SIMON FRASER UNIVERSITY

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1 SIMON FRASER UNIVERSITY BUEC 333: Statistics for Business and Economics. MIDTERM EXAM: PART I Instructor: Alex Jameson Appiah February. 27, Time: 50 mins. Name: St. Number # TA s Name/Tut Signature Instructions: Students must attempt all questions on this Exam. This is Exam is worth 50 points. Do not write below this line Question No. Maximum Marks Marks Obtained TOTAL 50

2 1. [8 pts.] You are a consultant for Simpleman Company. The company does business in both Canada and the US. Last year, sales averaged $100,000 per month in Canada and $250,000 in the US. The CEO suspects that business in Canada has been slipping in the past two months. (a).[2 pts.] State the null and alternative hypotheses to test the CEO s suspicion. (b). [2 pts. each] In three short sentences, show how you will conduct a formal test whether or not the suspicion of the CEO is justified. 2. [2 pts.] Ford Motor Company would like to compare sales from two different locations in Vancouver. Sales are recorded for a 20-month period in one location and then sales are recorded for another 20-month period for the other location. For this comparison, the appropriate method is (a). the paired t-test. (b). the independent t-test. (c). the F- test for difference between variances. (d). the Spearman s Rank correlation. 3. [3 pts.] If a null hypothesis is not rejected, then it is true. [1 pt.] G True or G False [2 pts.] Explain. 4. [5 pts.] In testing H o: µ = 20 against H 1: µ 20, we can calculate a single value of α for a given critical region and sample size, but we can not calculate a single value of β. [1 pt.] G True or G False [2 pts.] Explain.

3 5.. [3 pts.] All else equal, the closer the hypothesized mean is to the true mean, the greater is the power of the test. [1 pt.] G True or G False? [2 pts.] Explain. 6.[4 pts.] Your company is considering opening a new branch in Ghana. Ghana is a virgin market so the company wants to conduct a pilot study to assess the profitability of the Ghanaian market. (a).[2 pts.] Formulate the appropriate null and alternative hypotheses for testing the profitability of the Ghanaian market. (b). [2 pts.] State the possible Type I and Type II errors for this particular problem. 7. [3 pts.] (a). [2 pts.] Clearly distinguish between Cov(X,Y) and Corr(X,Y). (b). [1 pt.] What is/are the limitation(s) (if any) of any one of them.

4 8. [4 pts.] Explain (briefly) the following properties of regression coefficients: (a). [2 pts.] unbiased (b). [3 pts.] best 9. [3 pts.] A consumer group has complained that there are more defectives in Extralite light bulbs than claimed by the manufacturer. The company has rejected this claim, and insists that Extralite has an average life of 1000 hours. The company has consulted you for a formal test. If you are biased towards the company will you choose a small or large level of significance? Explain. 10. [2 pts.] Dave regressed Y on X (using Y as a dependent variable and X as an independent variable) and obtained a slope estimate, b, of Alex used the same data regressed X on Y. What will be Alex s slope estimate? 11. [3 pts.] Y Y = a + bx i

5 In the diagram above, show the following: (i). explained variability in Y; (ii). total variability in Y. (iii). unexplained variation. 12. [4 pts.] (a). [2 pts.] The t tests on β = 0 and ρ = 0 should yield the same result. Why? X (b). [2 pts.] Why do we not calculate the sample correlation between X and Y when X is a constant? 13. [3 pts.] What is the rationale behind the method of least squares?. 14. [3 pts]. In three very short sentences, explain the importance of regression analysis in business and economics. 15. [3 pts.] What is the importance of the Gauss-Markov theorem in regression analysis?

6 SIMON FRASER UNIVERSITY BUEC 333: Statistics for Business and Economics. MIDTERM EXAM: PART II Instructor: Alex Jameson Appiah February. 29, Time: 50 mins. Name: St. Number # TA s Name/Tut Signature Instructions: Students must attempt all questions. The is Exam is worth 50 pts. Do not write below this line Question No. Maximum Marks Marks Obtained TOTAL 50

7 1. [9 pts.] The manager of Simpleman Bookstore believes that the average daily credit allowance has increased over the past few months. The previous mean daily credit given was $32. A random sample of 12 accounts was taken and the sample mean was found to be $39.57, with a sample standard deviation of $ Has the manager grounds to believe that the mean daily limit has increased? Test this at the 5% level of significance. 2. [9 pts.] At the instance of a government inspector, a new safety device is installed in an assembly-line operation. After the installation of this device, a random sample of eight days output gave the following results for numbers of finished components produced: Management is concerned about the variability of daily output and views as undesirable any variance above 500. Test at the 10% significance level the null hypothesis that the population variance for daily output does not exceed 500.

