Exam 18: A Roadmap for Analyzing Data

SCENARIO 18-5 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 Scenario 18-5,to test the significance of the multiple regression model,the null hypothesis should be rejected when allowing for 1% probability of committing a type I error.

SCENARIO 18-12 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 Scenario 18-12,what are the degrees of freedom for the chi-square distribution when testing whether the model is a good-fitting model?

SCENARIO 18-3 A financial analyst wanted to examine the relationship between salary (in $1,000)and 4 variables: age (X₁ = Age),experience in the field (X₂ = Exper),number of degrees (X₃ = Degrees),and number of previous jobs in the field (X₄ = Prevjobs).He took a sample of 20 employees and obtained the following Microsoft Excel output: -Referring to Scenario 18-3,the analyst wants to use an F-test to test H₀ : $\beta$ ₁ = $\beta$ ₂ = $\beta$ ₃ = $\beta$ ₄ = 0 .The appropriate alternative hypothesis is .

SCENARIO 18-4 You decide to predict gasoline prices in different cities and towns in the United States for your term project.Your dependent variable is price of gasoline per gallon and your explanatory variables are per capita income,the number of firms that manufacture automobile parts in and around the city,the number of new business starts in the last year,population density of the city,percentage of local taxes on gasoline,and the number of people using public transportation.You collected data of 32 cities and obtained a regression sum of squares SSR= 122.8821.Your computed value of standard error of the estimate is 1.9549. -Referring to Scenario 18-4,what is the value of the coefficient of multiple determination?

SCENARIO 18-8 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, X ₂ = Salaries and X₃ = Spending: -Referring to Scenario 18-8,the null hypothesis H₀ : $\beta$ ₁ = $\beta$ ₂ = $\beta$ ₃ = 0 implies that percentage of students passing the proficiency test is not affected by any of the explanatory variables.

SCENARIO 18-8 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, X ₂ = Salaries and X₃ = Spending: -Referring to Scenario 18-8,which of the following is a correct statement?

An economist is interested to see how consumption for an economy (in $ billions)is influenced by gross domestic product ($ billions)and aggregate price (consumer price index).Annual data Copyright ©2019 Pearson Education,Inc. A Roadmap for Analyzing Data 18-23 From 30 years were collected.Which of the following would be the most appropriate analysis to perform?

SCENARIO 18-12 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 Scenario 18-11,what is the estimated probability that a school with a mean SAT score of 1100,a TOEFL criterion that is not at least 550,and the room and board expense of 7 thousand dollars will be a private school?

SCENARIO 18-2 One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X₁ ), the amount of insulation in inches ( X ₂ ), the number of windows in the house ( X₃ ), and the age of the furnace in years ( X ₄ ). Given below are the EXCEL outputs of two regression models. -Referring to Scenario 18-1,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?

SCENARIO 18-12 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 Scenario 18-12,what is the p-value of the test statistic when testing whether Teenager makes a significant contribution to the model in the presence of the other independent variables?

SCENARIO 18-3 A financial analyst wanted to examine the relationship between salary (in $1,000)and 4 variables: age (X₁ = Age),experience in the field (X₂ = Exper),number of degrees (X₃ = Degrees),and number of previous jobs in the field (X₄ = Prevjobs).He took a sample of 20 employees and obtained the following Microsoft Excel output: -Referring to Scenario 18-3,the analyst wants to use a t test to test for the significance of the coefficient of X₃.At a level of significance of 0.01,the department head would decide that $\beta$ ₃ $\neq$ 0 .

SCENARIO 18-8 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, X ₂ = Salaries and X₃ = Spending: -Referring to Scenario 18-8,the null hypothesis should be rejected at a 5% level of significance when testing whether daily mean of the percentage of students attending class has any effect on percentage of students passing the proficiency test,considering the effect of all the other independent variables.

SCENARIO 18-12 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 Scenario 18-10 Model 1,there is sufficient evidence that all of the explanatory variables are related to the number of weeks a worker is unemployed due to a layoff at a 10% level of significance.

The probability that a particular brand of smoke alarm will malfunction in the presence of smoke is 0.002.A batch of 100,000 such alarms was produced by independent production lines.Which of the following distributions would you use to figure out the probability that at most 5,000 of them will malfunction in case of a fire?

A researcher randomly sampled 30 graduates,18 males and 12 females,of an MBA program and recorded data concerning their starting salaries.Of primary interest to the researcher was the effect of gender on starting salaries.Statistics of the mean salaries of the females and males in the sample were computed.The sample standard deviations suggest that the variability of starting salaries of the two groups is almost the same.Suppose the starting salaries from both groups can be considered as normally distributed.Which of the following tests will be the most appropriate?

SCENARIO 18-8 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, X ₂ = Salaries and X₃ = Spending: -Referring to Scenario 18-8,which of the following is the correct null hypothesis to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables?

A contractor wants to forecast the number of contracts in future quarters,using quarterly data on number of contracts over the last 10 years.Which of the following would be the most appropriate analysis to perform?

SCENARIO 18-12 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 Scenario 18-11,what is the estimated probability that a school with a mean SAT score of 1250,a TOEFL criterion that is at least 550,and the room and board expense of 5 thousand dollars will be a private school?

SCENARIO 18-12 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 Scenario 18-10 Model 1,what is the standard error of estimate?

SCENARIO 18-12 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 Scenario 18-10 Model 1,which of the following is the correct null hypothesis to test whether being married or not makes a difference in the mean number of weeks a worker is unemployed due to a layoff while holding constant the effect of all the other independent variables?