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Statistics Informed Decisions Using Data 5th Edition Michael Sullivan III - Solutions

Researchers Alfred P. Rovai and Marcus D. Childress asked the following question: "How can resistance to reduction of computer anxiety among teacher education students be explained and predicted?" (Journal of Research on Technology in Education, 35(2)). To answer this research question, they
Researchers at Victoria University wanted to determine the factors that affect precision in shooting air pistols. "Inter- and Intra-Individual Analysis in Elite Sport: Pistol Shooting," Journal of Applied Biomechanics, 28-38, 2003. The explanatory variables werex1: Percent of the time the shooter's
Wanting to know if there is a linear relation among wind chill temperature, air temperature (in degrees Fahrenheit), and wind speed (in miles per hour), a researcher collected the following data for various days.(a) Find the least-squares regression equation y̅ = b0 + b1x1 + b2x2, where x1 is air
Wanting to know if there is a linear relation among heat index, air temperature (in degrees Fahrenheit), and dew point, a researched collected the following data for various days.(a) Find the least-squares regression equation yÌ… = b0 + b1x1 + b2x2, where x1 is air temperature, x2 is dew point,
A researcher wants to determine a model that can be used to predict the 28-day strength of a concrete mixture. The following data represent the 28-day and 7-day strength (in pounds per square inch) of a certain type of concrete along with the concrete's slump. Slump is a measure of the uniformity
An economist was interested in modeling the relation among annual income, level of education, and work experience. The level of education is the number of years of education beyond eighth grade, so 1 represents completing 1 year of high school, 8 means completing 4 years of college, and so on. Work
Go to www.pearsonhighered.com/sullivanstats to obtain the data file 14_3_19 using the file format of your choice. The data represent the SAT Math scores for students who took the exam in 2012, along with the percent of students who took the exam in the state, and the average and starting salaries
When testing whether there is a linear relation between the response variable and the explanatory variables, we use an F-test. If the P-value indicates that we reject the null hypothesis, H0: β1 = β 2 =...= βk = 0, what conclusion should we come to? Is it possible that one of the bi is zero if
Explain the difference between the coefficient of determination, R2, and the adjusted coefficient of determination, R2a dj. Which is better for determining whether an additional explanatory variable should be added to the regression model?
What is multicollinearity? How can we check for it? What are the consequences of multicollinearity?
True or False: The value of R2 never decreases as more explanatory variables are added to a regression model.
You obtain the multiple regression equation y̅ = 5 + 3x1 - 4x2 from a set of sample data.(a) Interpret the slope coefficients for x1 and x2.(b) Determine the regression equation with x1 = 10. Graph the regression equation with x1 = 10.(c) Determine the regression equation with x1 = 15. Graph the
You obtain the multiple regression equation y̅ = -5 - 9x1 + 4x2 from a set of sample data.(a) Interpret the slope coefficients for x1 and x2.(b) Determine the regression equation with x1 = 10. Graph the regression equation with x1 = 10.(c) Determine the regression equation with x1 = 15. Graph the
A multiple regression model has k = 3 explanatory variables. The coefficient of determination, R2, is found to be 0.653 based on a sample of n = 25 observations.(a) Compute the adjusted R2.(b) Compute the F-test statistic.(c) If one additional explanatory variable is added to the model and R2
A multiple regression model has k = 4 explanatory variables. The coefficient of determination, R2, is found to be 0.542 based on a sample of n = 40 observations.(a) Compute the adjusted R2.(b) Compute the F-test statistic.(c) If one additional explanatory variable is added to the model and R2
For the data set(a) Construct a correlation matrix between x1, x2, x3, and y. Is there any evidence that multicollinearity exists? Why?(b) Determine the multiple regression line with x1, x2, and x3 as the explanatory variables.(c) Assuming that the requirements of the model are satisfied, test H0:
The following data represent the time (minutes) it takes to drill an additional 5 feet from the depth indicated for both wet drilling and dry drilling conditions.(a) Draw a scatter diagram, treating depth as the explanatory variable and time as the response variable, but use a different plotting
Suppose we wish to develop a regression equation that models the selling price of a home. The researcher wishes to include the variable garage in the model. She has identified three possibilities for a garage: (1) attached, (2) detached (3) no garage. Define the indicator variables necessary to
Suppose we wish to develop a model with three explanatory variables, x1, x2, and x3.(a) Write a model that utilizes all three explanatory variables with no interaction.(b) Write a model that utilizes the explanatory variables x1 and x2 along with interaction between x1 and x2.(c) Write a model that
Suppose you want to develop a model that predicts the gas mileage of a car. The explanatory variables you are going to utilize arex1: city or highway drivingx2: weight of the carx3: tire pressure(a) Write a model that utilizes all three explanatory variables in an additive model with linear terms
