending
Pay pendng
(1) 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.
O Họ: Different proportion of Democrats and Republicans within each spending level.
H: Same proportion of Democrats and Republicans within each spending level.
O Ha: Same proportion of Democrats and Republicans within each spending level.
H: Same proportion of Democrats and Republicans within each spending level.
O Hg: Different proportion of Democrats and Republicans within each spending level.
H: Different proportion of Democrats and Republicans within each spending level.
O Họ: Same proportion of Democrats and Republicans within each spending level.
H: 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 57
O Yes
O No
What sampling distribution will you use?
O binomial
O chi-square
O uniform
O normal
O Student's t
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.)
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?
O Since the P-value > a, we fail to reject the null hypothesis.
O Since the -value > a, we reject the null hypothesis.
O Since the -value s a, we reject the null hypothesis.
O Since the P-value s a, we fail to reject the null hypothesis.
Transcribed Image Text: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 Less than S to 10 More than 5 Billion Billion 10 billion Party Row Total Democratic T 10 T 12 23 T Republican 45 12 17 18 47 Column Total 22 29 41 92 (1) 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.) 50 40 Perntage Perertage 20 10 10 Party Bpending Party Spending Perentage Perentage 10 e ban bilan Pary Bpending Pay pendng (1) 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. O Họ: Different proportion of Democrats and Republicans within each spending level. H: Same proportion of Democrats and Republicans within each spending level. O Ha: Same proportion of Democrats and Republicans within each spending level. H: Same proportion of Democrats and Republicans within each spending level. O Hg: Different proportion of Democrats and Republicans within each spending level. H: Different proportion of Democrats and Republicans within each spending level. O Họ: Same proportion of Democrats and Republicans within each spending level. H: 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 57 O Yes O No What sampling distribution will you use? O binomial O chi-square O uniform O normal O Student's t 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.) (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? O Since the P-value > a, we fail to reject the null hypothesis. O Since the -value > a, we reject the null hypothesis. O Since the -value s a, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis.
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