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MGMT 1000
Jean Adams

SCHULICH SCHOOL OF BUSINESS YORK UNIVERSITY SESSION: FALL 2006 Final Examination NAME: COURSE NO: OMIS1000 / OMIS2000 I.D. # : COURSE TITLE: Statistics for Management Decisions PROFESSORS: H. Cohen, O. Kaminer, A. Marshall, D. Nevo, S. Nevo NUMBER OF PAGES: 11 pages (NOT including this cover page) LENGTH OF EXAMINATION: 180 minutes (3 hours) EXAMINATION AIDS ALLOWED: Calculator; formula sheet supplied with text INSTRUCTIONS:  Please place your I.D. card on your desk.  Count the pages to be certain that there are no pages missing.  Write all and only your final answers in the space provided. We will not mark answers given elsewhere.  You are not allowed to use your own paper for rough work. You may only use the spaces on the exam.  Round all final answers to 4 decimal place.  You may assume that all populations described in this test are normally distributed.  If alpha is not given in the question use 0.05 You are not allowed to leave the examination room until one hour after the start of the exam and you must sign the sign-in sheet before leaving. Your examination paper must be handed in before you leave. When you are finished please leave the exam room quietly. Cheating on an examination will result in an “F” grade in this course and possible suspension from the University. Do not remove the staple from the exam. Do not write in the mark summary table below. Part I – Problem Recognition 24 marks Part II – True/False 17 marks Part III – Output Interpretation 12 marks Part IV – Problems Question 1 6 marks Question 2 12 marks Question 3 10 marks Question 4 9 marks Question 5 10 marks Sub-total 47 marks TOTAL 100 marks OMIS1000 / OMIS2000 Statistics Fall 2006 Final Examination Part I - Problem Recognition (24 marks, 3 marks each) Instructions: For each of the scenarios below, write the null and alternative hypotheses and indicate the most appropriate statistical test. You are not required to conduct the test, just choose the most suitable test from the following options: z test; t test; χ test; F test, ANOVA. Notes: (1) Be specific in your answers: specify the type of ANOVA required (one-way, randomized block, or two-way), or whether you use the t-test for equal variances or not; (2) When writing hypotheses for two population tests use meaningful indexing. For example, if the question asks to compare Canada and the US, write μ -μ as cppused to μ -μ ; (3) 1ri2e all relevant hypotheses for each of the questions. Hypotheses (H and H ): 1 A ski company in Whistler owns two ski shops, one near 0 A . Whistler and one near Blackcomb. The following data were collected from both stores: Whistler Blackcomb shop shop Mean sales $328 $435 Sample std. Dev. $104 $151 Sample size 35 days 30 days Test: The company would like to test for a difference in daily average goggle sales between the two stores Hypotheses (H a0d H ):A 2 The state lottery office claims that the average household . income of those people playing the lottery is greater than $37,000. They also know that the distribution of these households’ income is normal with a standard deviation of $5,756. To test their claim a sample of 25 households was studied. It was found that the average income in the sample was $36,243. Test: Hypotheses (H a0d H ):A 3 In random samples of 1000 people in the United States and . in France, 70% of the people in the Unites States and 75% of the people in France indicated that they were positive about the future economy. Does this provide strong evidence that the people in France are more optimistic about the economy? Test: Hypotheses (H a0d H ):A 4 The distributor of the post, a regional newspaper serving . North York is considering three types of dispensing machines or racks. Management wants to know if the different machines affect sales. These racks are designated as J-1000, D, and UV-57. Management also wants to know if the placement of the racks either inside or outside supermarkets affects sales. Each of six similar stores was randomly assigned a machine and location combination, and data were collected on the number of papers sold over four days. Test: Page 2 of 11 OMIS1000 / OMIS2000 Statistics Fall 2006 Final Examination 5 A pasta chef was experiencing difficulty in getting brands ofHypotheses (H 0nd H )A . pasta to be cooked just right. The main problem she experiences is with the speed of water absorption by the different pasta brands. Pasta with a faster rate of water absorption has a greater tendency to be overcooked. She decides to conduct an experiment in which two brands of pasta, one Canadian and one Italian, were cooked for either 4 or 8 minutes. The variable measured was the speed of water absorption in each case. The results were then