Exam 17: A Roadmap for Analyzing Data

TABLE 17-12 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0)and 15 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income,in thousands of dollars),lawn size (Lawn Size,in thousands of square feet),attitude toward outdoor recreational activities (Attitude 0 = unfavorable,1 = favorable),number of teenagers in the household (Teenager),and age of the head of the household (Age). The Minitab output is given below: -True or False: Referring to Table 17-12,the null hypothesis that the model is a good-fitting model cannot be rejected when allowing for a 5% probability of making a type I error.

TABLE 17-8 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily mean of the percentage of students attending class (% Attendance),mean teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable,X₁ = % Attendance,X₂ = Salaries and X₃ = Spending: -Referring to Table 17-8,what are the lower and upper limits of the 95% confidence interval estimate for the effect of a one dollar increase in mean teacher salary on the mean percentage of students passing the proficiency test?

True or False: A survey was conducted to determine how people rated the quality of programming available on television.Respondents were asked to rate the overall quality from 0 (no quality at all)to 100 (extremely good quality).A cumulative percentage polygon (ogive)can be used to present this information.

TABLE 17-10 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age),the number of years of education received (Edu),the number of years at the previous job (Job Yr),a dummy variable for marital status (Married: 1 = married,0 = otherwise),a dummy variable for head of household (Head: 1 = yes,0 = no)and a dummy variable for management position (Manager: 1 = yes,0 = no).We shall call this Model 1.The coefficient of partial determination ( )of each of the 6 predictors are,respectively,0.2807,0.0386,0.0317,0.0141,0.0958,and 0.1201. Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager.The results of the regression analysis are given below: -True or False: Referring to Table 17-10,Model 1,there is sufficient evidence that the number of weeks a worker is unemployed due to a layoff depends on at least one of the explanatory variables at a 10% level of significance.

TABLE 17-5 You worked as an intern at We Always Win Car Insurance Company last summer.You notice that individual car insurance premiums depend very much on the age of the individual,the number of traffic tickets received by the individual,and the population density of the city in which the individual lives.You performed a regression analysis in EXCEL and obtained the following information: -Referring to Table 17-5,the total degrees of freedom that are missing in the ANOVA table should be ________.

TABLE 17-12 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0)and 15 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income,in thousands of dollars),lawn size (Lawn Size,in thousands of square feet),attitude toward outdoor recreational activities (Attitude 0 = unfavorable,1 = favorable),number of teenagers in the household (Teenager),and age of the head of the household (Age). The Minitab output is given below: -True or False: Referring to Table 17-12,there is not enough evidence to conclude that LawnSize makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance.

TABLE 17-12 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0)and 15 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income,in thousands of dollars),lawn size (Lawn Size,in thousands of square feet),attitude toward outdoor recreational activities (Attitude 0 = unfavorable,1 = favorable),number of teenagers in the household (Teenager),and age of the head of the household (Age). The Minitab output is given below: -Referring to Table 17-12,what is the estimated probability that a 48-year-old home owner with a family income of $100,000,a lawn size of 5,000 square feet,a positive attitude toward outdoor recreation,and two teenagers in the household will purchase a lawn service?

TABLE 17-9 What are the factors that determine the acceleration time (in sec.)from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu.ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. The various residual plots are as shown below. The coefficient of partial determination ( )of each of the 5 predictors are,respectively,0.0380,0.4376,0.0248,0.0188,and 0.0312. The coefficient of multiple determination for the regression model using each of the 5 variables X_j as the dependent variable and all other X variables as independent variables ( )are,respectively,0.7461,0.5676,0.6764,0.8582,0.6632. -True or False: Referring to Table 17-9,the 0 to 60 miles per hour acceleration time of a coupe is predicted to be 0.7679 seconds higher than that of a sedan.

TABLE 17-11 A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on mean total Scholastic Aptitude Test score (SAT)at the university or college,the room and board expense measured in thousands of dollars (Room/Brd),and whether the TOEFL criterion is at least 550 (Toefl550 = 1 if yes,0 otherwise.)The dependent variable,Y,is school type (Type = 1 if private and 0 otherwise). -True or False: Referring to Table 17-11,the null hypothesis that the model is a good-fitting model cannot be rejected when allowing for a 5% probability of making a type I error.

TABLE 17-8 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily mean of the percentage of students attending class (% Attendance),mean teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable,X₁ = % Attendance,X₂ = Salaries and X₃ = Spending: -True or False: Referring to Table 17-8,there is sufficient evidence that all of the explanatory variables are related to the percentage of students passing the proficiency test at a 5% level of significance.