Suppose that the response variable y is related to the explanatory variables x1 and x2 by the regression equation.y̅ = 4 + 0.4x1 - 1.3x2(a) Construct a graph similar to Figure 21 showing the relationship between the expected value of y and x1 for x2 = 10, 20, and 30.(b) Construct a graph showing
Suppose that the response variable y is related to the explanatory variables x1 and x2 by the regression equationy̅ = 6 - 0.3x1 + 1.7x2(a) Construct a graph similar to Figure 21 showing the relationship between the expected value of y and x1 for x2 =10, 20, and 30.(b) Construct a graph showing the
In the European Union, it has become important to be able to determine an individual's age when legal documentation of the birth date of an individual is unavailable. In the article "Age Estimation in Children by Measurement of Open Apices in Teeth: a European Formula" (International Journal of
In the article "Bigger Teeth for Longer Life? Longevity and Molar Height in Two Roe Deer Populations" (Biology Letters [June, 2007] vol. 3 no. 3 268-270), researchers developed a model to predict the tooth height (in mm), y, of roe deer based on their age, x1, gender, x2 (0 = female, 1 = male), and
(a) Draw a scatter diagram of the data. What type of relation appears to exist between x and y?(b) Find the quadratic regression equation y̅ = b0 + b1x + b2x2.(c) Draw a residual plot against the fitted values, x, and x2. Also, draw a boxplot of the residuals. Are there any problems with the
In the 1950s, Franco Modigliani developed the Life Cycle Hypothesis. One tenet of this hypothesis is that income varies with age. The following data represent the annual income and age of a random sample of 15 adult Americans.(a) Draw a scatter diagram of the data. What type of relation appears to
The given data represent the percentage, y, of the population that is divorced for various ages, x, in the United States in 2010 based on sample data obtained from the United States Statistical Abstract in 2012.Age, x __________________ Percentage Divorced, y22 ...................................
An engineer collects the following data showing the speed and miles per gallon of a Toyota Camry.(a) Draw a scatter diagram of the data. What type of relation appears to exist between x and y?(b) Find the quadratic regression equation yÌ… = b0 + b1x + b2x2.(c) Draw a residual plot against the
The data to the right represent the time (in seconds) to complete a 400-meter race while a wind is blowing 2 meters per second in different directions. The wind direction is measured from the finishing straight (so 180 degrees is a head on wind). See the figure. The wind speed of 2 meters per
Researchers developed a model to explain the age gap between husbands and wives at first marriage. The model is below:y̅ = 0.0321x1 + 0.9848x2 + 0.5391x3 - 0.000145x42 + 3.8483wherey: Age gap at first marriage (male - female)x1: Percent of children aged 10 to 14 involved in child laborx2:
For the data set below, use a partial F-test to determine whether the variables x4 and x5 do not significantly help to predict the response variable, y. Use the a = 0.05 level of significance.
For the data set below, use a partial F-test to determine whether the variables x1 and x2 do not significantly help to predict the response variable, y. Use the a = 0.05 level of significance.
A realtor wanted to find a model that describes the asking price of houses in Greenville, South Carolina. She obtains a random sample of homes from the area.(a) Find the least-squares regression equation YÌ… = b0 + b1x1 + b2x2 + b3x3, where x1 is square footage, x2 is number of bedrooms, x3 is
A researcher is interested in developing a model that describes the gas mileage, measured in miles per gallon (mpg), of automobiles. Based on input from an engineer, she decides that the explanatory variables might be engine size (liters), curb weight (pounds), and horsepower. From a random sample
The data represent a variety of variables that may explain a pitcher's ERA (earned run average), or the mean number of earned runs (runs given up excluding those due to fielding errors) yielded by a pitcher over the course of nine innings pitched. The potential explanatory variables are strikeout
Suppose a nutritionist wants to develop a model that describes the amount of calories in a single serving of cereal. The potential explanatory variables for the model are protein (grams), fat (grams), sodium (milligrams), fiber (grams), carbs (grams of carbohydrates), sugars (grams), potass
The following data represent the cost of tires (in dollars) along with a variety of potential explanatory variables. Slalom time is the amount of time it took for a 3-series BMW to get through a slalom track, lap time is the amount of time it took the same car to complete a 1/3-mile lap, and
The value of a diamond is determined by the four C's: carat weight, color, clarity, and cut. Carat weight is the standard measure for the size of a diamond. Generally, the more a diamond weighs, the more valuable it will be. The Gemological Institute of America (GIA) determines the color of
(a) Construct a correlation matrix with price, acres, bedrooms, bathrooms, square feet, age, and rooms. Is there any reason to be concerned with multicollinearity based on the correlation matrix?(b) Find the least-squares regression equationyÌ… = b0 + b1x1 +b2x2 + b3x3 + b4x4 + b5x5 + b6x6,
What is the simple least-squares regression model? What are the requirements to perform inference on a simple least-squares regression line? How do we verify that these requirements are met?
