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intro stats
Stats Data And Models 5th Global Edition Richard De Veaux, Paul Velleman, David Bock - Solutions
Cell phone survey What about drawing a random sample only from cell phone exchanges? Discuss the advantages and disadvantages of such a sampling method compared with surveying randomly generated telephone numbers from non–cell phone exchanges. Do you think these advantages and disadvantages have
Phone surveys Any time we conduct a survey, we must take care to avoid undercoverage. Suppose we plan to select 500 names from the city phone book, call their homes between noon and 4 pm, and interview whoever answers, anticipating contacts with at least 200 people.a) Why is it difficult to use a
More survey questions Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question.a) Do you think high school students should be required to wear uniforms?b) Given humanity’s great tradition of exploration, do you
Survey questions Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question.a) Should companies that pollute the environment be compelled to pay the costs of cleanup?b) Given that 16-year-olds are old enough to drive in
Banning ephedra An online poll on a website asked:A nationwide ban of the diet supplement ephedra went into effect recently. The herbal stimulant has been linked to 155 deaths and many more heart attacks and strokes. Ephedra manufacturer NVE Pharmaceuticals, claiming that the FDA lacked proof that
Wording the survey Two members of the PTA committee in Exercises 26 and 27 have proposed different questions to ask in seeking parents’ opinions.Question 1: Should elementary school–age children have to pass high-stakes tests in order to remain with their classmates?Question 2: Should schools
Playground, act two The survey described in Exercise 29 asked: Many people believe this playground is too small and in need of repair. Do you think the playground should be repaired and expanded even if that means raising the entrance fee to the park?Describe two ways this question may lead to
Roller coasters An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to 3 hours for a 2-minute ride. Concerned about how patrons(who paid a large amount to enter the park and ride on the rides) feel about this, they survey every person in line for the
Playground Some people have been complaining that the children’s playground at a municipal park is too small and is in need of repair. Managers of the park decide to survey city residents to see if they believe the playground should be rebuilt.They hand out questionnaires to parents who bring
Churches For your political science class, you’d like to take a survey from a sample of all the Catholic church members in your city. A list of churches shows 16 Catholic churches within the city limits. Rather than try to obtain a list of all members of all these churches, you decide to pick 3
Four new sampling strategies have been proposed to help the PTA determine whether parents favor requiring elementary students to pass a test in order to be promoted to the next grade. For each, indicate what kind of sampling strategy is involved and what (if any) biases might result.a) Run a poll
Parent opinion, part 2 Let’s revisit the school system described in Exercise
Parent opinion, part 1 In a large city school system with 50 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this
Another mistaken poll Prior to the mayoral election discussed in Exercise 24, the newspaper also conducted a poll. The paper surveyed a random sample of registered voters stratified by political party, age, sex, and area of residence. This poll predicted that Amabo would win the election with 52%
Mistaken poll A local TV station conducted a “PulsePoll” about the upcoming mayoral election. Evening news viewers were invited to text in their votes, with the results to be announced on the late-night news. Based on the texts, the station predicted that Amabo would win the election with 52%
Orange samples Food-safety inspectors visit produce farms unannounced and take samples of a day’s worth of oranges to test for contamination. If the samples are found to contain dirt, antibiotics unsuited for human consumption, or other foreign matter, the oranges will be destroyed. The farm will
Snack foods A company packaging snack foods maintains quality control by randomly selecting 12 cases from each day’s production and weighing the bags. Then they open one bag from each case and inspect the contents.
Roadblock State police set up a roadblock to estimate the percentage of cars with up-to-date registration, insurance, and safety inspection stickers. They usually find problems with about 15% of the cars they stop.
Soil samples The Environmental Protection Agency took soil samples at 20 locations near a former industrial waste dump and checked each for evidence of toxic chemicals. They found no elevated levels of any harmful substances.
Mayoral race Hoping to learn what issues may resonate with voters in the coming election, the campaign director for a mayoral candidate selects four blocks from each of the city’s election districts. Staff members go there and interview all the adult residents they can find.
Social life A question posted on the gamefaqs.com website asked visitors to the site, “Do you have an active social life outside the Internet?” 22% of the 55,581 respondents said “No” or“Not really, most of my personal contact is online.”
Medical treatments Consumers Union asked all subscribers whether they had used alternative medical treatments and, if so, whether they had benefited from them. For almost all of the treatments, approximately 15% of those responding reported cures or substantial improvement in their condition.
