Statistics- ADM2304 The monthly cost of a prescription medication were checked

ADM2304Assignment 2Fall 2015ADM2304Assignment 2 (85 marks)Due Date: Tuesday, November 3, 2015 by 23:59Please include your integrity statement.General Instructions:When you perform a test of hypothesis, you must always use the 4-step approach: i. S1:the “Null” and“Alternative” hypotheses, ii. S2: calculate value of the test statistic, iii. S3: the level of significance andthe critical value of the statistic, iv. S4: your decision rule and the conclusion reached in not rejecting orrejecting the null hypothesis. When asked to calculate p–value, S5, relate the p-value to the level ofsignificance in reaching your conclusion.If you use Minitab to perform the hypothesis test, you must cut and paste the relevant output into yourassignment. This output simply verifies and occasionally replaces the manual computation of the teststatistic, p-value or the confidence interval. You must supply all the required steps, mentioned above, tomake your testing procedure complete.If the confidence coefficient (CC) or the level of significance (LS) are not specified, assume the defaultvalues to be 95% and 5% respectively. Use precision level of only 4 Decimal Digits (DD) whencalculations are done with a calculator.Question 1 (20 marks)(Common Data for Questions #1 and #2)City_1City_2125.05137.56142.50145.95117.49142.75121.99117.49141.64128.69130.29142.39121.99141.30153.43133.39150.82136.69157.15147.05131.49131.79144.69161.55143.06159.60131.93119.55150.39The monthly cost of a prescription medication were checked in two major cities in twodifferent provinces. ‘City_1’ and ‘City_2’ give the costs incurred by patients at differentpharmacies in the two cities. The data is given above and the values are in dollars. Sincethe cities were in different provinces, you should assume that the population variancesare not equal.Telfer School of ManagementUniversity of Ottawa1 ADM2304Assignment 2Fall 2015a. Manually test the hypothesis using the critical value approach whether there is adifference in the mean medication costs in these two cities.b. Calculate the p-value. What conclusion would you draw?c. Calculate a confidence interval for the difference in mean costs? Is it consistentwith the conclusion reached in part ‘a’?Question 2 (10 marks)Use the same data given in Qu.#1.a. Now for the same data, test whether there is a difference in the median monthlycosts of medications in the two cities.b. Specify with appropriate diagrams and justify which test is more appropriate:the test in part ‘a’ of Qu.#1 or in part ‘a’ of Qu.#2? What are the names of thesetests?Question 3 (25 marks)In this question, Weight1(lbs) refers to the weight in lbs of a client randomly selected justbefore the client started a six-week dieting program and Weight2(lbs) refers to the weightof the same client after the program was over. .Data for Qu.#3Client_Num12345678910Weight1(lbs)165.6176.4162.0189.0181.8171.0198.0189.0172.8198.0Weight2(lbs)158.4165.6171.0171.0167.4174.6174.6176.4165.6178.2a. Manually test the hypothesis that the dieting program is effective. State yourhypotheses and use the ‘critical value’ approach. What is the name of this test?Explain why this test should or should not be used.b. What is the asymmetric confidence interval for the mean difference in theweights before and after the dieting program was over? Is it consistent with theconclusion reached in part ‘a’?c. Based on this asymmetric confidence interval in ‘b’ above, state how muchminimum mean weight could be lost, after completing the dieting program.d. Calculate the p-value for this test. What conclusion would you draw?e. Now for the same data, test the hypothesis that the median difference in weightsbefore and after the dieting program is positive. What is the name of this test?f. Specify with diagrams and justify which test would be more appropriate? (part‘a’ or part ‘e’). What are the names of these respective methodologies?Telfer School of ManagementUniversity of Ottawa2 ADM2304Assignment 2Fall 2015Question 4 (20 marks)With looming elections, polls with independent samples were taken to obtain thefollowing data concerning the number of people who favor two different majorpolitical parties, Party1 and Party2 respectively.Party1Sample Size: 200Favor:68Party2300110a. Manually test the claim that there is a difference in the proportion of peoplewho prefer Party1 compared to Party2. Use a 5% level of significance.b. Find the appropriate 95% confidence interval for the hypothesis test youperformed in part ‘a’.c. Calculate the p-value for the test in part ‘a’ above. What conclusion wouldyou draw?You found that the proportions were so close that as a reasonable analyst, youtook a larger sample and the following results were obtained.Party1Sample Size: 1600Favor:550Party22400900d. Now manually test the hypothesis