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Statistics Informed Decisions Using Data 5th Edition Michael Sullivan III - Solutions
The Insurance Institute for Highway Safety conducts experiments in which cars are crashed into a fixed barrier at 40 mph. The barrier's deformable face is made of aluminum honeycomb, which makes the forces in the test similar to those involved in a frontal offset crash between two vehicles of the
Researcher Francisco Fuentes and his colleagues wanted to determine the most effective diet for reducing LDL cholesterol, the so-called "bad" cholesterol, among three diets: (1) a saturated-fat diet: 15% protein, 47% carbohydrates, and 38% fat (20% saturated fat, 12% monounsaturated fat, and 6%
An environmentalist wanted to determine if the mean acidity of rain differed among Alaska, Florida, and Texas. He randomly selected six rain dates at each of the three locations and obtained the following data:(a) State the null and alternative hypotheses.(b) Verify that the requirements to use the
The National Football League (NFL) combine is a forum in which players who want to play in the NFL demonstrate various skills. One skill that is measured is the 40-yard dash. Go to www.pearsonhighered.com/sullivanstats to obtain the data file 13_1_23 using the file format of your choice for the
Do people's political philosophy tend to change with age? One technique we may use to answer this question is to see if the mean age of conservatives, moderates, and liberals differ. Go to www.pearsonhighered.com/sullivanstats to obtain the data file SullivanStatsSurveyI using the file format of
An engineer wants to know if the mean strengths of three different concrete mix designs differ significantly. He randomly selects nine cylinders that measure 6 inches in diameter and 12 inches in height in which mixture 67-0-301 is poured, nine cylinders of mixture 67-0-400, and nine cylinders of
Researchers (Brian G. Feagan et al. "Erythropoietin with Iron Supplementation to Prevent Allogeneic Blood Transfusion in Total Hip Joint Arthroplasty," Annals of Internal Medicine, Vol. 133, No. 11) wanted to determine whether epoetin alfa was effective in increasing the hemoglobin concentration in
Researchers wanted to determine if the psychological profile of healthy children was different than for children suffering from recurrent abdominal pain (RAP) or recurring headaches. A total of 210 children and adolescents were studied and their psychological profiles were graded according to the
The following data represent the number of fish species living in various Andirondack Lakes and the pH of the lakes. From chemistry, we know pH is a measure of the acidity or basicity of a solution. Solutions with pH less than 7 are said to be acidic. As pH increases, the solution is said to be
In a study of adult smokers who wanted to quit, 657 subjects were randomly assigned to one of three treatment groups: subjects in Group 1 were given nicotine e-cigarettes, subjects in Group 2 were given nicotine patches, and subjects in Group 3 were given placebo e-cigarettes. The response variable
What are the requirements to perform a one-way ANOVA? Is the test robust?
What is the mean square due to treatment estimate of σ2? What is the mean square due to error estimate of σ2?
In a one-way ANOVA, explain what it means to reject the statement in the null hypothesis if three treatment groups are being compared.
In Problem, fill in the ANOVA table.
Find the critical value from the Studentized range distribution for: (a) α = 0.05, n = 10, k = 3 (b) α = 0.05, n = 24, k = 5 (c) α = 0.05, n = 32, k = 8 (d) H0: µ1 = µ2 = µ3 = µ4 = µ5, with n = 65 at a = 0.05.
In Problem 21 from Section 13.1, we rejected H0: µSF = µMED = µNCEP and concluded that there is at least one treatment that results in a mean LDL cholesterol that differs from the rest. Use Tukey's test to determine which pairwise means differ using a familywise error rate of a = 0.05.
Researchers studied the effect that varying levels of Ritalin and Adderall had on a child's ability to follow rules when the child is diagnosed with attention deficit hyperactivity disorder (ADHD). They randomly assigned children to one of five treatment groups: placebo, 10 mg of Ritalin, 17.5 mg
Researchers Sharon Peterson and Madeleine Sigman-Grant wanted to compare the overall nutrient intake of American children (ages 2 to 19) who exclusively use lean meats, mixed meats, or higher-fat meats. The data given on the next page represent the daily consumption of calcium (in mg) for a random
A researcher wants to determine the effect that smoking has on resting heart rate. She randomly selects seven individuals from three categories: (1) nonsmokers, (2) light smokers (fewer than 10 cigarettes per day), and (3) heavy smokers (10 or more cigarettes per day) and obtains the following
One measure of the value of a stock is its price to earnings ratio (or P/E ratio): the ratio of the price of a stock per share to the earnings per share and can be thought of as the price an investor is willing to pay for $1 of earnings in a company. A stock analyst wants to know whether the P/E
Researchers Sharon Peterson and Madeleine Sigman-Grant wanted to compare the overall nutrient intake of American children (ages 2 to 19) who exclusively use skim milk instead of 1%, 2%, or whole milk. The researchers combined children who consumed 1% or 2% milk into a "mixed milk" category. The
The comparisonwise error rate, denoted ac, is the probability of making a Type I error when comparing two means. It is related to the familywise error rate, a, through the formula 1 - α = (1 - αc)k, where k is the number of means being compared. (a) If the familywise error rate is a = 0.05 and k
A researcher wanted to determine if the mean time to complete a bachelor's degree was different depending on the selectivity of the first institution of higher education that was attended. The following data represent a random sample of 12th-graders who earned their degree within eight years.
