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Stats Data And Models 4th Edition Richard D. De Veaux, Paul D. Velleman, David E. Bock - Solutions

Suppose you have fit a linear model to some data and now take a look at the residuals. For each of the following possible residuals plots, tell whether you would try a re-expression and, if so, why.
A student experimenting with a pendulum counted the number of full swings the pendulum made in 20 seconds for various lengths of string. Her data are shown below.a) Explain why a linear model is not appropriate for using the Length of a pendulum to predict the Number of Swings in 20 seconds.b)
Ballplayers have been signing ever larger contracts. The highest salaries (in millions of dollars per season) for each year since 1874 is in the file on the CD. (Data in Baseball salaries 2013). Here are recent entries:a) Examine a scatterplot of the data. Does it look straight? b) Part of the
At a meeting of the International Astronomical Union (IAU) in Prague in 2006, Pluto was determined not to be a planet, but rather the largest member of the Kuiper belt of icy objects. Let's examine some facts. Here is a table of the 9 sun-orbiting objects formerly known as planets:a) Plot the
Let's look again at the pattern in the locations of the planets in our solar system seen in the table in Exercise 22.a) Re-express the distances to create a model for the Distance from the sun based on the planet's Position. b) Based on this model, would you agree with the International
The asteroid belt between Mars and Jupiter may be the remnants of a failed planet. If so, then Jupiter is really in position 6, Saturn is in 7, and so on. Repeat Exercise 23, using this revised method of numbering the positions. Which method seems to work better?Exercise 23Let's look again at the
The model you found in Exercise 22 is a relationship noted in the 17th century by Kepler as his Third Law of Planetary Motion. It was subsequently explained as a consequence of Newton's Law of Gravitation. The models for Exercises 23-25 relate to what is sometimes called the Titius-Bode "law," a
The value of a log is based on the number of board feet of lumber the log may contain. (A board foot is the equivalent of a piece of wood 1 inch thick, 12 inches wide, and 1 foot long. For example, a 2" Ã— 4" piece that is 12 feet long contains 8 board feet.) To estimate the amount of lumber in
Listed below are the Olympic record men's weight-lifting performances as of 2014.a) Create a linear model for the Weight Lifted in each Weight Class. b) Check the residuals plot. Is your linear model appropriate? c) Create a better model by re-expression Total Weight Lifted and explain how you
The data in the next column list the Life Expectancy for white males in the United States every decade during the past 110 years (1 = 1900 to 1910, 2 = 1911 to 1920, etc.). Create a model to predict future increases in life expectancy.
In Exercise 28 you examined the record weight-lifting performances for the Olympics. You found a re-expression of Total Weight Lifted.a) Find a model for Total Weight Lifted by re-expressing Weight Class instead of Total Weight Lifted.b) Compare this model to the one you found in Exercise 24.c)
Researchers studying how a car's Fuel Efficiency varies with its Speed drove a compact car 200 miles at various speeds on a test track. Their data are shown in the table.Create a linear model for this relationship and report any concerns you may have about the model.
The table below shows that as the number of oranges on a tree increases, the fruit tends to get smaller. Create a model for this relationship, and express any concerns you may have. Number of Average Oranges/Tree Weight/Fruit (lb) 50 ………………………… 0.60 100
Insurance companies and other organizations use actuarial tables to estimate the remaining lifespans of their customers. On the next page are the estimated additional years of life for black males in the United States, according to a 2013 National Vital Statistics Report.
A 1996 study examined the growth of grapefruit trees in Texas, determining the average trunk Diameter (in inches) for trees of varying Ages:a) Fit a linear model to these data. What concerns do you have about the model?b) If data had been given for individual trees instead of averages, would you
In Chapter 8, Exercise 9, we created a linear model describing the trend in the number of passengers departing from the Oakland (CA) airport each month since the start of 1997. Here's the residual plot, but with lines added to show the order of the values in time:a) Can you account for the pattern
In Chapter 4, we examined the wind speeds in the Hopkins forest over the course of a year. Here's the scatterplot we saw then (Data in Hopkins Forest 2011):a) Describe the pattern you see here.b) Should we try re-expressing either variable to make this plot straighter? Explain.
