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PMBA 305 Module #4: Two-Sample Tests and Simple Linear Regression Spring '13




Question;PMBA 305 - Spring '13;Quantitative Aspects of Decision Making;Module #4: Two-Sample;Tests and Simple Linear Regression;[1];In an article in Marketing 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);8;3;6;9;2;5;6;3;Price (y);16;74;40;19;124;36;33;89;a);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).


Paper#52634 | Written in 18-Jul-2015

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