252x0731 4 6 07 ECO252 QBA2 THIRD EXAM April 16 2007 TAKE HOME SECTION Name Student Number Class days and time Please Note Computer problems 2 and 3 should be turned in with the exam 2 In problem 2 the 2 way ANOVA table should be checked The three F tests should be done with a 5 significance level and you should note whether there was i a significant difference between drivers ii a significant difference between cars and iii significant interaction In problem 3 you should show on your third graph where the regression line is Check what your text says about normal probability plots and analyze the plot you did Explain the results of the t and F tests using a 5 significance level 2 III Do the following 20 points Note Look at 252thngs 252thngs on the syllabus supplement part of the website before you start and before you take exams Show your work State H 0 and H 1 where appropriate You have not done a hypothesis test unless you have stated your hypotheses run the numbers and stated your conclusion Use a 95 confidence level unless another level is specified Answers without reasons or accompanying calculations usually are not acceptable Neatness and clarity of explanation are expected This must be turned in when you take the in class exam Note that from now on neatness means paper neatly trimmed on the left side if it has been torn multiple pages stapled and paper written on only one side 1 Ken Black A national travel organization wanted to determine whether there is a significant difference between the cost of premium gas in various regions of the country The following data was gathered in July 2006 Because the brand of gas may confuse the results data is blocked by brand Data Display Row 1 2 3 4 5 6 Brand A B C D E F City 1 3 47 3 43 3 44 3 46 3 46 3 44 City 2 3 40 3 41 3 41 3 45 3 40 3 43 City 3 3 38 3 42 3 43 3 40 3 39 3 42 City 4 3 32 3 35 3 36 3 30 3 39 3 39 City 5 3 50 3 44 3 45 3 45 3 48 3 49 a Mark your problem VERSION a is 1 through 4 add a to the city 4 column If 100 To personalize these data let the last digit of your student number be a If a is zero use the original numbers If a is 5 through 9 add 0 04 a so he adds 0 04 9 100 100 05 to the city 5 column Example Seymour Butz number is 090909 to column 5 subtracts 05 and gets the table below Version 9 Row 1 2 3 4 5 6 Brand A B C D E F City 1 3 47 3 43 3 44 3 46 3 46 3 44 City 2 3 40 3 41 3 41 3 45 3 40 3 43 City 3 3 38 3 42 3 43 3 40 3 39 3 42 City 4 3 32 3 35 3 36 3 30 3 39 3 39 City 5 3 45 3 39 3 40 3 40 3 43 3 44 a Do a 2 way ANOVA on these data and explain what hypotheses you test and what the conclusions are Show your work 6 b Using your results from a present two different confidence intervals for the difference between numbers of defects for the best and worst worker and for the defects from the best and second best times Explain which of the intervals show a significant difference and why 3 1 252x0731 4 6 07 c What other method could we use on these data to see if city makes a difference while allowing for crossclassification Under what circumstances would we use it Try it and tell what it tests and what it shows 3 d Extra credit Check you results on the computer The Minitab setup for both 2 way ANOVA and the corresponding non parametric method is the same as the extra credit in the third graded assignment or the third computer problem You may want to use and compare the Statistics pull down menu and ANOVA or Nonparametrics to start with Explain your results 4 12 2 A local official wants to know how land value affects home price The official collects the following data Home price is the dependent variable and Land Value is the independent variable Both are in thousands of dollars If you don t know what dependent and independent variables are stop work until you find out Row 1 2 3 4 5 6 7 8 9 10 HomePr 67 63 60 54 58 36 76 87 89 92 LandVal 7 0 6 9 5 5 3 7 5 9 3 8 8 9 9 6 9 9 10 0 To personalize the data let g be the second to last digit in your student number Mark your problem VERSION g Subtract g from 92 which is the last home price a Compute the regression equation Y b b x to predict the home price on the basis of land value 0 1 3 You may check your results on the computer but let me see real or simulated hand calculations b Compute R 2 2 c Compute s e 2 d Compute s b0 and do a significance test on b0 2 e Use your equation to predict the price of the average home that is on land worth 9000 Make this into a 95 interval 3 f Make a graph of the data Show the trend line and the data points clearly If you are not willing to do this neatly and accurately don t bother 2 26 3 A sales manager is trying to find out what method of payment works best Salespersons are randomly assigned to payment by commission salary or bonus Data for units sold in a week is below Row 1 2 3 4 5 6 7 8 9 10 11 12 13 Commission 25 35 20 30 25 30 26 17 31 30 Salary 25 25 22 20 25 23 22 25 20 26 24 Bonus 28 41 21 31 26 26 46 32 27 35 23 22 26 To personalize the data let g be the second to last digit in your student number Subtract 2 g from 46 in the last column Mark your problem VERSION g Example Payme Well s student number is 000090 so she subtracts 18 and gets the following numbers 2 252x0731 4 6 07 Version 9 Row 1 2 3 4 5 6 7 8 9 10 11 12 13 Commission 25 35 20 30 25 30 26 17 31 30 Salary 25 25 22 20 25 23 22 25 20 26 24 Bonus 28 41 21 31 26 26 28 32 27 35 23 22 26 a State your null hypothesis and test it by doing a 1 way ANOVA on these data and explain whether the test tells us that …
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