252x0631 11/15/06 ECO252 QBA2THIRD EXAMNov 30and Dec 1, 2006TAKE 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. 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. Because so much of this exam is based on student numbers, there is a penalty for failing to state your correct student number.1) Bassett et al. give the following numbers for the year and the number of pensioners in the United Kingdom. Pensioners are in millions. The 2000 number is a bit shaky, so subtract the last digit of your student number divided by 10 from the 12.00 that you see there. Label your answer to this problem with a version number. (Example: Good ol’ Seymour’s student number is 123456, so the 12.000 becomes 12.000 - 0.6 = 11.400 and he labels it Version 6.) 'Pensioners' is the dependent variable and 'Year' is the independent variable, so what you are going to get is a trend line. If you don’t know what dependent and independent variables are, stop work until you find out. Year Pensioners 1 1966 6.679 2 1971 7.677 3 1975 8.321 4 1976 8.510 5 1977 8.637 6 1978 8.785 7 1979 8.937 8 2000 12.000Bassett et. al. strongly suggest that you change the base year to something other than the year zero. They recommend that you subtract 1970 from every number in the ‘Year’ column, so that 1966 becomes -4 and 2000 becomes 30. This will make your computations easier.a. Compute the regression equation Y b b x 0 1to predict the number of pensioners in each year. (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 1bs and do a significance test on 1b(2)e. Use your equation to predict the number of pensioners in 2005 and 2006. Using the 2006 number, create a prediction interval for the number of pensioners for that year. Explain why a confidence interval for the number of pensioners is inappropriate. (3)f. Make a graph of the data. Show the trend line clearly. If you are not willing to do this neatly and accurately, don’t bother. (2)1252x0631 11/15/06 g. What percent rise in pensioners did the equation predict for 2006? What percent rise does it predict for 2050? The population of the United Kingdom grew at roughly 0.31% a year over the last quarter of the 20th century. Can you intelligently guess what is wrong? (1) [15]2) The Lees in their text ask whether experience makes a difference in student earnings and present the following data for student earnings versus years of work experience. To personalize these data, take the second to last digit of your student number call it a. Clearly label the problem with a version number based on your student number. Then take your a, multiply it by 0.5 and add it to the 13 in the lower left corner. . (Example: Good ol’ Seymour’s student number is 123456, so the 13 becomes 13 + 0.5(5) = 13 + 2.5 = 15.5 and he labels it Version 5.) Each column is to be regarded as an independent random sample. Years of Work Experience 1 2 3 16 19 24 21 20 21 18 21 22 13 20 25 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 experience matters or not. (4)b) Using your results from a) present two different confidence intervals for the difference between earnings for those with 1 and 3 years experience. Explain (i) under what circumstances you would use each interval and (ii) whether the intervals show a significant difference. (2)b) What other method could we use on these data to see if years of experience make a difference? Under what circumstances would we use it? Try it and tell what it tests and what it shows. (3) [24]c) (Extra Credit) Do a Levene test on these data and explain what it tests and shows. (4) 3) (Abronovic) A group of 4 workers produces defective pieces at the rates shown below during different times of the day. Personalize the data by subtracting the last digit of your student number from the 14 in the lower right corner. Use the number subtracted to label this as a version number. (Example: Good ol’ Seymour’s student number is 123456, so the 13 becomes 14 - 6 =8 and he labels it Version 8.) Time Worker’s NameApple Plum Pear MelonEarly Morning10 11 8 12Late Morning9 8 7 10Early Afternoon12 13 11 11Late Afternoon13 14 10 14Sum of Row 1 = 41, SSQ of Row 1 = 429, Sum of Column 1 = 44, SSQ of Column 1 = 494,Sum of Row 2 = 34, SSQ of Row 2 = 294, Sum of Column 2 = 46, SSQ of Column 2 = 550,Sum of Row 3 = 47, SSQ of Row 3 = 555, Sum of Column 3 = 36, SSQ of Column 3 = 334,a) Do a 2-way ANOVA on these data and explain what hypotheses you test and what the conclusions are. (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)c) What other method could we use on these data to see if years of experience make a difference while allowing for
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