Exam 18: A Roadmap for Analyzing Data

A physician and president of a Tampa Health Maintenance Organization (HMO)are attempting to show the benefits of managed health care to an insurance company.The physician believes that certain types of doctors are more cost-effective than others.To investigate this,the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialties - General Practice (GP),Internal Medicine (IM),Pediatrics (PED),and Family Physicians (FP)- and recorded the total charges per member per month for each.A second variable which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate.To investigate this,the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above.So,information on charges for 40 doctors (20 foreign and 20 USA medical school graduates)was obtained for each of the 4 specialties.Which of the following tests will be the most appropriate to find out if the primary specialty and the origin of medical school degree interact to affect the charges?

Are Japanese managers more motivated than American managers? A randomly selected group of 100 managers from each group were administered the Sarnoff Survey of Attitudes Toward Life (SSATL),which measures motivation for upward mobility.The mean and standard deviation of the SSATL scores are computed.The standard deviations of the SSATL scores suggest that the standard deviation from the two groups is very different.Which of the following tests will be the most appropriate?

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,the null hypothesis should be rejected at a 10% level of significance when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff.

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,what is the value of the calculated F test statistic that is missing from the output for testing whether the whole regression model is significant?

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 estimated odds ratio for a 48-year-old home owner with a family income of $100,000,a lawn size of 5,000 square feet,a negative attitude toward outdoor recreation,and one teenager in the household?

SCENARIO 18-7 As a project for his business statistics class,a student examined the factors that determined parking meter rates throughout the campus area.Data were collected for the price per hour of parking,blocks to the quadrangle,and one of the three jurisdictions: on campus,in downtown and off campus,or outside of downtown and off campus.The population regression model hypothesized is Y_i = $\alpha$ + $\beta$ ₁ X_1i + $\beta$ ₂ X _2i + $\beta$ ₃ X _3i + $\varepsilon$ where Y is the meter price X₁ is the number of blocks to the quad X₂ is a dummy variable that takes the value 1 if the meter is located in downtown and off campus and the value 0 otherwise X₃ is a dummy variable that takes the value 1 if the meter is located outside of downtown and off campus,and the value 0 otherwise The following Excel results are obtained. -Referring to Scenario 18-7,what is the correct interpretation for the estimated coefficient for X₂?

A realtor wants to compare the variability of sales-to-appraisal ratios of residential properties sold in four neighborhoods (A,B,C,and D).Four properties are randomly selected from each neighborhood and the ratios recorded for each were collected.Which of the following tests will be the most appropriate?

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 estimated odds ratio for 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?

A debate team of 4 members for a high school will be chosen randomly from a potential group of 15 students.Ten of the 15 students have no prior competition experience while the others have some degree of experience.Which of the following distributions would you use to determine the probability that none of the members chosen for the team have any competition experience?

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 odds ratio for a school with an mean SAT score of 1250,a TOEFL criterion that is at least 550,and the room and board expense of 5 thousand dollars?

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 some of the explanatory 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 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 at a 10% level of significance.

A sample of 100 fuses from a very large shipment is found to have 10 that are defective.Based on this information,which of the following will you construct to learn about the proportion of fuses that are defective?

SCENARIO 18-6 A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in pounds).Two variables thought to affect weight-loss are client's length of time on the weight loss program and time of session.These variables are described below: Partial output from Microsoft Excel follows: -Referring to Scenario 18-6,what is the experimental unit for this analysis?

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 related to one of the explanatory 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 18-12, which of the following is the correct interpretation for the Income slope coefficient?

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 p-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?

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,when the builder used a simple linear regression model with house size (House)as the dependent variable and education (School)as the independent variable,he obtained an r² value of 23.0%.What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?

An investor wanted to forecast the price of a certain stock.He collected the mean daily price for the stock over the past 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 18-10 and using both Model 1 and Model 2,what are the null and alternative hypotheses for testing whether the independent variables that are not significant individually are also not significant as a group in explaining the variation in the dependent variable at a 5% level of significance?