ADM2304X Assignment#2 Spring-Summer 2017 ADM2304X Prof.: Dr. Suren Phansalker Assignment#2 (100 Marks) 1. Due Date & Time: Must be Uploaded by Sunday, June 11, 2017 by 23:30 hrs. 2. Integrity Statement: Must be Printed/ Signed and Attached. General Instructions: When you perform a test of hypothesis, you must always use the 4-step approach: i. S1:the \"Null\" and \"Alternate\" hypotheses, ii. S2: manually calculate value of the test statistic, iii. S3: specify the level of significance and the critical value of the statistic, iv. S5: use appropriate decision rule and then reach a conclusion about not rejecting or rejecting the null hypothesis. S5: If asked to calculate p-value,do so and relate the p-value to the level of significance in reaching your conclusion. If you use MiniTab to perform the hypothesis test, you must 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 standard and complete. If Confidence Coefficient (CC) and Level of Significance (LS) are not specified, assume the default values of 95% and 5% respectively. Use precision level of only 4 Decimal Digits (DD) and no more or no less, when calculations are done with a calculator. Please Note: Assignment#2 is posted on Brightspace and must be uploaded to Brightspace in the '.pdf' format before the Due Date & Time . Question#1(25 marks) Sample_BMI 34.74 31.95 30.34 16.79 38.57 33.55 25.29 26.70 26.49 30.98 22.12 22.28 29.73 33.18 25.63 20.78 24.14 29.35 26.15 23.56 30.45 28.49 22.35 28.58 22.11 a. A sample of size 25 has already been drawn and given above. This column is named 'Sample_BMI'. Calculate manually and find a 95% confidence interval for this population BMI. Explain what it means? b. Based on the data in 'Sample_BMI', test the hypothesis that the population mean is less than 29.50. Use a level of significance of 5%. c. Calculate the appropriate asymmetrical confidence interval or bound for the the test you performed in part 'b'. Explain if this calculated bound is consistent with the conclusion you reached in your test. d. You want to estimate the average BMI of the population. If you want to calculate a 98% confidence interval with a margin of error of 0.75 units of BMI, what sample size would you recommend? Assume for this subquestion in part 'd', that the population standard deviation of BMI is 6.0 units. Dr. Suren Phansalker Telfer School of Management 1 University of Ottawa ADM2304X Question#2 Assignment#2 Spring-Summer 2017 (20 Marks) : Common Data for Qu.#2 and Qu.#3. RE-Agenc1 RE-Agenc2 2652 2820 2592 3024 2904 2736 3168 3024 2772 3180 2532 2664 2736 2760 2676 2820 3180 2820 2652 2856 3150 2790 Two Real Estate Agencies, RE-Agenc1 and RE-Agenc2 evaluated properties chosen with two independent random samples of income properties. The evaluation data is given above and the values are in thousands of dollars. Assume unequal population variances when doing this question #1. a. Test the hypothesis that there is no difference in the mean values of evaluations of the two real estate agencies. Use the 'Critical Value' approach. b. Calculate the p-Value for this test. What conclusion would you draw? c. Calculate the Confidence Interval for the difference in mean values of evaluation? Is it consistent with the conclusion reached in part 'a'? Question#3 (30 Marks) Use the same data given in Qu.#2. But now assume equal population variances. a. Test the hypothesis that there is no difference in the mean values of evaluations of the two real estate agencies. Use the 'Critical Value' approach. b. Calculate the p-Value for this test. What conclusion would you draw? c. Calculate the Confidence Interval for the difference in mean values of evaluation? Is it consistent with the conclusion reached in part 'a'? d. Equal population variance or unequal population variance: how do you make the choice? Explain in brief. e. Now for the same data, Test the hypothesis that there is no difference in the median values of evaluations of the two agencies. What is the name of this test? f. Specify with appropriate diagrams and justify which methodology would be more appropriate: methodology used in part 'a' of Qu.#1 or in part 'd' of Qu.#2? What are the names of these respective tests and their methodologies? Dr. Suren Phansalker Telfer School of Management 2 University of Ottawa ADM2304X Assignment#2 Spring-Summer 2017 Qu.#4 (30 Marks) In this Question, Value1K$ refers the value of randomly selected properties listed in year 2015 and Value2K$ refers the values of the same properties listed in year 2016. All the values are in thousands of dollars. Data for Qu.#4 Property# 1 2 3 4 5 6 7 8 9 10 Value1$K 1584 1656 1710 1710 1674 1746 1746 1764 1656 1782 Value2$K 1656 1764 1620 1890 1818 1710 1980 1890 1728 1980 a. Test the hypothesis that the mean of the difference in the listed values of the properties in the two years is non-existent. What is the name of this test? Explain why this test is the appropriate test. b. What is the Confidence Interval for the mean of the difference in the values of the properties in the two years? Is it consistent with the conclusion reached in part 'a'? c. Based on this Confidence Interval in 'b' above, state how much more or less, is the mean of the difference in values for years 2016 and 2015. Calculate the percentage changes in the 'minimum', 'maximum' and 'mean' values of the properties in the in the year 2016 compared to year 2015. 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 value of the difference in values in the two years is non-existent. What is the name of this test? f. Specify with diagrams and justify which methodology would be more appropriate? Methodology used in part 'a' or in part 'e'. What are the names of these respective methodologies? N.B. Although the Due Date for uploading this Assignment is June 11, 2017, please complete most of it before your Mid-Term Exam and then, upload it in time after the Mid-Term if you so choose. It will be an excellent practice and preparation for part of what you are responsible for the Mid-Term Exam. Dr. Suren Phansalker Telfer School of Management 3 University of Ottawa