Download the data file 14_cr_10.txt at www.pearsonhighered.com/sullivanstats. The data represent a variety of variables measured on players in the 2015 National Football League (NFL) combine. Suppose you want to build a model to predict a player's weight. The following variables were measured:y:
A biology professor wants to investigate the relation between the seat location chosen by a student on the first day of class and their cumulative grade point average (GPA). He randomly selected an introductory biology class and obtained the following information for the 38 students in the
The following data represent the square footage and rents for apartments in Queens, New York and Nassau County, New York. For this problem, only consider the Queens data.(a) What are the estimates of b0 and b1? What is the mean rent of a 900-square-foot apartment in Queens?(b) Compute the standard
The following data represent the number of calories per serving and the number of grams of sugar per serving for a random sample of high-protein and moderate protein energy bars.(a) Draw a scatter diagram of the data, treating calories as the explanatory variable. What type of relation, if any,
The following data represent the price of a random sample of used Chevy Camaros by age.(a) Determine the least-squares regression equation, treating age as the explanatory variable.(b) A normal probability plot of the residuals indicates that the residuals are approximately normally distributed.
In the book Super Crunchers, author lan Ayres presents the model y̅ = 12.15 + 0.00117x1 + 0.0614x2 - 0.00386x3, where y represents the quality of a wine, x1 represents total rainfall in the winter prior to harvest (in inches), x2 represents the average temperature during the growing season (in
A statistics instructor wishes to investigate the relation between a student's final course grade and grades on a midterm exam and a major project. She selects a random sample of 10 statistics students and obtains the following information:(a) Construct a correlation matrix between course grade,
Suppose you want to develop a model that predicts the revenue per visit to a company's web site. The explanatory variables you are going to use are x1: household income x2: time spent on the web site x3: gender (a) Write a model that utilizes all three explanatory variables in an additive model
The data in Problem 3 represent the square footage and rent for apartments in the borough of Queens and Nassau County, New York.(a) On the same graph, draw a scatter diagram for both Queens and Nassau County apartments treating square footage as the explanatory variable, but use a different
Describe the difference between parametric statistical procedures and nonparametric statistical procedures?
Explain the idea of efficiency?
List the advantages of using nonparametric statistical procedures?
List the disadvantages of using nonparametric statistical procedures?
The following data represent the arrival status of American Airlines Flight 0715 from Washington DC's Ronald Reagan Airport to Chicago's O'Hare International Airport for 15 consecutive flights.L O O O O O O L L L O L O O OStatus is indicated as on time (O) or late (L), defined as more than 10
The quality-control manager of a bottling company wants to discover whether a filling machine overor underfills 16-ounce bottles randomly. The following data represent the filling status of 20 consecutive bottles:A A A A A A A R R R R A A A A A A A R RA bottle is rejected (R) if it is either
The quality-control manager of a candy company wants to discover whether a filling machine overor underfills 16-ounce bags randomly. The following data represent the filling status of 18 consecutive bags:A A A A A R R R A A A A A A A A A AA bag is rejected (R) if it is either overfilled or
Does a stock price fluctuate randomly from day to day? A stock analyst selected 45 consecutive days in 2015 in which the stock of Boeing Corporation was traded and computed the daily percentage change in the stock. He indicated positive percentage changes with a P and negative percentage changes
Does the Dow Jones Industrial Average (DJIA) fluctuate randomly from quarter to quarter? (A quarter refers to a quarter of the year. For example, January-March is the first quarter.) A stock analyst selected 40 consecutive quarters and computed the percentage change in the DJIA. He indicated
In a least-squares regression model, the residuals are assumed to be random. The following data represent the life expectancy of a male born in the given year.The least-squares regression equation, treating year as the independent variable, is yÌ‚ = 0.2056x - 337.1973. The residuals from left to
A quality-control inspector tracks the compressive strength of parts created by an injection molding process. If the process is in control, the strengths should fluctuate randomly around the target value of 75 psi. The inspector measures the strength of 20 parts as they come off the production line
What is meant by random? Explain what a run is.
