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Department
Quantitative Methods
Course
QMS 202
Professor
Charles Barkley
Semester
Winter

Description
QMS 202 Review Exam Note: This is intended only as an example and may be quite different in content and structure from current exams. Question 1 (Marks 10) A management team is developing the critical path procedures for the production of a jet engine. The installation of the rotary fans is one of the more complicated steps in building the engine. The standard deviation for this installation is 3.0 hours. What size sample should be taken if they wish to be 99% confident that an estimate of the mean installation time is correct to within 2.5 hours? Question 2 ( Marks 10) In March of this year, just prior to the ''Academy Awards'' where the "best'' movie was honoured, a reporter in the Toronto Sun Newspaper wrote that, as far as the general public was concerned, different movies would be preferred by different age groups. A recent survey of Toronto residents included a request to identify their favourite movie released in 2000 and another about their age category. Using the cross tabulation of the poll results below determine if the Sun is correct. Age Movie < 20 20 to 34 35 to 50 50 to 65 > 65 Gladiator 30 50 20 10 6 Crouching Tiger,Sleeping Dragon 90 50 40 30 10 Traffic 40 30 10 10 5 Erin Brockovich 20 20 10 10 10 No Preference 15 10 0 5 5 Question 3 (Marks 5.5) Recently there was a study of the relative performance of Cable (tv cable;, Rogers etc.) vs ADSL (telephone; Bell etc.) access to the internet. A survey of 1000 internet users yielded the following table. Cable ADSL Neither # of internet users 400 450 150 Download (to a PC) Speed Average 1.3 meg/sec 1.4 meg/sec N/A Standard Deviation .4 meg/sec .3 meg/sec Upload (from a PC) Speed Average .4 meg/sec .08 meg/sec Standard Deviation .5 meg/sec .3 meg/sec # of internet users reporting at least one occurance 45 25 3 of disrupted service in the last week a] Is it reasonable to conclude that there is a significantly higher proportion of disruptions of service for Cable users than for ADSL users? b] On average, can one be sure that Cable Download speeds are significantly slower than ADSL Download speeds? Assume the speeds are normally distributed with equal variances. Question 4 (Marks 10) Purolator Fedex Vancover 6.1 days Vancover 5.8 Winnepeg 3.3 Winnepeg 2.1 Monteal 0.5 Monteal 0.7 Thunder Bay 2.9 Thunder Bay 1.9 Regina ** Regina 1.5 Edmonton 3.1 Edmonton 2.4 Calgary 2.1 Calgary 2.0 Saskatoon 2.3 Saskatoon 2.4 Quebec City 1.9 Quebec City 0.9 Halifax 3.0 Halifax ** Gateway sells Millions in computer parts on the Feb each year and ships within one day by courier either Peculator or Fedex . Gateway has been using these two different courier companies but is considering only using one - the service that is "fastest" on average. Last week Gateway used both services and kept track of the time: required by each service to deliver a randomly selected shipment to major cities from its central warehouse in Toronto. These times are listed on the table above. Test to determine if Fedex is "better" in terms of average shipping times than Purolator. Question 5 (Marks 10,5) Multiple Comparisons Dependent Variable: Absolute Value of the Difference Between the Customer's Price Estimate and the Actual Price ($000) Tukey HSD Mean Std. Sig. 95% Confidence Interval Differenc Error e (I-J) (I) Brands of (J) Brands of Lower Upper Competing Competing Bound Bound Automobiles Automobiles Chrysler GM -31.00 11.242 .048 -61.77 -.23 Toyota -31.00 11.781 .063 -63.24 1.24 Honda -53.75 10.821 .000 -83.36 -24.14 GM Chrysler 31.00 11.242 .048 .23 61.77 Toyota .00 12.692 1.00 -34.73 34.73 Honda -22.75 11.807 .241 -55.06 9.56 Toyota Chrysler 31.00 11.781 .063 -1.24 63.24 GM .00 12.692 1.00 -34.73 34.73 Honda -22.75 12.320 .274 -56.47 10.97 Honda Chrysler 53.75 10.821 .000 24.14 83.36 GM 22.75 11.807 .241 -9.56 55.06 Toyota 22.75 12.320 .274 -10.97 56.47 CHRYSLER GM TOYOTA HONDA 1 25 35 91 26 2 37 13 37 79 3 46 79 37 124 4 18 57 59 67 5 19 80 39 85 6 27 56 79 69 7 26 79 89 8 46 99 9 14 10 2 Since the recent slump in new car sales Ford of Canada believes potential customers (shoppers) are more sensitive to the prices of competing brands of new cars. Ford has randomly surveyed potential customers and asked each to indicate the Brand and price of one competing braid of automobile. The actual price was determined and absolute difference between the shoppers estimate and the actual price is reported above. a] Test to see if the average deference between the shoppers guess and the actual price is the same for all four competing brands. Use a = .05 . b] Is it appropriate to use the information provided in the 1st table above which was part of an SPSS output. If no, explain why. If yes, determine which of these competing brand(s), if any, that have prices which are significantly better or worse understood by shoppers? Question 6: ( Marks 5,5.3.2) A bottler of "Double Rum'' is attempting to understand how sales are influenced by the price of their product. To do this, the company randomly choose a small city and offered their rum at different prices in different weeks. Using rum sales per week as the dependent variable, the company conducted a simple linear regression on the data below: Week *Price($) **Sales 1 31.30 100 2 31.60 90 3 31.80 90 4 32.00 40 5 32.40 38 6 32.90 32 * price of a 750 ml bottle of ''Double Rum' ** bottles sold per week. a] What is the least squares linear regression model for predicting bottles sold/week based on the pice/bottle ? b] At
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