Gallup At its website (www.gallup.com), the Gallup Poll publishes results of a new survey each day. Scroll down to the end, and you’ll find a statement that includes words such as these:Results are based on telephone interviews with 1016 national adults, aged 18 and older, conducted March 7–10,
Drug tests Major League Baseball tests players to see whether they are using performance-enhancing drugs. Officials select a team at random, and a drug-testing crew shows up unannounced to test all 33 players on the team. Each testing day can be considered a study of drug use in Major League
Student center survey For their class project, a group of statistics students decide to survey the student body to assess opinions about the proposed new student center. Their sample of 220 contained 55 first-year students, 55 sophomores, 55 juniors, and 55 seniors.a) Do you think the group was
Roper Through their Roper Reports Worldwide, GfK Roper conducts a global consumer survey to help multinational companies understand different consumer attitudes throughout the world.Within 30 countries, the researchers interview 1000 people aged 13–65. Their samples are designed so that they get
Surveying employees The company of Exercise 2 is considering ways to survey their employees. For each of these proposed designs, identify the problem.a) Leave a stack of surveys out in the employee cafeteria so people can pick them up and return them.b) Stuff a questionnaire in the mailbox of each
Student samples The university administration of Exercise 1 is considering a variety of ways to sample students for a survey.For each of these proposed survey designs, identify the problem.a) Publish an advertisement inviting students to visit a website and answer questions.b) Set up a table in the
Happy employees The company plans to have the head of each corporate division hold a meeting of their employees to ask whether they are happy on their jobs. They will ask people to raise their hands to indicate whether they are happy. What problems do you see with this plan?SECTION 10.7
Survey students What problems do you see with asking the following question of students? “Are you the first member of your family to seek higher education?”
Satisfactory satisfaction samples For each scenario, determine the sampling method used by the managers from Exercise 2.a) Use the company e-mail directory to contact 150 employees from among those employed for less than 5 years, 150 from among those employed for 5–10 years, and 150 from among
Sampling A&M students For each scenario, identify the kind of sample used by the university administrators from Exercise 1:a) Select several dormitories at random and contact everyone living in the selected dorms.b) Using a computer-based list of registered students, contact 200 freshmen, 200
Is this a simple random sample?SECTION 10.4
Sampling satisfaction A company hoping to assess employee satisfaction surveys employees by assigning computer-generated random numbers to each employee on a list of all employees and then contacting all those whose assigned random number is divisible by
Sampling students A professor teaching a large lecture class of 450 students samples her class by rolling a die. Then, starting with the row number on the die (1 to 6), she passes out a survey to every fourth row of the large lecture hall. She says that this is a simple random sample because
Satisfied respondents The company’s annual report states,“Our survey shows that 87.34% of our employees are ‘very happy’ working here.” Comment on that claim. Use appropriate statistics terminology.SECTION 10.3
A&M again The president of the university plans a speech to an alumni group. He plans to talk about the proportion of students who responded in the survey that they are the first in their family to attend college, but the first draft of his speech treats that proportion as the actual proportion of
Satisfied workers The managers of a large company wished to know the percentage of employees who feel “extremely satisfied”to work there. The company has roughly 33,000 employees. They contacted a random sample of employees and asked them about their job satisfaction, obtaining 418 completed
University education Administrators at a university were interested in estimating the percentage of students who are the first in their family to go to college. The student body has about 50,000 members. How might the administrators answer their question by applying the three Big Ideas?
Least squares Consider the four points (200,1950),(400,1650), (600,1800), and (800,1600). The least squares line is yn = 1975 - 0.45x. Explain what “least squares” means, using these data as a specific example.
Least squares Consider the four points (10,10),(20,50), (40,20), and (50,80). The least squares line is yn = 7.0 + 1.1x. Explain what “least squares” means, using these data as a specific example.