Suppose that there is sufficient evidence to reject H0: µ1 = µ2 = µ3 using a one-way ANOVA. The mean square error from ANOVA is determined to be 26.2. The sample means are x̅1 = 9.5, x̅2 = 9.1, x̅3 = 18.1, with n1 = n2 = n3 = 5. Use Tukey's test to determine which pairwise means are
Suppose there is sufficient evidence to reject H0: µ1 = µ2 = µ3 = µ4 using a one-way ANOVA. The mean square error from ANOVA is determined to be 26.2. The sample means are x̅1 = 42.6, x̅2 = 49.1, x̅3 = 46.8, x̅4 = 63.7, with n1 = n2 = n3 = n4 = 6. Use Tukey's test to determine which
The following data are taken from three different populations known to be normally distributed, with equal population variances based on independent simple random samples.(a) Test the hypothesis that each sample comes from a population with the same mean at the a = 0.05 level of significance. That
The following data are taken from four different populations that are known to be normally distributed, with equal population variances based on independent simple random samples.(a) Test the hypothesis that each sample comes from a population with the same mean at the a = 0.05 level of
An agricultural researcher wanted to know whether the mean number of plants for each plot type differed. A one-way ANOVA was performed to test H0: µSP = µSD = µNT. The null hypothesis was rejected with a P-value of 0.007. The researcher proceeded to conduct Tukey's test using StatCrunch to
An agricultural researcher wanted to determine if the mean soybean yield differed for different plot types. A one-way ANOVA was performed to test H0: µL = µNT = µCP. The null hypothesis was rejected with a P-value of 0.038. The researcher proceeded to conduct Tukey's test to determine
In Problem 19 from Section 13.1, we rejected H0: µWM = µBM = µWF = µBF and concluded that the mean profit for the four race-gender groups differ. Use Tukey's test to determine which pairwise means differ using a familywise error rate of a = 0.05.
Given the following ANOVA output, answer the questions that follow:(a) The researcher wants to test H0: µ1 = µ2 = µ3 against H1: at least one of the means is different. Based on the ANOVA table, what should the researcher conclude?(b) What is the mean square due to error?(c) The following
A travel agent wanted to know whether the price (in dollars) of Marriott, Hyatt, and Sheraton Hotels differed significantly. She knew that location of the hotel is a factor in determining price, so she blocked each hotel by location. After randomly selecting six cities and obtaining the room rate
Researchers at NASA wanted to determine the effects of space flight on a rat's daily consumption of water. The following data represent the water consumption (in milliliters per day) at lift-off minus 1, return plus 1, and 1 month after return for six rats sent to space on the Spacelab Sciences 1
Researchers Olivia Carrillo-Gamboa and Richard Gunst presented the following data in their article, "Measurement-Error-Model Collinearities." The data represent the compressive strength (in pounds per square inch) of a random sample of concrete 2 days, 7 days, and 28 days after pouring.(a) Normal
David Elkington, the Chief Executive Officer (CEO) of InsideSales.com, wondered whether the cycles of the moon affect sales. He got the idea from his father-in-law, who said that emergency rooms are crowded when the moon is full. There are eight phases of the moon: New Moon, Waning Crescent, Third
How does the completely randomized design differ from a randomized complete block design?
What requirements must be satisfied to analyze a randomized complete block design?
Name the two ways that a researcher can deal with explanatory variables in a designed experiment.