that 1.0% more people prefer Party2 thanthey prefer Party1. Use a 5% level of significance.e. Find the appropriate 95% asymmetric confidence interval (CI) for the testperformed in part ‘d’ above. Is this CI consistent with the conclusion youreached in the hypothesis?Telfer School of ManagementUniversity of Ottawa3 ADM2304Assignment 2Fall 2015Question 5 (10 marks)All political parties seem to be wooing the "Middle Class". According to standardincome ranges for a family of four, the following data were obtained with a simplerandom sample. ‘Oi’ are the observed frequencies and ‘pi’ are the assumed proportions.Income_ClassIC1: Poor:IC2: Lower Middle_Class:IC3: Middle_Class:IC4: Upper Middle_Class:IC5: Affluent:IC6: Wealthy:Oi253580302010pi0.100.200.500.100.080.02a. Test if the data supports the assumed probabilities. Use the ‘critical value’approach.b. If a proposed change in tax law is going to benefit only families in the topthree income brackets, test the hypothesis that less than 36% of families willbenefit if the new change in the tax bill is passed and becomes law. Reachyour conclusion by calculating the p-value.c. What is the maximum percentage of families that will benefit from thisproposed tax law?Telfer School of ManagementUniversity of Ottawa4

ADM2304Assignment 2Fall 2015ADM2304Assignment 2 (85 marks)Due Date: Tuesday, November 3, 2015 by 23:59Please include your integrity statement.General Instructions:When you perform a test of hypothesis, you must always use the 4-step approach: i. S1:the “Null” and“Alternative” hypotheses, ii. S2: calculate value of the test statistic, iii. S3: the level of significance andthe critical value of the statistic, iv. S4: your decision rule and the conclusion reached in not rejecting orrejecting the null hypothesis. When asked to calculate p–value, S5, relate the p-value to the level ofsignificance in reaching your conclusion.If you use Minitab to perform the hypothesis test, you must cut and paste the relevant output into yourassignment. This output simply verifies and occasionally replaces the manual computation of the teststatistic, p-value or the confidence interval. You must supply all the required steps, mentioned above, tomake your testing procedure complete.If the confidence coefficient (CC) or the level of significance (LS) are not specified, assume the defaultvalues to be 95% and 5% respectively. Use precision level of only 4 Decimal Digits (DD) whencalculations are done with a calculator.Question 1 (20 marks)(Common Data for Questions #1 and #2)City_1City_2125.05137.56142.50145.95117.49142.75121.99117.49141.64128.69130.29142.39121.99141.30153.43133.39150.82136.69157.15147.05131.49131.79144.69161.55143.06159.60131.93119.55150.39The monthly cost of a prescription medication were checked in two major cities in twodifferent provinces. ‘City_1’ and ‘City_2’ give the costs incurred by patients at differentpharmacies in the two cities. The data is given above and the values are in dollars. Sincethe cities were in different provinces, you should assume that the population variancesare not equal.Telfer School of ManagementUniversity of Ottawa1 ADM2304Assignment 2Fall 2015a. Manually test the hypothesis using the critical value approach whether there is adifference in the mean medication costs in these two cities.b. Calculate the p-value. What conclusion would you draw?c. Calculate a confidence interval for the difference in mean costs? Is it consistentwith the conclusion reached in part ‘a’?Question 2 (10 marks)Use the same data given in Qu.#1.a. Now for the same data, test whether there is a difference in the median monthlycosts of medications in the two cities.b. Specify with appropriate diagrams and justify which test is more appropriate:the test in part ‘a’ of Qu.#1 or in part ‘a’ of Qu.#2? What are the names of thesetests?Question 3 (25 marks)In this question, Weight1(lbs) refers to the weight in lbs of a client randomly selected justbefore the client started a six-week dieting program and Weight2(lbs) refers to the weightof the same client after the program was over. .Data for Qu.#3Client_Num12345678910Weight1(lbs)165.6176.4162.0189.0181.8171.0198.0189.0172.8198.0Weight2(lbs)158.4165.6171.0171.0167.4174.6174.6176.4165.6178.2a. Manually test the hypothesis that the dieting program is effective. State yourhypotheses and use the ‘critical value’ approach. What is the name of this test?Explain why this test should or should not be used.b. What is the asymmetric confidence interval for the mean difference in theweights before and after the dieting program was over? Is it consistent with theconclusion reached in part ‘a’?c. Based on this asymmetric confidence interval in ‘b’ above, state how muchminimum mean weight could be lost, after completing the dieting program.d. Calculate the p-value for this test. What conclusion would you draw?e. Now for the same