8 3. [9 pts.] Of a random sample of 199 audit partners in Canadian accounting firms, 104 indicated some measure of agreement with the statement: Cash flow from operations is a valid measure of profitability. Test at the 10% level of significance against a two-sided alternative the null hypothesis that one-half of the members of this population would agree with this statement. 4. [9 pts.] Of a random sample of 200 cars manufactured by Ford, 28 needed an engine overhaul before reaching 100,000 miles. A second sample, obtained independent of the first, consisted of 150 cars produced by GM; 48 of them required an engine overhaul before 100,000 miles. Both sets of cars were subjected to the same weather conditions, maintenance program and driving conditions. Determine whether there is any difference between the proportion of Ford cars and GM cars that required an engine overhaul before 100,000 miles.

9 5. [14 pts.] The Table below shows Unemployment Rate and Average Family Income in Province Unemploy- Average Family ment Rate Income ($000) (%) Newfoundland Prince Edward Island Nova Scotia New Brunswick Quebec Ontario Manitoba Saskatchewan Alberta British Columbia Let x = unemployment rate, and y = average family income. The following calculations can be made from the table: = ; = 12,508.5; = ; SSE = 84.1 (a). [2 pts.] Find the correlation coefficient r and interpret it.

10 (b). [4 pts.] Find the least squares regression equation. Interpret the estimates a and b. 2 (c). [4 pts.] Find the Coefficient of Determination (R ). Interpret it.

11 (d). [4 pts.] Test the hypothesis that the slope parameter is zero against the one-sided alternative that it negative.

12 SIMON FRASER UNIVERSITY BUEC 333: Statistics for Business and Economics. MIDTERM EXAM: PART II Instructor: Alex Jameson Appiah March 7, Time: 50 mins. Name: St. Number # TA s Name/Tut Signature Instructions: Students must attempt all questions. The is Exam is worth 50 pts. All questions carry equal marks. Do not write below this line Question No. Maximum Marks Marks Obtained TOTAL 50

13 1. [9 pts.] The average distance for stopping a certain make of automobile while it is traveling 30 miles an hour is 60 feet. The engineering department of the company has designed a new brake system thought to be more effective. To test this invention, the new brake system is installed in 64 cars; tests show that the average distance for stopping a car at a speed of 30 miles an hour is 53.5 feet, with standard deviation of 4 feet. Does the difference of 6.5 feet indicate that the new brake system is more effective than the old? Use α = [9 pts.] The federal government wishes to determine whether there is a regional difference in the patronage of CBC television programs. Ontario and B.C. were chosen as representatives of the East and West. A sample of 1,500 families was taken from BC out which 232 families were found to be patronizing CBC programs on one day. Another sample of 2,500 families were taken from Ontario out of which 252 families patronized the programs on the same day. In view of these findings, can we conclude that there is a regional difference in the patronage of CBC? Use α of 0.05.

14 3. [9 pts.] Simpleman Dog Chow comes in 10-, 25-, and 50-pound bags. The owners are concerned about the variation in the weight of the 50-pound bags because they have recently acquired a new mechanical packaging device. A random sample of the weights of 15 bags (in pounds) was obtained, with the following results: 51.2, 47.5, 50.8, 51.5, 49.5, 51.1, 51.3, 50.7, 46.7, 49.2, 52.1, 48.3, 51.6, 49.2, 51.5 Test the null hypothesis that the variation in the weight of all Dow Chow bags from Simpleman is at most [9 pts.] A survey of practicing certified public accountants on attitudes to women in the profession was carried out. Survey respondents were asked to react on a scale from one (strongly disagree) to five (strongly agree) to the statement: Women in public accounting are given the same job assignments as men. For a sample of 186 male accountants, the mean response was and the sample standard deviation was.839. For an independent random sample of 172 female accountants, the mean respondents the mean response was 3.68 and the sample standard deviation was.966. Test, at the 1% significance level, the null hypothesis that the two population means are equal against the alternative that the true mean is higher for male accountants.

15 5. [14 pts.] The Table below shows data on Average Family Income and Square footage of Homes for ten families in Simpleland. Average Square Footage Family Income (in hundreds of ($000) square feet) Let x = average family income, and y = square footage. The following calculations can be made from the table: = 17,330; = 5,370; = 9,522 SSE = (a). [2 pts.] Find the correlation coefficient r and interpret it.

16 (b). [4 pts.] Find the least squares regression equation. Interpret the estimates a and b. 2 (c). [4 pts.] Find the Coefficient of Determination (R ). Interpret it.

17 (d). [4 pts.] Test the hypothesis that the slope parameter is zero against the one-sided alternative that it negative.