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Name: Statistics Davidson College Economics 105, Aug - Dec 2005 Mark C. Foley
Review # 3
Due in Ch. 3140 by 4 p.m. Tuesday. Directions : This review is untimed, closed-book, closed-notes (except for your formula sheet). You should use Excel to do your work (and thus rounding will not be necessary), but you may also use a calculator. Report all final answers to 5 decimal places, unless otherwise directed, and don’t round, just report the 5 decimal places you see in Excel. Remember to write out the formulas and fill in their parts by copying values from your Excel worksheet. There are 100 points on the exam. Each problem is worth 20 points. You must show all your work to receive full credit. Any assumptions you make and intermediate steps should be clearly indicated. Do not simply write down a final answer to the problems without an explanation. Please turn in your formula sheet with your exam. Honor Pledge Start times End times
Problem 1 An unnamed bank in Charlotte is interested in determining whether a relationship exists between commuting time of its employees and the level of stress they feel. A sample of 116 employees were surveyed. There is a copy of this data in the file P:\Economics\Eco 105 (Statistics)\ exam3_data.xls on the worksheet labeled “Problem 1.” Stress Level Commuting time High Moderate Low Under 15 minutes 9 5 18 15 - 45 minutes 17 8 28 Over 45 minutes 18 6 7 (a) Is there evidence of a significant relationship between commuting time and stress level at the 1% level? Conduct the test on the test statistic scale. Report the test statistic and critical values to 5 decimal places. (Numbers leading up to those need not be reported so precisely, but you should use Excel to do your calculations to avoid rounding.) (b) What is the p-value for the test in part (a)? Report 5 decimal places.
(c) Clearly evaluate the regression model’s goodness of fit according to R^2 (coefficient of determination) and the standard error of the model. Again, you may use Excel to check, but write down formulas and show the values that make up each formula. (d) Calculate and interpret a 93% confidence interval for the population slope parameter. Report 5 decimal places. Again, you may use Excel to check, but write down formulas and show me the values that make up each formula. (e) Use the confidence interval in part (e) to test, at the 7% significance level, the hypothesis that the effect of Weight on Miles per Gallon is different from 0.
Problem 3 Answer the following using the same data and regression as in Problem 2. (a) Calculate the standard error for the estimated slope coefficient. Report 5 decimal places. Again, you may use Excel to check, but write down formulas and show the values that make up each formula. (b) Use a t-test to test at the 5% level whether there is evidence of a negative effect of Weight on Miles per Gallon. Write down the null and alternative hypotheses. Conduct your test by
comparing the p-value to^ ^. Report the p-value to 5 decimal places.
Again, you may use Excel to check, but write down formulas and show the values that make up each formula. (c) Calculate the 95% confidence interval for the average Miles per Gallon for cars weighing 4,000 pounds. Again, you may use Excel to check, but write down formulas and show the values that make up each formula. (d) Without doing further calculations, would the 95% confidence interval for the average Miles per Gallon for cars weighing 3,800 pounds be narrower or wider? Explain.
Problem 5 Consider the sample data on 121 cars in the file P:\Economics\Eco 105 (Statistics)
exam3_data.xls, on the worksheet labeled “Problem 5.” (a) Estimate the following regression, MPGi ^ ^0 ^ 1 Weighti ^ 2 SUVi ^ i , where SUV is a dummy variable equal to 1 if the vehicle is an SUV (sport utility vehicle), and 0 if not. You will need to create the dummy variable. Write down the sample regression function and interpret 2
^ ˆ.
(b) Looking at your regression results, is the effect of SUV on miles per gallon significant? (c) Write down the null and alternative hypotheses for the whole model F-test. Conduct the test using your output. Use the 1% significance level.
(d) Does the effect of weight on miles per gallon differ by SUV? Write down the relevant sample regression, null and alternative hypotheses, and conduct the appropriate hypothesis test. (e) Draw a graph for part (d) illustrating the sample regression lines for SUVs and non-SUVs. Identify the values to 5 decimal places of all intercepts and slopes.