Given the following ANOVA output, answer the questions that follow:(a) The researcher wants to test H0: µ1 = µ2 = µ3 against H1: at least one of the means is different. Based on the ANOVA table, what should the researcher conclude?(b) What is the mean square due to error?(c) The following
Given the following ANOVA output, answer the questions that follow:(a) The researcher wants to test H0: µ1 = µ2 = µ3 = µ4 against H1: at least one of the means is different. Based on the ANOVA table, what should the researcher conclude? (b) What is the mean square due to error? (c) Explain why
Given the following ANOVA output, answer the questions that follow:(a) The researcher wants to test H0: µ1 = µ2 = µ3 = µ4 against H1: at least one of the means is different. Based on the ANOVA table, what should the researcher conclude? (b) What is the mean square due to
In Problems, assume that the data come from populations that are normally distributed with the same variance.(a) Test H0: µ1 = µ2 = µ3 against H1: at least one of the means is different, where µ1 is the mean for treatment 1, and so on, at the a = 0.05 level of significance.(b) If the
An automotive engineer wanted to determine whether the octane of gasoline used in a car increases gas mileage. Recognizing that car and driver are variables that affect gas mileage, he selected six different brands of car and assigned a driver to each car, so he blocked by car type and driver. For
A medical researcher wanted to determine the effectiveness of coagulants on the healing rate of a razor cut on lab mice. Because healing rates of mice vary from mouse to mouse, the researcher decided to block by mouse. First, the researcher gave each mouse a local anesthesia and then made a 5-mm
The Insurance Institute for Highway Safety regularly tests cars for various safety factors. In one such test, the institute tests the bumpers in 5-mile per hour (mph) crashes. The following data represent the cost of repairs (in dollars) after four different 5-mph crashes on small utility vehicles.
Given the following ANOVA output, answer the questions that follow.(a) Is there evidence of an interaction effect? Why or why not? (b) Based on the P-value, is there evidence of a difference in the means from factor A? Based on the P-value, is there evidence of a difference in the means from factor
Given the following ANOVA output, answer the questions that follow.(a) Is there evidence of an interaction effect? Why or why not? (b) Based on the P-value, is there evidence of a difference in the means from factor A? Based on the P-value, is there evidence of a difference in the means from factor
Given the following ANOVA output, answer the questions that follow.(a) Is there evidence of an interaction effect? Why or why not? (b) Based on the P-value, is there evidence of a difference in the means from factor A? Based on the P-value, is there evidence of a difference in the means from factor
Given the following ANOVA output, answer the questions that follow.(a) Is there evidence of an interaction effect? Why or why not? (b) Based on the P-value, is there evidence of a difference in the means from factor A? Based on the P-value, is there evidence of a difference in the means from factor
In Problems, assume that the data come from populations that are normally distributed with the same variance.(a) Determine whether there is significant interaction between factor A and factor B.(b) If there is no significant interaction, determine if there is a significant difference in the means
A family physician wanted to know if age and gender were factors that explained levels of serum cholesterol (in mg/dL) in her adult patients. She randomly selects two patients for each category of data and obtains the following results:Serum cholesterols are known to be approximately normally
In an online psychology experiment sponsored by the University of Mississippi, researchers asked study participants to respond to various stimuli. Participants were randomly assigned to one of three treatment groups:Group 1, the simple group, required to respond as quickly as possible after a
An engineer wants to know if the mean strengths of three different concrete mix designs differ significantly. He also suspects that slump may be a predictor of concrete strength. Slump is a measure of the uniformity of the concrete, with a higher slump indicating a less uniform mixture. The
An obstetrician wanted to determine the impact that three experimental diets had on the birth weights of pregnant mothers. She randomly selected 27 pregnant mothers in the first trimester of whom 9 were 20 to 29 years old, 9 were 30 to 39 years old, and 9 were 40 or older. For each age group, she
The following data represent the cost of an oil change (in dollars) in three different geographic regions for two types of service centers. A specialty chain is an oil change facility that specializes in oil changes, while a general service station provides a wide array of services in addition to
Do gender and seating arrangement in college classrooms affect student attitude? In a study at a large public university in the United States, researchers surveyed students to measure their level of feeling at ease in the classroom. Participants were shown different classroom layouts and asked
Explain the differences among the completely randomized design, randomized complete block design, and factorial design.
Explain what an interaction effect is. Why is it dangerous to analyze main effects if there is an interaction effect?
Determine whether the interaction plot suggests that significant interaction exists among the factors.1.2. 3. 4.
(a) Use the same analysis as that presented in Example 2 to conjecture whether interaction exists between factor A and factor B.(b) Draw an interaction plot to verify your conjecture from part (a).