recorded an analyzed. Test: Hypotheses (H 0nd H )A 6 A large milling machine produces steel rods to certain . specifications. The machine is considered to be running normally if the standard deviation of the diameter of the rods is 0.15 millimeters. As line supervisor, you need to test to see whether the machine is operating normally. You take a sample of 25 rods and find that the sample standard deviation is 0.19. Test: Hypotheses (H 0nd H )A 7 Are medical students more motivated than law students? A . randomly selected group of each were administered a survey of attitudes toward life, which measures motivation for upward mobility. The scores are summarized below (higher scores mean greater motivation). Medical Law Students Students Sample Size 250 100 Mean Score 83.5 80.2 Pop. Std. Dev. 11.2 9.2 Test: Hypotheses (H 0nd H )A 8. In a recent survey, college students were asked the amount of time (in hours) they spend weekly watching television and surfing on the Internet. The researchers were interested in determining whether the time spent on both activities was equal. They collected the following data: Person # 1 2 3 4 5 6 7 8 Internet 2 7 3 8 9 15 7 2 TV 4 15 5 3 4 4 4 8 Test: Page 3 of 11 OMIS1000 / OMIS2000 Statistics Fall 2006 Final Examination Part II – True/False (17 marks, 1 mark each) Instructions: Next to each question mark an “X” in the column for ‘True’ of ‘False’. True False 1. In a simple regression model, if the regression model is deemed to be statistically significant, it means that the regression slope coefficient is significantly greater than zero. 2. In a hypothesis test, the p-value measures the probability that the alternative hypothesis is true. 3. If a hypothesis test is conducted for a population mean where only non-negative values can be sampled, a null and alternative hypothesis of the form: H : μ0= 100, H : μ a ≠ 100, will result in a one-tailed hypothesis test since the statistic can only assume non- negative values. 4. Two variables have a correlation coefficient that is very close to zero. This means that there is probably no relationship between the two variables. 5. All other things held constant, increasing the level of confidence for a confidence interval estimate for the difference between two population means will result in a wider confidence interval estimate. 6. The method used in regression analysis for incorporating a categorical variable (no. of categories = 5) into the model is by organizing the categorical variable into five dummy variables. 7. In a recent one-way ANOVA test, Mean SSW was equal to 1,590 and the Mean SSB was equal to 310. Therefore, SST is equal to 1,900. 8. A local medical center has advertised that the mean wait for services will be less than 15 minutes (but more than 0 minutes). Given this claim, the hypothesis test for the population mean should be a one-tailed test with the rejection region in the lower (left- hand) tail of the sampling distribution. 9. Consider the following regression equation: ŷ = 356 + 18.0x – 1.5x . T2e x var1able is a quantitative variable and the x2variable is a dummy with values 1 and 0. Given this, we can interpret the slope coefficient on variable x 2s follows: holding x c1nstant, if the value of x2is changed from 1 to 0, the average value of y will increase by 2.5 units. 10.The coefficient of determination measures the percentage of variation in the independent variable that is explained by the dependent variables in the model. 11. A perfect correlation between two variables will always produce a correlation coefficient of +1.0. 12.The prediction interval developed from a simple linear regression model will be at its narrowest point when the value of x used to predict y is equal to the mean value of x. 13. When testing a hypothesis about the variability of a population, the statistical requirements call for us to convert the variance to standard deviation and run a chi- square test. 14. When the expected cell frequencies are smaller than 30, the cells should be combined in a meaningful way such that the expected cell frequencies do exceed 30. 15. If it is known that a simple linear regression model explains 56 percent of the variation in the dependent variable and that the slope on the regression equation is negative, then we also know that the correlation between x and y is approximately (- 0.75). 16.In estimating the difference between two population means, if a 95 percent confidence interval includes zero, than we can conclude that there is a 95 percent chance that the difference between the two population means is zero. 17. In a multiple regression analysis, even if only some of the independent variables have values equal to zero, the regression intercept, b ,0can
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