data, test the hypothesis that the median difference in weightsbefore and after the dieting program is positive. What is the name of this test?f. Specify with diagrams and justify which test would be more appropriate? (part‘a’ or part ‘e’). What are the names of these respective methodologies?Telfer School of ManagementUniversity of Ottawa2 ADM2304Assignment 2Fall 2015Question 4 (20 marks)With looming elections, polls with independent samples were taken to obtain thefollowing data concerning the number of people who favor two different majorpolitical parties, Party1 and Party2 respectively.Party1Sample Size: 200Favor:68Party2300110a. Manually test the claim that there is a difference in the proportion of peoplewho prefer Party1 compared to Party2. Use a 5% level of significance.b. Find the appropriate 95% confidence interval for the hypothesis test youperformed in part ‘a’.c. Calculate the p-value for the test in part ‘a’ above. What conclusion wouldyou draw?You found that the proportions were so close that as a reasonable analyst, youtook a larger sample and the following results were obtained.Party1Sample Size: 1600Favor:550Party22400900d. Now manually test the hypothesis that 1.0% more people prefer Party2 thanthey prefer Party1. Use a 5% level of significance.e. Find the appropriate 95% asymmetric confidence interval (CI) for the testperformed in part ‘d’ above. Is this CI consistent with the conclusion youreached in the hypothesis?Telfer School of ManagementUniversity of Ottawa3 ADM2304Assignment 2Fall 2015Question 5 (10 marks)All political parties seem to be wooing the "Middle Class". According to standardincome ranges for a family of four, the following data were obtained with a simplerandom sample. ‘Oi’ are the observed frequencies and ‘pi’ are the assumed proportions.Income_ClassIC1: Poor:IC2: Lower Middle_Class:IC3: Middle_Class:IC4: Upper Middle_Class:IC5: Affluent:IC6: Wealthy:Oi253580302010pi0.100.200.500.100.080.02a. Test if the data supports the assumed probabilities. Use the ‘critical value’approach.b. If a proposed change in tax law is going to benefit only families in the topthree income brackets, test the hypothesis that less than 36% of families willbenefit if the new change in the tax bill is passed and becomes law. Reachyour conclusion by calculating the p-value.c. What is the maximum percentage of families that will benefit from thisproposed tax law?Telfer School of ManagementUniversity of Ottawa4

ADM2304Assignment 2Fall 2015ADM2304Assignment 2 (85 marks)Due Date: Tuesday, November 3, 2015 by 23:59Please include your integrity statement.General Instructions:When you perform a test of hypothesis, you must always use the 4-step approach: i. S1:the “Null” and“Alternative” hypotheses, ii. S2: calculate value of the test statistic, iii. S3: the level of significance andthe critical value of the statistic, iv. S4: your decision rule and the conclusion reached in not rejecting orrejecting the null hypothesis. When asked to calculate p–value, S5, relate the p-value to the level ofsignificance in reaching your conclusion.If you use Minitab to perform the hypothesis test, you must cut and paste the relevant output into yourassignment. This output simply verifies and occasionally replaces the manual computation of the teststatistic, p-value or the confidence interval. You must supply all the required steps, mentioned above, tomake your testing procedure complete.If the confidence coefficient (CC) or the level of significance (LS) are not specified, assume the defaultvalues to be 95% and 5% respectively. Use precision level of only 4 Decimal Digits (DD) whencalculations are done with a calculator.Question 1 (20 marks)(Common Data for Questions #1 and #2)City_1City_2125.05137.56142.50145.95117.49142.75121.99117.49141.64128.69130.29142.39121.99141.30153.43133.39150.82136.69157.15147.05131.49131.79144.69161.55143.06159.60131.93119.55150.39The monthly cost of a prescription medication were checked in two major cities in twodifferent provinces. ‘City_1’ and ‘City_2’ give the costs incurred by patients at differentpharmacies in the two cities. The data is given above and the values are in dollars. Sincethe cities were in different provinces, you should assume that the population variancesare not equal.Telfer School of ManagementUniversity of Ottawa1 ADM2304Assignment 2Fall 2015a. Manually test the hypothesis using the critical value approach whether there is adifference in the mean medication costs in these two cities.b. Calculate the p-value. What conclusion would you draw?c. Calculate a confidence interval for the difference in mean costs? Is it consistentwith the conclusion reached in part ‘a’?Question 2 (10 marks)Use the same data given in Qu.#1.a. Now for the same data, test whether there is a difference in the median monthlycosts of medications in the two cities.b. Specify with appropriate diagrams and justify which test is more appropriate:the test in part ‘a’ of Qu.