Gators Wildlife researchers monitor many wildlife populations by taking aerial photographs. Can they estimate the weights of alligators accurately from the air? Here is a regression analysis of the Weight of alligators (in pounds) and their Length (in inches) based on data collected about captured
Hard water In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 20 large towns. In addition, the water hardness was recorded as the calcium concentration (parts per million, ppm) in the drinking water. The
Heptathlon revisited again We saw the data for the women’s 2016 Olympic heptathlon in Exercise 73. Are the two jumping events associated? Perform a regression of the long-jump results on the high-jump results.a) What is the regression equation? What does the slope mean?b) What percentage of the
Body fat It is difficult to determine a person’s body fat percentage accurately without immersing him or her in water.Researchers hoping to find ways to make a good estimate immersed 20 male subjects, then measured their waists and recorded their weights shown in the table at the top of the next
Climate change 2016, revisited In Exercise 69, we saw the relationship between CO2 measured at Mauna Loa and average global temperature anomaly from 1959 to 2016. Here is a plot of average global temperatures plotted against the yearly final value of the Dow Jones Industrial Average for the same
Climate change 2016 The earth’s climate is getting warmer.The most common theory attributes the increase to an increase in atmospheric levels of carbon dioxide (CO2), a greenhouse gas. The mean annual carbon dioxide in parts per million (ppm)measured at the top of a mountain and the mean annual
Birthrates 2015 The table shows the number of live births per 1000 population in the United States, starting in 1965. (National Center for Health Statistics, www.cdc.govchs/)a) Make a scatterplot and describe the general trend in Birthrates. (Enter Year as years since 1900: 65, 70, 75, etc.)b) Find
Bridges We saw in this chapter that in a certain town, older bridges were in worse condition than newer ones. The given town is a rural area. Is this relationship true in cities as well?Here are data on the Condition (as measured by the state Department of Transportation Condition Index) and Age at
Cost of living 2016 A website records the cost of living (COL)for 100 cities around the world. It reports the typical cost of a number of staples. Here are a scatterplot and regression relating the cost of a cappuccino to the cost of a third of a liter of water:a) Using this information, describe
A second helping of burgers In Exercise 63, you created a model that can estimate the number of Calories in a burger when the Fat content is known.a) Explain why you cannot use that model to estimate the fat content of a burger with 600 calories.b) Using an appropriate model, estimate the fat
Chicken Chicken sandwiches are often advertised as a healthier alternative to beef because many are lower in fat. Tests on 11 brands of fast-food chicken sandwiches produced the following summary statistics and scatterplot from a graphing calculator:a) Do you think a linear model is appropriate in
Burgers revisited In Chapter 6, you examined the association between the amounts of Fat and Calories in fast-food hamburgers.Here are the data:a) Create a scatterplot of Calories vs. Fat.b) Interpret the value of R2 in this context.c) Write the equation of the line of regression.d) Use the
Veggie burger 2014 Burger King introduced a meat-free burger in 2002. The nutrition label for the 2014 BK Veggie burger (no mayo) is shown here: (Data in Burger King items)a) Use the regression model created in this chapter, Fat = 8.4 + 0.91 Protein, to predict the fat content of this burger from
More used cars 2014 Use the advertised prices for Toyota Corollas given in Exercise 59 to create a linear model for the relationship between a car’s Age and its Price.a) Find the equation of the regression line.b) Explain the meaning of the slope of the line.c) Explain the meaning of the
Drug abuse revisited Chapter 6, Exercise 42 examines results of a survey conducted in the United States and 10 countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. Below is the scatterplot. Summary statistics showed that the mean percent that
Used cars 2014 A website lists numerous used cars for sale within a 250-mile radius of a town. The table lists the ages of the cars and the advertised prices.a) Make a scatterplot for these data.b) Describe the association between Age and Price of a used car.c) Do you think a linear model is
Wildfires 2015—sizes We saw in Exercise 57 that the number of fires was nearly constant. But has the damage they cause remained constant as well? Here’s a regression that examines the trend in Acres per Fire (in hundreds of thousands of acres)together with some supporting plots:a) Is the
Wildfires 2015 The number of wildfires in a country has been declining. A scatterplot and analysis of the amount of land(in millions of acres) lost to wildfires is shown below.a) Is a linear model appropriate for these data? Explain.b) Interpret the slope in this context.c) Can we interpret the
SAT, take 2 Suppose we wanted to use SAT math scores to estimate verbal scores based on the information in Exercise 53.a) What is the correlation?b) Write the equation of the line of regression predicting verbal scores from math scores.c) In general, what would a positive residual mean in this
