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WCU ECO 252 - ECO 252 Third Exam

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252x0731 4/6/07 ECO252 QBA2THIRD EXAMApril 16, 2007TAKE 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 0H and 1H 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 Brand City 1 City 2 City 3 City 4 City 5 1 A 3.47 3.40 3.38 3.32 3.50 2 B 3.43 3.41 3.42 3.35 3.44 3 C 3.44 3.41 3.43 3.36 3.45 4 D 3.46 3.45 3.40 3.30 3.45 5 E 3.46 3.40 3.39 3.39 3.48 6 F 3.44 3.43 3.42 3.39 3.49To personalize these data, let the last digit of your student number be a. Mark your problem ‘VERSIONa.’ If a is zero, use the original numbers. If a is 1 through 4, add 100a to the city 4 column. Ifais 5 through 9, add 10004.0ato the city 5 column. Example: Seymour Butz’ number is 090909, so he adds 05.100904.0  to column 5 (subtracts .05) and gets the table below.Version 9Row Brand City 1 City 2 City 3 City 4 City 5 1 A 3.47 3.40 3.38 3.32 3.45 2 B 3.43 3.41 3.42 3.35 3.39 3 C 3.44 3.41 3.43 3.36 3.40 4 D 3.46 3.45 3.40 3.30 3.40 5 E 3.46 3.40 3.39 3.39 3.43 6 F 3.44 3.43 3.42 3.39 3.44a) 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)1252x0731 4/6/07 c) What other method could we use on these data to see if city makes a difference while allowing for cross-classification? 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 thethird 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 HomePr LandVal 1 67 7.0 2 63 6.9 3 60 5.5 4 54 3.7 5 58 5.9 6 36 3.8 7 76 8.9 8 87 9.6 9 89 9.9 10 92 10.0To 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 0 1to predict the home price on the basis of land value. (3).You may check your results on the computer, but let me see real or simulated hand calculations.b) ComputeR2. (2)c) Compute se. (2)d) Compute 0bs and do a significance test on 0b(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 Commission Salary Bonus 1 25 25 28 2 35 25 41 3 20 22 21 4 30 20 31 5 25 25 26 6 30 23 26 7 26 22 46 8 17 25 32 9 31 20 27 10 30 26 35 11 24 23 12 22 13 26To personalize the data let g be the second to last digit in your student number. Subtract g2 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. 2252x0731 4/6/07 Version 9Row Commission Salary Bonus 1 25 25 28 2 35 25 41 3 20 22 21 4 30 20 31 5 25 25 26 6 30 23 26 7 26 22 28 8 17 25 32 9 31 20 27 10 30 26 35 11 24 23 12 22 13 26a) State your null hypothesis and test it by doing a 1-way ANOVA on these data and explain whether the test tells us that payment method matters or not. (4)b) Using your results from a) present individual and Tukey intervals for the difference between earnings for all three possible contrasts. Explain (i) under what circumstances you would use each interval and (ii) whether the intervals show a significant difference. (2)c) What other method could we use on


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