We have evidence against the null hypothesis that the data are random if there are either too few or too many runs. Explain the logic behind this criterion.
Madison Bumgarner is a pitcher for the San Francisco Giants. He throws a four-seam fastball pitch (F) to complement his cutter (C). One inning, Bumgarner threw 20 pitches. The following sequence represents the pitches he threw, in order.F F C F C C F F F C F C C F C C C C F CConduct a runs test for
A certain NFL coach likes to select the first 15 offensive plays before the game begins. The coach can select either a running play (R) or a pass play (P). The following sequence represents the first 15 plays, in order:R P P P R P R R P R R R P R RTest the randomness of the coach's play selection
The following data represent the arrival status of Southwest Flight 0426 from Dallas' Love Field to San Antonio International Airport for 14 consecutive flights.L O O L L L O O L O O O O LStatus is indicated as on time (O) or late (L), defined as more than 10 minutes after the scheduled arrival.
Use the sign test to test the given alternative hypothesis at the α = 0.05 level of significance.The median is less than 8. An analysis of the data reveals that there are 13 minus signs and 8 plus signs.
Zillow.com allows people to research real estate listings. One feature is the "Zestimate," which represents the price Zillow believes the property should sell for. If the Zestimate is accurate, the median difference between the actual selling price and the Zestimate should be zero. The following
The following data represent the salaries of 14 randomly selected baseball players in the 2014 season (data are in thousands of dollars, so 3250 means $3,250,000).
A random sample of 18 three-year-old Chevrolet Impalas was obtained in the St. Louis, Missouri area, and the number of miles on each car was recorded as follows:Test the hypothesis that the median number of miles on three year-old Impalas is less than 40,428 miles, the median miles driven over
Women Gamers A study of 100 randomly selected computer and video game players found that 38 were women (based on data from the Entertainment Software Association). Using an α = 0.01 level of significance, does this indicate that less than 50% of gamers are women?The only requirement for the sign
In a study of 2302 U.S. adults surveyed online by Harris Interactive 1243 respondents indicated that they tend to not trust the press. Using an a = 0.05 level of significance, does this indicate that more than half of U.S. adults tend to not trust the press?The only requirement for the sign test is
The median is more than 50. An analysis of the data reveals that there are 7 minus signs and 12 plus signs.Use the sign test to test the given alternative hypothesis at the α = 0.05 level of significance.
Locate the efficiency of the sign test in Section 15.1 for both large samples and small samples. What do these values indicate?
In the large-sample case, we compareto -za, regardless of whether we are conducting a left-tailed or right-tailed test. Provide a justification for this.
Write a paragraph that describes the logic of the test statistic in a right-tailed sign test?
Write a paragraph that describes the logic of the test statistic in a two-tailed sign test?
The median is different from 100. An analysis of the data reveals that there are 21 minus signs and 28 plus signs.Use the sign test to test the given alternative hypothesis at the α = 0.05 level of significance.
The median is different from 68. An analysis of the data reveals that there are 45 plus signs and 27 minus signs.Use the sign test to test the given alternative hypothesis at the α = 0.05 level of significance.
The median is more than 12. The following data were obtained from a random sample:Use the sign test to test the given alternative hypothesis at the Î± = 0.05 level of significance.
The median is less than 15. The following data were obtained from a random sample:Use the sign test to test the given alternative hypothesis at the Î± = 0.05 level of significance.
In 2002, the median pH level of the rain in Glacier National Park, Montana, was 5.25. A biologist thinks that the acidity of rain has decreased since then, which would suggest the pH has increased. She obtains a random sample of 15 rain dates in 2015 and obtains the following data:Test the
According to TeacherSalaryInfo.com, the median salary of a teacher in Illinois is $57,283. A politician obtains the following data based on a random sample of 12 teachers in a district currently experiencing financial difficulty. Do the data support the belief that the teachers in the district are
A researcher believes the median from population 1 is less than the median from population 2 in matched-pairs data. How would you define MD? How would you compute the differences?