Success in college Colleges use SAT scores in the admissions process because they believe these scores provide some insight into how a high school student will perform at the college level.Suppose the entering freshmen at a certain college have mean combined SAT scores of 1247, with a standard
Interest rates and mortgages 2015 again In Chapter 6, Exercise 40, we saw a plot of mortgages in the United States(in trillions of 2013 dollars) vs. the interest rate at various times over the past 25 years. The correlation is r = -0.845. The mean mortgage amount is $8.207 T and the mean interest
Income and housing revisited In Chapter 6, Exercise 39, we learned that the Office of Federal Housing Enterprise Oversight(OFHEO) collects data on various aspects of housing costs around the United States. Here’s a scatterplot (by state) of the Housing Cost Index (HCI) vs. the Median Family
Attendance 2016, last inning Refer again to the regression analysis for home average attendance and games won by baseball teams, seen in Exercise 44.a) Write the equation of the regression line.b) Estimate the Home Average Attendance for a team with 750 Runs.c) Interpret the meaning of the slope of
Last cigarette Take another look at the regression analysis of tar and nicotine content of the cigarettes in Exercise 43.a) Write the equation of the regression line.b) Estimate the Nicotine content of cigarettes with 4 milligrams of Tar.c) Interpret the meaning of the slope of the regression line
Attendance 2016, revisited Consider again the regression of Home Average Attendance on Runs for the baseball teams examined in Exercise 44.a) What is the correlation between Runs and Home Average Attendance?b) What would you predict about the Home Average Attendance for a team that is 2 standard
Another cigarette Consider again the regression of Nicotine content on Tar (both in milligrams) for the cigarettes examined in Exercise 43.a) What is the correlation between Tar and Nicotine?b) What would you predict about the average Nicotine content of cigarettes that are 2 standard deviations
Attendance 2016, revisited In Chapter 6, Exercise 45 looked at the relationship between the number of runs scored by American League baseball teams and the average attendance at their home games for the 2016 season. Here are the scatterplot, the residuals plot, and part of the regression analysis
Cigarettes Is the nicotine content of a cigarette related to the“tar”? A collection of data (in milligrams) on 29 cigarettes produced the scatterplot, residuals plot, and regression analysis shown:a) Do you think a linear model is appropriate here? Explain.b) Explain the meaning of R2 in this
Last ride Consider the roller coasters (with the outlier removed)described in Exercise 30 again. The regression analysis gives the model Duration = 87.22 + 0.389 Drop.a) Explain what the slope of the line says about how long a roller coaster ride may last and the height of the coaster.b) A new
More real estate Consider the Albuquerque home sales from Exercise 29 again. The regression analysis gives the model Price = 47.82 + 0.061 Size.a) Explain what the slope of the line says about housing prices and house size.b) What price would you predict for a 3000-square-foot house in this
SI jinx Players in any sport who are having great seasons, turning in performances that are much better than anyone might have anticipated, often are pictured on the cover of Sports Illustrated. Frequently, their performances then falter somewhat, leading some athletes to believe in a “Sports
ESP People who claim to have “extrasensory perception (ESP)”participate in a screening test in which they have to guess which of several images someone is thinking of. You and a friend both took the test. You scored 2 standard deviations above the mean, and your friend scored 1 standard
Another ride The regression of Duration of a roller coaster ride on the height of its initial Drop, described in Exercise 30, had R2 = 29.4%.a) What is the correlation between Drop and Duration?b) What would you predict about the Duration of the ride on a coaster whose initial Drop was 1 standard
Real estate redux The regression of Price on Size of homes in Albuquerque had R2 = 71.4,, as described in Exercise 29.a) What is the correlation between Size and Price?b) What would you predict about the Price of a home 1 SD above average in Size?c) What would you predict about the Price of a home
More misinterpretations A sociology student investigated the association between a country’s Literacy Rate and Life Expectancy, and then drew the conclusions listed below. Explain why each statement is incorrect. (Assume that all the calculations were done properly.)a) The R2 of 64% means that
Misinterpretations A biology student who created a regression model to use a bird’s Height when perched for predicting its Wingspan made these two statements. Assuming the calculations were done correctly, explain what is wrong with each interpretation.a) My R2 of 93% shows that this linear model
Coasters 2015 again Exercise 30 examined the association between the Duration of a roller coaster ride and the height of its initial Drop, reporting that R2 = 29.4,. Write a sentence(in context, of course) summarizing what the R2 says about this regression.