For each of the models listed below, predict y when x = 2.a) ln ŷ = 1.2 + 0.8xb) √ ŷ = 1.2 + 0.8xc) 1 / ŷ = 1.2 + 0.8xd) ŷ = 1.2 + 0.8 lnxe) log ŷ = 1.2 + 0.8 logx
For each of the following scenarios, decide if the outcome is random. a) Flip a coin to decide who takes out the trash. Is who takes out the trash random? b) A friend asks you to quickly name a professional sports team. Is the sports team named random? c) Names are selected out of a hat to decide
An elementary school teacher with 25 students plans to have each of them make a poster about two different states. The teacher first numbers the states (in alphabetical order, from 1-Alabama to 50-Wyoming), then uses a random number table to decide which states each student gets. Here are the
Your state's BigBucks Lottery prize has reached $100,000,000, and you decide to play. You have to pick five numbers between 1 and 60, and you'll win if your numbers match those drawn by the state. You decide to pick your "lucky" numbers using a random number table. Which numbers do you play, based
Explain why each of the following stimulations fails to model the real situation properly: a) Use a random integer from 0 through 9 to represent the number of heads when 9 coins are tossed. b) A basketball player takes a foul shot. Look at a random digit, using an odd digit to represent a good shot
Explain why each of the following simulations fails to model the real situation:a) Use random numbers 2 through 12 to represent the sum of the faces when two dice are rolled.b) Use a random integer from 0 through 5 to represent the number of boys in a family of 5 children.c) Simulate a baseball
You're pretty sure that your candidate for class president has about 55% of the votes in the entire school. But you're worried that only 100 students will show up to vote. How often will the underdog (the one with 45% support) win? To find out, you set up a simulation.a) Describe how you will
For each of the following scenarios, decide if the outcome is random. a) You enter a contest in which the winning ticket is selected from a large drum of entries. Was the winner of the contest random? b) When playing a board game, the number of spaces you move is decided by rolling a six-sided die.
When drawing five cards randomly from a deck, which is more likely, two pairs or three of a kind? A pair is exactly two of the same denomination. Three of a kind is exactly 3 of the same denomination. (Don't count three 8's as a pair—that's 3 of a kind. And don't count 4 of the same kind as two
In the chapter's example, 20% of the cereal boxes contained a picture of Hope Solo, 30% Danica Patrick, and the rest Blake Griffin. Suppose you buy five boxes of cereal. Estimate the probability that you end up with a complete set of the pictures. Your simulation should have at least 20 runs.
Suppose you really want the Hope Solo picture. How many boxes of cereal do you need to buy to be pretty sure of getting at least one? First, define what "pretty sure" means to you. Then run a simulation with at least 10 trials.
You take a quiz with 6 multiple choice questions. After you studied, you estimated that you would have about an 80% chance of getting any individual question right. What are your chances of getting them all right? Use at least 20 trials.
A friend of yours who took the multiple choice quiz in Exercise 23 got all 6 questions right, but now claims to have guessed blindly on every question. If each question offered 4 possible answers, do you believe her? Explain, basing your argument on a simulation involving at least 10 trials.
You are about to take the road test for your driver's license. You hear that only 34% of candidates pass the test the first time, but the percentage rises to 72% on subsequent retests. Estimate the average number of tests drivers take in order to get a license. Your simulation should use at least
As in Exercise 29, assume that your chance of passing the driver's test is 34% the first time and 72% for subsequent retests. Estimate the percentage of those tested who still do not have a driver's license after two attempts.
Late in NCAA basketball games, foul shots are often "one and one," meaning a player gets a second shot only if he makes the first shot. Suppose a player has made 72% of his foul shots this season. Estimate the number of points he will score in a one-and-one situation.
A person with type O-positive blood can receive blood only from other type O donors. About 44% of the U.S. population has type O blood. At a blood drive, how many potential donors do you expect to examine in order to get three units of type O blood?
To attract shoppers, a supermarket runs a weekly contest that involves "scratch-off" cards. With each purchase, customers get a card with a black spot obscuring a message. When the spot is scratched away, most of the cards simply say, "Sorry—please try again.” But during the week, 100 customers
A technology store holds a contest to attract shoppers. Once an hour, someone at checkout is chosen at random to play in the contest. Here's how it works: An ace and four other cards are shuffled and placed face down on a table. The customer gets to turn over cards one at a time, looking for the
Many couples want to have both a boy and a girl. If they decide to continue to have children until they have one child of each sex, what would the average family size be? Assume that boys and girls are equally likely.