Find the critical value from the Studentized range distribution for:(a) α = 0.05, n = 16, k = 7(b) α = 0.05, n = 30, k = 6(c) α = 0.01, n = 42, k = 4Use q0.01,40,4 since q0.01,42,4 is not in the table.(d) Find the critical value from the Studentized range distribution for H0: µ1 = µ2 = µ3 =
Suppose that there is sufficient evidence to rejectH0: µ1 = µ2 = µ3 = µ4 using a one-way ANOVA. The mean square error from ANOVA is determined to be 373. The sample means are x̅1 = 78, x̅2 = 64, x̅3 = 70, x̅4 = 47, with n1 = n2 = n3 = n4 = 31. Use Tukey's test to determine which pairwise
A researcher took water samples from a stream running through a forest and groundwater in the forest. The samples were collected over the course of a year. Each sample was analyzed for the concentration of dissolved organic carbon (mg/L) in it and categorized according to the type of water
Desiring to grade timber mechanically, engineers studied the modulus of rupture in lb/in.2, for a sample of untreated green, 7 inch by 9 inch, mixed oak timbers, sorted by grade: select structural, No. 1, No. 2, and below grade. A one-way ANOVA was performed to testH0: µselect = µNo. 1
In a study of students at Lewis & Clark Community College, a professor compared the chosen seat location of students in mathematics courses to their overall grade point average (GPA). He randomly selected 10 students from each of three seat locations: (1) front, (2) middle, and (3) back. The
Four different catapult designs are being tested for their ability to launch water balloons. The experimenter decides to block by person firing. The distances (in feet) achieved for each catapult are given.(a) What is the response variable in this study?(b) Explain why it makes sense to block by
An investigator for the state police wants to determine the effectiveness of three different defensive driving training programs to see if there are gender differences. Five subjects of each gender who recently received speeding tickets are assigned to each program. At the end of the program, each
The following data represent commute times (in minutes) and a score on a well-being survey.(a) Treating commute time as the explanatory variable, x, determine the estimates of ß0 and ß1.(b) Compute the standard error of the estimate, se.(c) Determine sb1.(d) A normal probability plot of the
The following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean. Does atmospheric pressure play a role in the wind speed of a hurricane?(a) Treating atmospheric pressure as the explanatory
As concrete cures, it gains strength. The following data represent the 7-day and 28-day strength (in pounds per square inch) of a certain type of concrete:(a) Treating the 7-day strength as the explanatory variable, x, determine the estimates of ß0 and ß1.(b) Compute the standard error of the
Every year the Federal Trade Commission (FTC) must report tar and nicotine levels in cigarettes to Congress. Tar and nicotine levels of over 1200 brands of cigarettes are given to Congress and a random sample of those appear in the following table:(a) Treating the amount of tar as the explanatory
The variable "2013 Cost" represents the four-year cost including tuition, supplies, room and board, the variable "Annual ROI" represents the return on investment for graduates of the school-essentially how much you would earn on the investment of attending the school-the variable "Grad Rate"
In 1969, Dr. Michael R. Pelton of the University of Tennessee initiated a long-term study of the American black bear (Ursus americanus) population in Great Smoky Mountains National Park. One aspect of the study was to develop a model that could be used to predict a bear's weight (since it is not
The following data represent the total compensation for 12 randomly selected chief executive officers (CEOs) and the company's stock performance in 2013.(a) Treating compensation as the explanatory variable, x, determine the estimates of ß0 and ß1.(b) Assuming the residuals are normally
A bear market is a market condition in which the price of the security falls. A bear market in the stock market is defined as a condition in which market declines by 20% or more over the course of at least two months. The following data represent the number of months and percentage change in the
The following data represent the population of the United States for the years 1900-2010:An ecologist is interested in finding an equation that describes the population of the United States over time.(a) Determine the least-squares regression equation, treating year as the explanatory variable.(b)
The time it takes for a planet to complete its orbit around the sun is called the planet's sidereal year. Johann Kepler studied the relation between the sidereal year of a planet and its distance from the sun in 1618. The following data show the distances that the planets are from the sun and their
The output shown was obtained from Minitab.(a) The least-squares regression equation is Å· = 1.3962x + 12.396. What is the predicted value of y at x = 10? (b) What is the mean of y at x = 10?(c) The standard error, se, is 2.167. What is an estimate of the standard deviation of y at x = 10?(d) If
Zillow.com is a site that can be used to assess the value of homes in your neighborhood. The organization provides a list of homes for sale as well as a Zestimate, which is the price Zillow believes the home will sell for. The following data represent the Zestimate and sale price (in thousands of
Why is it important to perform graphical as well as analytical analyses when analyzing relations between two quantitative variables?
Why don't we conduct inference on the linear correlation coefficient?
(a) What are the estimates of ß0 and ß1?(b) Compute the standard error, the point estimate for s.(c) Determine sb1.(d) Assuming the residuals are normally distributed, testH0: ß1 = 0 versus H1: b1 ≠0 at the α = 0.05 level of significance.1.2.3.