#1 or in part ‘a’ of Qu.#2? What are the names of thesetests?Question 3 (25 marks)In this question, Weight1(lbs) refers to the weight in lbs of a client randomly selected justbefore the client started a six-week dieting program and Weight2(lbs) refers to the weightof the same client after the program was over. .Data for Qu.#3Client_Num12345678910Weight1(lbs)165.6176.4162.0189.0181.8171.0198.0189.0172.8198.0Weight2(lbs)158.4165.6171.0171.0167.4174.6174.6176.4165.6178.2a. Manually test the hypothesis that the dieting program is effective. State yourhypotheses and use the ‘critical value’ approach. What is the name of this test?Explain why this test should or should not be used.b. What is the asymmetric confidence interval for the mean difference in theweights before and after the dieting program was over? Is it consistent with theconclusion reached in part ‘a’?c. Based on this asymmetric confidence interval in ‘b’ above, state how muchminimum mean weight could be lost, after completing the dieting program.d. Calculate the p-value for this test. What conclusion would you draw?e. Now for the same data, test the hypothesis that the median difference in weightsbefore and after the dieting program is positive. What is the name of this test?f. Specify with diagrams and justify which test would be more appropriate? (part‘a’ or part ‘e’). What are the names of these respective methodologies?Telfer School of ManagementUniversity of Ottawa2 ADM2304Assignment 2Fall 2015Question 4 (20 marks)With looming elections, polls with independent samples were taken to obtain thefollowing data concerning the number of people who favor two different majorpolitical parties, Party1 and Party2 respectively.Party1Sample Size: 200Favor:68Party2300110a. Manually test the claim that there is a difference in the proportion of peoplewho prefer Party1 compared to Party2. Use a 5% level of significance.b. Find the appropriate 95% confidence interval for the hypothesis test youperformed in part ‘a’.c. Calculate the p-value for the test in part ‘a’ above. What conclusion wouldyou draw?You found that the proportions were so close that as a reasonable analyst, youtook a larger sample and the following results were obtained.Party1Sample Size: 1600Favor:550Party22400900d. Now manually test the hypothesis that 1.0% more people prefer Party2 thanthey prefer Party1. Use a 5% level of significance.e. Find the appropriate 95% asymmetric confidence interval (CI) for the testperformed in part ‘d’ above. Is this CI consistent with the conclusion youreached in the hypothesis?Telfer School of ManagementUniversity of Ottawa3 ADM2304Assignment 2Fall 2015Question 5 (10 marks)All political parties seem to be wooing the "Middle Class". According to standardincome ranges for a family of four, the following data were obtained with a simplerandom sample. ‘Oi’ are the observed frequencies and ‘pi’ are the assumed proportions.Income_ClassIC1: Poor:IC2: Lower Middle_Class:IC3: Middle_Class:IC4: Upper Middle_Class:IC5: Affluent:IC6: Wealthy:Oi253580302010pi0.100.200.500.100.080.02a. Test if the data supports the assumed probabilities. Use the ‘critical value’approach.b. If a proposed change in tax law is going to benefit only families in the topthree income brackets, test the hypothesis that less than 36% of families willbenefit if the new change in the tax bill is passed and becomes law. Reachyour conclusion by calculating the p-value.c. What is the maximum percentage of families that will benefit from thisproposed tax law?Telfer School of ManagementUniversity of Ottawa4

ADM2304Assignment 2Fall 2015ADM2304Assignment 2 (85 marks)Due Date: Tuesday, November 3, 2015 by 23:59Please include your integrity statement.General Instructions:When you perform a test of hypothesis, you must always use the 4-step approach: i. S1:the “Null” and“Alternative” hypotheses, ii. S2: calculate value of the test statistic, iii. S3: the level of significance andthe critical value of the statistic, iv. S4: your decision rule and the conclusion reached in not rejecting orrejecting the null hypothesis. When asked to calculate p–value, S5, relate the p-value to the level ofsignificance in reaching your conclusion.If you use Minitab to perform the hypothesis test, you must cut and paste the relevant output into yourassignment. This output simply verifies and occasionally replaces the manual computation of the teststatistic, p-value or the confidence interval. You must supply all the required steps, mentioned above, tomake your testing procedure complete.If the confidence coefficient (CC) or the level of significance (LS) are not specified, assume the defaultvalues to be 95% and 5% respectively. Use precision level of only 4 Decimal Digits (DD) whencalculations are done with a calculator.Question 1 (20 marks)(Common Data