To determine the effectiveness of an exercise regimen, a physical therapist randomly selects 10 women to participate in a study. She measures their waistlines (in inches) both before and after a rigorous 8-week exercise program and obtains the data shown. Is the median waistline before the exercise
A physical therapist wishes to learn whether an exercise program increases flexibility. She measures the flexibility (in inches) of 12 randomly selected subjects both before and after an intensive 8-week training program and obtains the data shown. Is the median flexibility before the exercise
Hemoglobin helps the red blood cells transport oxygen and remove carbon dioxide. Researchers at NASA wanted to discover the effects of space flight on a rat's hemoglobin. The following data represent the hemoglobin (in grams per deciliter) at lift-off minus 3 days (H-L3) and immediately upon return
Blood clotting is due to a sequence of chemical reactions. The protein thrombin initiates blood clotting by working with another protein, prothrombin. It is common to measure an individual's blood clotting time as prothrombin time, the time between the start of the thrombin- prothrombin reaction
The following data represent the weekday rental rate for a compact car charged by two car-rental companies, Avis and Hertz, in 11 locations. Is Avis cheaper than Hertz? Use the Î± = 0.05 level of significance.
A researcher wants to know if the octane level of gasoline affects the gas mileage of a car. She randomly selects 10 cars and puts 5 gallons of 87-octane gasoline in the tank. On a closed track, each car is driven at 50 miles per hour until it runs out of gas. The experiment is repeated, with each
Researchers at NASA wanted to learn the effects of spaceflight on a rat's red blood cell count (RBC). The following data represent the RBC at lift-off minus 3 days (RBC-L3) and immediately upon return (RBC-R0) of 27 rats sent to space on the Spacelab Sciences 1 flight.They used Minitab to test
Researchers at the University of Mississippi wanted to learn the reaction times of students to different stimuli. In the following data, the reaction times for subjects were measured after they received a simple stimulus and a go/no-go stimulus. The simple stimulus was an auditory cue, and the time
The median length of stay for substance-abuse outpatient treatment completers is 107 days for those referred by the criminal justice system. The following data represent the length of stays for a random sample of substance abuse outpatient treatment completers who were referred by an employer.Using
The median length of stay for male substance-abuse outpatient treatment completers is 105 days. The following data represent the length of stays for a random sample of female substance-abuse outpatient treatment completers.Using the Wilcoxon signed-ranks test at the Î± = 0.05 level of
Use the Wilcoxon matched-pairs signedranks test to test the given hypotheses at the α = 0.05 level of significance. The dependent samples were obtained randomly.1. Hypotheses: H0: MD = 0 versus H1: MD > 0 with n = 12 and T- = -16.2. Hypotheses: H0: MD = 0 versus H1: MD > 0 with n = 20 and T-
Use the Mann-Whitney test to test the given hypotheses at the a = 0.05 level of significance. The independent samples were obtained randomly.1. Hypotheses: H0: Mx = My versus H1: Mx ≠ My with n1 = 12, n2 = 15, and S = 1702. Hypotheses: H0: Mx = My versus H1: Mx ≠ My with n1 = 10, n2 = 8, and S
A researcher wants to know if the median weight of NFL offensive tackles is higher than the median weight of NFL defensive tackles. He randomly selected 10 offensive tackles and 8 defensive tackles and obtained the following data:Do the data indicate that offensive tackles are heavier? Use the Î±
Researchers wanted to discover whether the median amount of bacteria in carpeted rooms was greater than that in uncarpeted rooms. To determine the amount of bacteria in a room, researchers pumped the air from the room over a Petri dish at the rate of 1 cubic foot per minute for 8 carpeted rooms and
Researchers at NASA wanted to judge the effects of spaceflight on a rat's tibia. The following data represent the length (in millimeters) of the right tibia upon return from the Spacelab Life Sciences 2 flight for a flight (experimental) group and ground (control) group of six rats each.Does the
An environmentalist wants to determine if the median amount of calcium (mg/L) in rainwater in Lincoln County, Nebraska, is different from that in the rainwater in Clarendon County, South Carolina. She randomly selects 22 weeks in the Nebraska location in which it rained at least once during the
An environmentalist wants to determine if the median amount of potassium (mg/L) in rainwater in Lincoln County, Nebraska, is different from that in the rainwater in Clarendon County, South Carolina. She randomly selects 22 weeks in the Nebraska location in which it rained at least once during the

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