HW_12_S10[1]

# HW_12_S10[1] - AEM 2100 Spring 2010 Homework 12 1 Name...

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AEM 2100 Name: _________________ Spring 2010 Section:_________________ Homework 12 1.) Each of a random sample of ten college freshmen takes a mathematics aptitude test both before and after undergoing an intensive training course designed to improve such test scores. Then the scores for each student are paired, as shown in the table below. Student Before After 1 60 70 2 73 80 3 42 40 4 88 94 5 66 79 6 77 86 7 90 93 8 63 71 9 55 70 10 96 97 \ a.) Calculate and interpret the p-value for testing whether the mean change equals zero. b.) Construct and interpret a 90% confidence interval for the population mean difference of scores. c.) Explain the correspondence between the result of the significance test (use a 10% level of significance) and the result of the confidence interval. What assumptions does each inference make? 2.) A scatter diagram includes the data points (x = 3, y = 8), (x = 5, y = 18), (x = 7, y = 30), and (x = 9, y = 32). Two regression lines are proposed: (1) ö y = 5 + 3x and (2) ö y = -2 + 4x. Using the least squares criterion, which of these regression lines is the better fit to the data? Explain.

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3.) The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. A random sample of 12 equal-sized stores is selected, with the following results. Store Shelf Space (X) (Feet) Weekly Sales (Y) (S) 1 5 160 2 5 220 3 5 140 4 10 190 5 10 240 6 10 260 7 15 230 8 15 270 9 15 280 10 20 260 11 20 290 12 20 310 a.) Develop a scatter diagram for these data. b.) Use the least squares method to develop the estimated regression equation. Interpret the meaning of the slope in this problem. c.) Predict the mean weekly sales of pet food for stores with 8 feet of shelf space for pet food. d.) Determine the coefficient of determination, and interpret its meaning (be sure to include your ANOVA table.) e.) Determine the standard error of the estimate. f.) How useful do you think this regression model is for predicting sales? 4.) A study is to be made of the relative effectiveness of two kinds of cough medicines designed to increase sleep for people with colds. Six people with colds are given medicine A the first night and medicine B the second night. Their hours of sleep each night are recorded.
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