Real estate again The regression of Price on Size of homes in Albuquerque had R2 = 71.4,, as described in Exercise 29.Write a sentence (in context, of course) summarizing what the R2 says about this regression.
What slope again? If you create a regression model for estimating the Height of a pine tree (in feet) based on the Circumference of its trunk (in inches), is the slope most likely to be 0.1, 1, 10, or 100? Explain.
What slope? If you create a regression model for predicting the Weight of a car (in pounds) from its Length (in feet), is the slope most likely to be 3, 30, 300, or 3000? Explain.
Coasters 2015, revisited The dataset on roller coasters lists the Duration of the ride in seconds in addition to the Drop height in feet for some of the coasters. One coaster (the “Tower of Terror”) is unusual for having a large drop but a short ride.After setting it aside, a regression to
Real estate A random sample of records of home sales from Feb. 15 to Apr. 30, 1993, from the files maintained by the Albuquerque Board of Realtors gives the Price and Size (in square feet) of 117 homes. A regression to predict Price(in thousands of dollars) from Size has an R2 of 71.4%. The
Last tank! For Exercise 16’s regression model predicting fuel economy (in mpg) from the car’s engine size, se = 3.522.Explain in this context what that means.
Last bowl! For Exercise 15’s regression model predicting potassium content (in milligrams) from the amount of fiber (in grams) in breakfast cereals, se = 30.77. Explain in this context what that means.
Another car The correlation between a car’s engine size and its fuel economy (in mpg) is r = -0.774. What fraction of the variability in fuel economy is accounted for by the engine size?
Cereal again The correlation between a cereal’s fiber and potassium contents is r = 0.903. What fraction of the variability in potassium is accounted for by the amount of fiber that servings contain?
More engine size In Exercise 16, the regression model CombinedMPG = 33.46 - 3.23 Displacement relates cars’engine size to their fuel economy (Combined mpg). Explain what the slope means.
Another bowl In Exercise 15, the regression model Potassium = 38 + 27 Fiber relates fiber (in grams) and potassium content (in milligrams) in servings of breakfast cereals.Explain what the slope means.
Engine size again Exercise 16 describes a regression model that uses a car’s engine displacement to estimate its fuel economy.In this context, what does it mean to say that a certain car has a positive residual?
More cereal Exercise 15 describes a regression model that estimates a cereal’s potassium content from the amount of fiber it contains. In this context, what does it mean to say that a cereal has a negative residual?
Engine size In Chapter 6, Exercise 41 we examined the relationship between the fuel economy (CombinedMPG) and Displacement (in liters) for 1211 models of cars. (Data in Fuel economy 2016) Further analysis produces the regression model CombinedMPG = 33.46 - 3.23 Displacement. If the car you are
Cereals For many people, breakfast cereal is an important source of fiber in their diets. Cereals also contain potassium, a mineral shown to be associated with maintaining a healthy blood pressure. An analysis of the amount of fiber (in grams)and the potassium content (in milligrams) in servings of
Disk drives 2016, residuals again Here is a scatterplot of the residuals from the regression of the hard drive prices on their sizes from Exercise 6.a) Are any assumptions or conditions violated? If so, which ones?b) What would you recommend about this regression? 300 100 0 Residuals -100 -300 0 10
Residual plots Here are residual plots (residuals plotted against predicted values) for three linear regression models.Indicate which condition appears to be violated (Linearity, Outlier, or Equal Spread) in each case. a) Residuals 20 15 10 5. -10- -15- -20 -10 0 10 20 30 40 50 60 70 Fitted Values
Disk drives encore For the hard drive data of Exercise 6, find and interpret the value of R2.
Bookstore sales last time For the regression model for the bookstore of Exercise 5, what is the value of R2 and what does it mean?
Disk drives 2016, residuals Here are the residuals for a regression of Price on Capacity for the hard drives of Exercise 6(based on the hand-computed coefficients).a) Which residual contributes the most to the sum that is minimized by the least squares criterion?b) Five of the residuals are
Bookstore sales once more Here are the residuals for a regression of Sales on Number of Sales People Working for the bookstore of Exercise 5:a) What are the units of the residuals?b) Which residual contributes the most to the sum that was minimized according to the least squares criterion to find
Sophomore slump again? An online investment blogger advises investing in mutual funds that have performed badly the past year because “regression to the mean tells us that they will do well next year.” Is he correct?
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