for Questions #1 and #2)City_1City_2125.05137.56142.50145.95117.49142.75121.99117.49141.64128.69130.29142.39121.99141.30153.43133.39150.82136.69157.15147.05131.49131.79144.69161.55143.06159.60131.93119.55150.39The monthly cost of a prescription medication were checked in two major cities in twodifferent provinces. ‘City_1’ and ‘City_2’ give the costs incurred by patients at differentpharmacies in the two cities. The data is given above and the values are in dollars. Sincethe cities were in different provinces, you should assume that the population variancesare not equal.Telfer School of ManagementUniversity of Ottawa1 ADM2304Assignment 2Fall 2015a. Manually test the hypothesis using the critical value approach whether there is adifference in the mean medication costs in these two cities.b. Calculate the p-value. What conclusion would you draw?c. Calculate a confidence interval for the difference in mean costs? Is it consistentwith the conclusion reached in part ‘a’?Question 2 (10 marks)Use the same data given in Qu.#1.a. Now for the same data, test whether there is a difference in the median monthlycosts of medications in the two cities.b. Specify with appropriate diagrams and justify which test is more appropriate:the test in part ‘a’ of Qu.#1 or in part ‘a’ of Qu.#2? What are the names of thesetests?Question 3 (25 marks)In this question, Weight1(lbs) refers to the weight in lbs of a client randomly selected justbefore the client started a six-week dieting program and Weight2(lbs) refers to the weightof the same client after the program was over. .Data for Qu.#3Client_Num12345678910Weight1(lbs)165.6176.4162.0189.0181.8171.0198.0189.0172.8198.0Weight2(lbs)158.4165.6171.0171.0167.4174.6174.6176.4165.6178.2a. Manually test the hypothesis that the dieting program is effective. State yourhypotheses and use the ‘critical value’ approach. What is the name of this test?Explain why this test should or should not be used.b. What is the asymmetric confidence interval for the mean difference in theweights before and after the dieting program was over? Is it consistent with theconclusion reached in part ‘a’?c. Based on this asymmetric confidence interval in ‘b’ above, state how muchminimum mean weight could be lost, after completing the dieting program.d. Calculate the p-value for this test. What conclusion would you draw?e. Now for the same data, test the hypothesis that the median difference in weightsbefore and after the dieting program is positive. What is the name of this test?f. Specify with diagrams and justify which test would be more appropriate? (part‘a’ or part ‘e’). What are the names of these respective methodologies?Telfer School of ManagementUniversity of Ottawa2 ADM2304Assignment 2Fall 2015Question 4 (20 marks)With looming elections, polls with independent samples were taken to obtain thefollowing data concerning the number of people who favor two different majorpolitical parties, Party1 and Party2 respectively.Party1Sample Size: 200Favor:68Party2300110a. Manually test the claim that there is a difference in the proportion of peoplewho prefer Party1 compared to Party2. Use a 5% level of significance.b. Find the appropriate 95% confidence interval for the hypothesis test youperformed in part ‘a’.c. Calculate the p-value for the test in part ‘a’ above. What conclusion wouldyou draw?You found that the proportions were so close that as a reasonable analyst, youtook a larger sample and the following results were obtained.Party1Sample Size: 1600Favor:550Party22400900d. Now manually test the hypothesis that 1.0% more people prefer Party2 thanthey prefer Party1. Use a 5% level of significance.e. Find the appropriate 95% asymmetric confidence interval (CI) for the testperformed in part ‘d’ above. Is this CI consistent with the conclusion youreached in the hypothesis?Telfer School of ManagementUniversity of Ottawa3 ADM2304Assignment 2Fall 2015Question 5 (10 marks)All political parties seem to be wooing the "Middle Class". According to standardincome ranges for a family of four, the following data were obtained with a simplerandom sample. ‘Oi’ are the observed frequencies and ‘pi’ are the assumed proportions.Income_ClassIC1: Poor:IC2: Lower Middle_Class:IC3: Middle_Class:IC4: Upper Middle_Class:IC5: Affluent:IC6: Wealthy:Oi253580302010pi0.100.200.500.100.080.02a. Test if the data supports the assumed probabilities. Use the ‘critical value’approach.b. If a proposed change in tax law is going to benefit only families in the topthree income brackets, test the hypothesis that less than 36% of families willbenefit if the new change in the tax bill is passed and becomes law. Reachyour conclusion by calculating the p-value.c. What is the maximum percentage of families that will benefit from thisproposed tax law?Telfer School of ManagementUniversity of Ottawa4

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