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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 Party Less than 5 Billion 5 to 10 Billion More than 10 billion Row Total Democratic 14 25 45 Republican 13 16 18 47 Column Total 19 30 43 92 (a) 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.) Penage Perentage -10 b Paty Spending S-10 bo Paty Spending bon Perentage Perentage ben S-10 ban Paty Spending Paty Spendng (b) Use a 1% level of significance to test whether congressional members of each political party spent designated amounts in the same proportions. O What is the level of significance? State the null and alternate hypotheses. O Ho: Different proportion of Democrats and Republicans within each spending level.H,: Same proportion of Democrats and Republicans within each spending level. Ho: Different proportion of Democrats and Republicans within each spending level.H,: Different proportion of Democrats and Republicans within each spending level. Ha: Same proportion of Democrats and Republicans within each spending level.H,: Different proportion of Democrats and Republicans within each spending level. Ho: Same proportion of Democrats and Republicans within each spending level.H,: Same proportion of Democrats and Republicans within each spending level. () 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.)

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 14 25 45 Republican 13 16 18 47 Column Total 19 30 43 92 (a) 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.) Penage Perentage -10 b Paty Spending S-10 bo Paty Spending bon Perentage Perentage ben S-10 ban Paty Spending Paty Spendng (b) Use a 1% level of significance to test whether congressional members of each political party spent designated amounts in the same proportions. O What is the level of significance? State the null and alternate hypotheses. O Ho: Different proportion of Democrats and Republicans within each spending level.H,: Same proportion of Democrats and Republicans within each spending level. Ho: Different proportion of Democrats and Republicans within each spending level.H,: Different proportion of Democrats and Republicans within each spending level. Ha: Same proportion of Democrats and Republicans within each spending level.H,: Different proportion of Democrats and Republicans within each spending level. Ho: Same proportion of Democrats and Republicans within each spending level.H,: Same proportion of Democrats and Republicans within each spending level. () 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.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 Party Less than 5 Billion 5 to 10 Billion More than 10 billion Row Total Democratic 6 14 25 45 Republican 13 16 18 47 Column Total 19 30 43 92 (a) 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.) Percentage Percentage 20 d bilion 5-10 bilon 10bilon d bilion S-10 bon 10 bilon Paty pending Paty Spending 60 50 Perentage Perentage d bilion S-10 bilon 10 bilon S bilion 5-10 bilon 10 bilon Paty Spendng Paty Spending (b) Use a 1% level of significance to test whether congressional members of each political party spent designated amounts in the same proportions. ( ) What is the level of significance? State the null and alternate hypotheses. O Ho: Different proportion of Democrats and Republicans within each spending level.H,: Same proportion of Democrats and Republicans within each spending level. O H: Different proportion of Democrats and Republicans within each spending level.H,: Different proportion of Democrats and Republicans within each spending level. O H,: Same proportion of Democrats and Republicans within each spending level.H,: Different proportion of Democrats and Republicans within each spending level. O Hạ: Same proportion of Democrats and Republicans within each spending level.H,: Same proportion of Democrats and Republicans within each spending level. (ii) 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? O Yes O No What sampling distribution will you use? O uniform O normal O binomial O chi-square Student's t What are the degrees of freedom? (iii) Find estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) O P-value > 0.100 O 0.050 < P-value < 0.100 O 0.025 < P-value < 0.050 O 0.010 < P.value < 0.025 O 0.005 < P.value < 0.010 O P-value < 0.005
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 Party Less than 5 Billion 5 to 10 Billion More than 10 billion Row Total Democratic 6 14 25 45 Republican 13 16 18 47 Column Total 19 30 43 92 (a) 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.) Percentage Percentage 20 d bilion 5-10 bilon 10bilon d bilion S-10 bon 10 bilon Paty pending Paty Spending 60 50 Perentage Perentage d bilion S-10 bilon 10 bilon S bilion 5-10 bilon 10 bilon Paty Spendng Paty Spending (b) Use a 1% level of significance to test whether congressional members of each political party spent designated amounts in the same proportions. ( ) What is the level of significance? State the null and alternate hypotheses. O Ho: Different proportion of Democrats and Republicans within each spending level.H,: Same proportion of Democrats and Republicans within each spending level. O H: Different proportion of Democrats and Republicans within each spending level.H,: Different proportion of Democrats and Republicans within each spending level. O H,: Same proportion of Democrats and Republicans within each spending level.H,: Different proportion of Democrats and Republicans within each spending level. O Hạ: Same proportion of Democrats and Republicans within each spending level.H,: Same proportion of Democrats and Republicans within each spending level. (ii) 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? O Yes O No What sampling distribution will you use? O uniform O normal O binomial O chi-square Student's t What are the degrees of freedom? (iii) Find estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) O P-value > 0.100 O 0.050 < P-value < 0.100 O 0.025 < P-value < 0.050 O 0.010 < P.value < 0.025 O 0.005 < P.value < 0.010 O P-value < 0.005
Republicah Column Total 19 30 43 92 (a) 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 Perentage 30 Perentage 20 13% 10 Obilen 5-10 bilon 10bilon 5-10 blion 10 bilon Paty pending Party Spending Perentage Perentage 20 10 4 bilen S-10 bion Sbilon 6-10 bilon 10bilon 10 bilon Party Spending Paty Spending (b) Use a 1% level of significance to test whether congressional members of each political party spent designated amounts in the same proportions. () What is the level of significance? State the null and alternate hypotheses. O Ho: Different 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. O Ho: Same proportion of Democrats and Republicans within each spending level.H,: Same proportion of Democrats and Republicans within each spending level. (i) 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? O Yes O No What sampling distribution will you use? O uniform O normal O binomial O chi-square O Student's t What are the degrees of freedom? (i) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) OP-value > 0.100 O 0.050 < P-value < 0.100 O 0.025 < P-value < 0.050 O 0.010 < P-value < 0.025 O 0.005 < P-value < 0.010 O P-value < 0.005 (iv) 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 > a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. Since the P-value sa, we reject the null hypothesis. Since the P-value s a, we fail to reject the null hypothesis. (v) 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 O 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.
Transcribed Image Text:Republicah Column Total 19 30 43 92 (a) 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 Perentage 30 Perentage 20 13% 10 Obilen 5-10 bilon 10bilon 5-10 blion 10 bilon Paty pending Party Spending Perentage Perentage 20 10 4 bilen S-10 bion Sbilon 6-10 bilon 10bilon 10 bilon Party Spending Paty Spending (b) Use a 1% level of significance to test whether congressional members of each political party spent designated amounts in the same proportions. () What is the level of significance? State the null and alternate hypotheses. O Ho: Different 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. O Ho: Same proportion of Democrats and Republicans within each spending level.H,: Same proportion of Democrats and Republicans within each spending level. (i) 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? O Yes O No What sampling distribution will you use? O uniform O normal O binomial O chi-square O Student's t What are the degrees of freedom? (i) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) OP-value > 0.100 O 0.050 < P-value < 0.100 O 0.025 < P-value < 0.050 O 0.010 < P-value < 0.025 O 0.005 < P-value < 0.010 O P-value < 0.005 (iv) 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 > a, we fail to reject the null hypothesis. O Since the P-value > a, we reject the null hypothesis. Since the P-value sa, we reject the null hypothesis. Since the P-value s a, we fail to reject the null hypothesis. (v) 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 O 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.
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