(a) Predict the mean wind speed of all hurricanes whose atmospheric pressure is 950 mb.(b) Construct a 95% confidence interval for the mean wind speed found in part (a).(c) Predict the wind speed of a randomly selected hurricane whose atmospheric pressure is 950 mb.(d) Construct a 95% prediction
(a) Predict the mean 28-day strength of concrete whose 7-day strength is 2550 psi.(b) Construct a 95% confidence interval for the mean 28-day strength of concrete whose 7-day strength is 2550 psi.(c) Predict the 28-day strength of concrete whose 7-day strength is 2550 psi.(d) Construct a 95%
Use the results of Problem 16 in Section 14.1 to answer the following questions:(a) Predict the mean nicotine content of all cigarettes whose tar content is 12 mg.(b) Construct a 95% confidence interval for the tar content found in part (a).(c) Predict the nicotine content of a randomly selected
Use the results of Problem 17 in Section 14.1 to answer the following questions:(a) Predict the mean annual ROI of all four-year schools whose 2013 cost is $180,000.(b) Construct a 95% confidence interval for the mean annual ROI found in part (a).(c) Predict the annual ROI of a randomly selected
Use the results of Problem 18 from Section 14.1 to answer the following questions:(a) Predict the mean weight of American black bears with a total length of 154.5 cm.(b) Construct a 95% confidence interval for the mean weight of American black bears with a total length of 154.5 cm.(c) Predict the
(a) Explain why it does not make sense to construct confidence or prediction intervals based on the least-squares regression equation.(b) Construct a 95% confidence interval for the mean stock return.
Use the results of Problem 20 from Section 14.1 to answer the following:(a) Explain why it does not make sense to construct confidence or prediction intervals based on the least-squares regression equation.(b) Construct a 95% confidence interval for the mean percent change during a bear market.
Can a photograph of an individual be used to predict their intelligence? Researchers at Charles University in Prague, Czech Republic, had 160 raters analyze the photos of 80 students and asked each rater to rate the intelligence and attractiveness of the individual in the photo on a scale from one
(a) Predict the mean value of y if x = 7.(b) Construct a 95% confidence interval for the mean value of y if x = 7.(c) Predict the value of y if x = 7.(d) Construct a 95% prediction interval for the value of y if x = 7.(e) Explain the difference between the prediction in parts (a) and (c).
(a) Predict the mean value of y if x = 8.(b) Construct a 95% confidence interval for the mean value of y if x = 8.(c) Predict the value of y if x = 8.(d) Construct a 95% prediction interval for the value of y if x = 8.(e) Explain the difference between the prediction in parts (a) and (c).
Using the sample data from Problem 7 in Section 14.1,(a) Predict the mean value of y if x = 1.4.(b) Construct a 95% confidence interval for the mean value of y if x = 1.4.(c) Predict the value of y if x = 1.4.(d) Construct a 95% prediction interval for the value of y if x = 1.4.
Using the sample data from Problem 8 in Section 14.1,(a) Predict the mean value of y if x = 1.8.(b) Construct a 95% confidence interval for the mean value of y if x = 1.8.(c) Predict the value of y if x = 1.8.(d) Construct a 95% prediction interval for the value of y if x = 1.8.
(a) Predict the mean well-being index composite score of all individuals whose commute time is 20 minutes.(b) Construct a 90% confidence interval for the mean well-being index composite score of all individuals whose commute time is 20 minutes.(c) Predict the well-being index composite score of
(a) Predict the mean interest rate of all individuals whose credit score is 730.(b) Construct a 90% confidence interval for the mean interest rate of all individuals whose credit score is 730.(c) Predict the interest rate of Kaleigh, whose credit score is 730.(d) Construct a 90% prediction interval
a) Predict the mean head circumference of children who are 25.75 inches tall.(b) Construct a 95% confidence interval for the mean head circumference of children who are 25.75 inches tall.(c) Predict the head circumference of a randomly selected child who is 25.75 inches tall.(d) Construct a 95%
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:
For the data set(a) Construct a correlation matrix between x1, x2, x3, x4, and y. Is there any evidence that multicollinearity may be a problem?(b) Determine the multiple regression line using all the explanatory variables listed. Does the F-test indicate that we should reject H0: b1 = b2 = b3 = b4
For the following data set(a) Construct a correlation matrix between x1, x2, x3, x4, and y. Is there any evidence that multicollinearity may be a problem?(b) Determine the multiple regression line using all the explanatory variables listed. Does the F-test indicate that we should reject H0: b1 = b2
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