Exam 18: A Roadmap for Analyzing Data

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 decide?

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,what do 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?

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 alternative hypothesis H₁ : At least one of $\beta$ _j $\neq$ 0 for j = 1,2,3 implies that percentage of students passing the proficiency test is affected by all of the explanatory variables.

The weight of a randomly selected cookie from a production line can most likely be modeled by which of the following distributions?

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 degrees of freedom of the test statistic 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?

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,_____of the variation in the number of weeks a worker is unemployed due to a layoff can be explained by the six independent variables after taking into consideration the number of independent variables and the number of observations.

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 test 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 18-8 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,predict the percentage of students passing the proficiency test for a school which has a daily mean of 95% of students attending class,a mean teacher salary of 40,000 dollars,and an instructional spending per pupil of 2,000 dollars.

Suppose the probability of finding a defective spot in an area on a piece of glass is the ratio of that area to the total area of the glass and the probability is the same across the whole glass.Which of the following distributions would you use to determine the probability of finding a defective spot in a randomly selected one square inch area on a piece of 10 feet by 10 feet glass?

Suppose the light bulbs in a factory burn out at a rate of 50 bulbs per month.Which of the following distributions would you use to determine the probability that the next two light bulbs will burn out 2 days apart?

The director of admissions at a state college is interested in seeing if admissions status (admitted,waiting list,denied admission)at his college is related to the type of community (urban,rural,suburban)in which an applicant resides.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,_____of the variation in the number of weeks a worker is unemployed due to a layoff can be explained by whether the worker is head of household while controlling for 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 18-2,what is your decision and conclusion for the test H₀ : $\beta$ ₂ = 0 vs.H₁ : $\beta$ ₂ $\lt$ 0 at the $\alpha$ = 0.01 level of significance using Model 1 ?

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,you can conclude that mean teacher salary has no impact on the mean percentage of students passing the proficiency test at a 5% level of significance using the 95% confidence interval estimate for $\beta$ ₂ .

Suppose the probability of producing a defective light bulb from a production line is the same over an interval of 90 minutes.Which of the following distributions would you use to determine the probability that a defective light bulb will be produced in a 15 minutes interval?

Data were collected on the amount of detergent used in gallons in a month by 25 drive-through car wash operations in Phoenix.You can use a time-series plot to process this information.

A certain type of new business succeeds 60% of the time.Suppose that 3 such businesses open (where they do not compete with each other,so it is reasonable to believe that their relative successes would be independent).Which of the following distributions would you use to determine the probability that all of them will fail?

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 six independent variables (Age,Edu,Job Yr,Married,Head and Manager)is (are)insignificant in affecting the dependent variable using a 5% level of significance after considering the effect of the remaining 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 Model 1,the null hypothesis H₀ : $\beta$ ₁ = $\beta$ ₂ = $\beta$ ₃ = $\beta$ ₄ = $\beta$ ₅ = $\beta$ ₆ = 0 implies that the number of weeks a worker is unemployed due to a layoff is not affected by any of the explanatory variables.

A Paso Robles wine producer wanted to forecast the cases of Merlot wine sold.The number of cases of merlot wine sold in a 28-year period was collected.Which of the following would be the most appropriate analysis to perform?