PMBA 305 – Spring ’13 Quantitative Aspects of Decision Making

PMBA 305 – Spring ’13Quantitative Aspects of Decision MakingModule #4: Two-Sample Tests and Simple Linear Regression[1] In an article inMarketing Science, Silk and Berndt investigate the output of advertising agencies. They describe ad agency output by finding the shares of dollar billing volume coming from various media categories such as network television, spot television, newspaper, radio, and so forth.Suppose that a random sample of 400 U.S. advertising agencies gives an average percentage share of billing volume from network television equal to 7.46 percent with a standard deviation of 1.42 percent. Further, suppose that a random sample of 400 U.S. advertising agencies gives an average percentage share of billing volume from spot television commercials equal to 12.44 percent with a standard deviation of 1.55 percent.Using the sample information, does it appear that the mean percentage share of billing volume from spot television commercials for the U.S. advertising agencies is greater than the mean percentage share of billing volume from network television? Explain.[2] A random sample of the birth weights of 186 babies has a mean of 3103g and a standard deviation of 696g (based on data from “Cognitive Outcomes of Preschool Children with Prenatal Cocaine Exposure,” by Singer et al., Journal of the American Medical Association, Vol. 291, No. 20). These babies were born to mothers who did not use cocaine during their pregnancies. Further, a random sample of the birth weights of 190 babies born to mothers who used cocaine during their pregnancies has a mean of 2700g and a standard deviation of 645g. Does cocaine use appear to affect the birth weight of a baby? Substantiate you conclusion.[4] An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars of this model and collected the following information on the ages (in years) and prices (in hundreds of dollars) of these cars. The data are in USEDCAR.xls.Age (x)83692563Price (y)16744019124363389a) Find the value of the linear correlation coefficient r.b) Find the value of the coefficient of determination r2, and interpret the meaning for this problem.c) At the 0.05 level of significance, is there a significant linear relationship between two variables?d) Determine the adequacy of the fit of the model.e) Evaluate whether the assumptions of regression (LINE) have been seriously violated.f) If there is a linear correlation, what is the regression equation?g) Interpret the meaning of the slope b1 in this problem.h) Interpret the meaning of the Y-intercept b0 in this problem. Will it make sense to you as far as this model is concerned? Explain why.i) Set up a 95% confidence interval estimate of the population slope.j) Set up a 95% confidence interval estimate of the average price for all cars of this model after 7 years.k) Set up a 95% confidence interval of the average price of a car of this model after 7 years.l) Explain the difference in the results obtained in (j) and (k).