TABLE 17-10 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age),the number of years of education received (Edu),the number of years at the previous job (Job Yr),a dummy variable for marital status (Married: 1 = married,0 = otherwise),a dummy variable for head of household (Head: 1 = yes,0 = no)and a dummy variable for management position (Manager: 1 = yes,0 = no).We shall call this Model 1.The coefficient of partial determination ( )of each of the 6 predictors are,respectively,0.2807,0.0386,0.0317,0.0141,0.0958,and 0.1201. Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager.The results of the regression analysis are given below: -Referring to Table 17-10,Model 1,________ of the variation in the number of weeks a worker is unemployed due to a layoff can be explained by the six independent variables.

TABLE 17-8 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily mean of the percentage of students attending class (% Attendance),mean teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable,X₁ = % Attendance,X₂ = Salaries and X₃ = Spending: -True or False: Referring to Table 17-8,there is sufficient evidence that the percentage of students passing the proficiency test depends on at least one of the explanatory variables at a 5% level of significance.

TABLE 17-8 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily mean of the percentage of students attending class (% Attendance),mean teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable,X₁ = % Attendance,X₂ = Salaries and X₃ = Spending: -True or False: Referring to Table 17-8,the null hypothesis H₀ : β₁ = β₂ = β₃ = 0 implies that the percentage of students passing the proficiency test is not related to one of the explanatory variables.

TABLE 17-10 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age),the number of years of education received (Edu),the number of years at the previous job (Job Yr),a dummy variable for marital status (Married: 1 = married,0 = otherwise),a dummy variable for head of household (Head: 1 = yes,0 = no)and a dummy variable for management position (Manager: 1 = yes,0 = no).We shall call this Model 1.The coefficient of partial determination ( )of each of the 6 predictors are,respectively,0.2807,0.0386,0.0317,0.0141,0.0958,and 0.1201. Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager.The results of the regression analysis are given below: -True or False: Referring to Table 17-10,Model 1,the alternative hypothesis H₁ : At least one of β_j ≠ 0 for j = 1,2,3,4,5,6 implies that the number of weeks a worker is unemployed due to a layoff is affected by all of the explanatory variables.

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club.She would now like to determine whether or not the mean age of her customers is more than 30.If so,she plans to alter the entertainment to appeal to an older crowd.If not,no entertainment changes will be made.Which of the following tests will you perform to help her make a decision?

To test the effectiveness of a business school preparation course,8 students took a general business test before and after the course.Suppose the before and after exam scores are both normally distributed.Which of the following tests will be the most appropriate?

TABLE 17-12 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 15 did not have a lawn service (code 0)and 15 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income,in thousands of dollars),lawn size (Lawn Size,in thousands of square feet),attitude toward outdoor recreational activities (Attitude 0 = unfavorable,1 = favorable),number of teenagers in the household (Teenager),and age of the head of the household (Age). The Minitab output is given below: -True or False: Referring to Table 17-12,there is not enough evidence to conclude that Income makes a significant contribution to the model in the presence of the other independent variables at a 0.05 level of significance.

TABLE 17-5 You worked as an intern at We Always Win Car Insurance Company last summer.You notice that individual car insurance premiums depend very much on the age of the individual,the number of traffic tickets received by the individual,and the population density of the city in which the individual lives.You performed a regression analysis in EXCEL and obtained the following information: -Referring to Table 17-5,to test the significance of the multiple regression model,what is the form of the null hypothesis?

TABLE 17-1 A real estate builder wishes to determine how house size (House)is influenced by family income (Income),family size (Size),and education of the head of household (School).House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is in years.The builder randomly selected 50 families and ran the multiple regression.Microsoft Excel output is provided below: -Referring to Table 17-1,suppose the builder wants to test whether the coefficient on Income is significantly different from 0.What is the value of the relevant t-statistic?

TABLE 17-10 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age),the number of years of education received (Edu),the number of years at the previous job (Job Yr),a dummy variable for marital status (Married: 1 = married,0 = otherwise),a dummy variable for head of household (Head: 1 = yes,0 = no)and a dummy variable for management position (Manager: 1 = yes,0 = no).We shall call this Model 1.The coefficient of partial determination ( )of each of the 6 predictors are,respectively,0.2807,0.0386,0.0317,0.0141,0.0958,and 0.1201. Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager.The results of the regression analysis are given below: -Referring to Table 17-10,Model 1,what is the value of the test statistic when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of all the other independent variables?