ADM2304 Assignment 2 Fall 2015 ADM2304 Assignment 2 (85 marks) Due Date: Tuesday, November 3, 2015 by 23:59 Please 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 and the critical value of the statistic, iv. S4: your decision rule and the conclusion reached in not rejecting or rejecting the null hypothesis. When asked to calculate p-value, S5, relate the p-value to the level of significance in reaching your conclusion. If you use Minitab to perform the hypothesis test, you must cut and paste the relevant output into your assignment. This output simply verifies and occasionally replaces the manual computation of the test statistic, p-value or the confidence interval. You must supply all the required steps, mentioned above, to make your testing procedure complete. If the confidence coefficient (CC) or the level of significance (LS) are not specified, assume the default values to be 95% and 5% respectively. Use precision level of only 4 Decimal Digits (DD) when calculations are done with a calculator. Question 1 (20 marks) (Common Data for Questions #1 and #2) City_1 City_2 125.05 137.56 142.50 145.95 117.49 142.75 121.99 117.49 141.64 128.69 130.29 142.39 121.99 141.30 153.43 133.39 150.82 136.69 157.15 147.05 131.49 131.79 144.69 161.55 143.06 159.60 131.93 119.55 150.39 The monthly cost of a prescription medication were checked in two major cities in two different provinces. 'City_1' and 'City_2' give the costs incurred by patients at different pharmacies in the two cities. The data is given above and the values are in dollars. Since the cities were in different provinces, you should assume that the population variances are not equal. Telfer School of Management University of Ottawa 1 ADM2304 Assignment 2 Fall 2015 a. Manually test the hypothesis using the critical value approach whether there is a difference 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 consistent with 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 monthly costs 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 these tests? Question 3 (25 marks) In this question, Weight1(lbs) refers to the weight in lbs of a client randomly selected just before the client started a six-week dieting program and Weight2(lbs) refers to the weight of the same client after the program was over. . Data for Qu.#3 Client_Num 1 2 3 4 5 6 7 8 9 10 Weight1(lbs) 165.6 176.4 162.0 189.0 181.8 171.0 198.0 189.0 172.8 198.0 Weight2(lbs) 158.4 165.6 171.0 171.0 167.4 174.6 174.6 176.4 165.6 178.2 a. Manually test the hypothesis that the dieting program is effective. State your hypotheses 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 the weights before and after the dieting program was over? Is it consistent with the conclusion reached in part 'a'? c. Based on this asymmetric confidence interval in 'b' above, state how much minimum 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 weights before 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 Management University of Ottawa 2 ADM2304 Assignment 2 Fall 2015 Question 4 (20 marks) With looming elections, polls with independent samples were taken to obtain the following data concerning the number of people who favor two different major political parties, Party1 and Party2 respectively. Party1 Sample Size: 200 Favor: 68 Party2 300 110 a. Manually test the claim that there is a difference in the proportion of people who prefer Party1 compared to Party2. Use a 5% level of significance. b. Find the appropriate 95% confidence interval for the hypothesis test you performed in part 'a'. c. Calculate the p-value for the test in part 'a' above. What conclusion would you draw? You found that the proportions were so close that as a reasonable analyst, you took a larger sample and the following results were obtained. Party1 Sample Size: 1600 Favor: 550 Party2 2400 900 d. Now manually test the hypothesis that 1.0% more people prefer Party2 than they prefer Party1. Use a 5% level of significance. e. Find the appropriate 95% asymmetric confidence interval (CI) for the test performed in part 'd' above. Is this CI consistent with the conclusion you reached in the hypothesis? Telfer School of Management University of Ottawa 3 ADM2304 Assignment 2 Fall 2015 Question 5 (10 marks) All political parties seem to be wooing the "Middle Class". According to standard income ranges for a family of four, the following data were obtained with a simple random sample. 'Oi' are the observed frequencies and 'pi' are the assumed proportions. Income_Class IC1: Poor: IC2: Lower Middle_Class: IC3: Middle_Class: IC4: Upper Middle_Class: IC5: Affluent: IC6: Wealthy: Oi 25 35 80 30 20 10 pi 0.10 0.20 0.50 0.10 0.08 0.02 a. 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 top three income brackets, test the hypothesis that less than 36% of families will benefit if the new change in the tax bill is passed and becomes law. Reach your conclusion by calculating the p-value. c. What is the maximum percentage of families that will benefit from this proposed tax law? Telfer School of Management University of Ottawa 4