Suppose a couple will continue having children until they have at least two children of each sex (two boys and two girls). How many children might they expect to have?
You are playing a children's game in which the number of spaces you get to move is determined by the rolling of a die. You must land exactly on the final space to win. If you are 10 spaces away, how many turns might it take you to win?
You are three spaces from a win in Parcheesi. On each turn, you will roll two dice. To win, you must roll a total of 3 or roll a 3 on one of the dice. How many turns might you expect this to take?
A basketball player with a 65% shooting percentage has just made 6 shots in a row. The announcer says this player "is hot tonight! She's in the zone!" Assume the player takes about 20 shots per game. Is it unusual for her to make 6 or more shots in a row during a game?
The World Series ends when a team wins 4 games. Suppose that sports analysts consider one team a bit stronger, with a 55% chance to win any individual game. Estimate the likelihood that the underdog wins the series.
Four couples at a dinner party play a board game after the meal. They decide to play as teams of two and to select the teams randomly. All eight people write their names on slips of paper. The slips are thoroughly mixed, then drawn two at a time. How likely is it that every person will be teamed
Suppose the couples in Exercise 41 choose the teams by having one member of each couple write their names on the cards and the other people each pick a card at random. How likely is it that every person will be teamed with someone other than the person he or she came with?
A company with a large sales staff announces openings for three positions as regional managers. Twenty-two of the current salespersons apply, 12 men and 10 women. After the interviews, when the company announces the newly appointed managers, all three positions go to women. The men complain of job
A proud legislator claims that your state's new law banning texting and hand-held phones while driving reduced occurrences of infractions to less than 10% of all drivers. While on a long drive home from your college, you notice a few people seemingly texting. You decide to count everyone using
For the board game described in Exercise 3, how will you combine components to model a trial? What is the response variable? Exercise 3 Playing a board game", you are stuck in jail until you roll "doubles" (same numbers) on a pair of dice. You will simulate using random digits to estimate how many
For the burger joint contest described in Exercise 4, how will you combine components to model a trial? What is the response variable? Exercise 4 Your local burger joint gives away a game piece with each purchase. Game pieces are labeled Burger, Fries, and Shake and are equally likely to be
Many states run lotteries, giving away millions of dollars if you match a certain set of winning numbers. How are those numbers determined? Do you think this method guarantees randomness? Explain.
Many kinds of games people play rely on randomness. Cite three different methods commonly used in the attempt to achieve this randomness, and discuss the effectiveness of each.
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 student
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 employee with the
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 500
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 200 contained 50 first-year students, 50 sophomores, 50 juniors, and 50 seniors. a) Do you think the group was using an SRS? Why? b)
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 40 players on the team. Each testing day can be considered a study of drug use in Major League Baseball. a) What
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, 2014....
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 20% of those responding reported cures or substantial improvement in their condition. Identify the following
A question posted on the gamefaqs.com website on August 1, 2011, 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." Identify the following items (if possible). If you
Hoping to learn what issues may resonate with voters in the coming election, the campaign director for a mayoral candidate selects one block from each of the city's election districts. Staff members go there and interview all the adult residents they can find. Identify the following items (if
Administrators at Texas A&M University were interested in estimating the percentage of students who are the first in their family to go to college. The A&M student body has about 46,000 members. How might the administrators answer their question by applying the three Big Ideas?
The Environmental Protection Agency took soil samples at 16 locations near a former industrial waste dump and checked each for evidence of toxic chemicals. They found no elevated levels of any harmful substances. Identify the following items (if possible). If you can't tell, then say so—this
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 10% of the cars they stop. Identify the following items (if possible). If you can't tell, then say so—this often
A company packaging snack foods maintains quality control by randomly selecting 10 cases from each day's production and weighing the bags. Then they open one bag from each case and inspect the contents. Identify the following items (if possible). If you can't tell, then say so—this often happens
Dairy inspectors visit farms unannounced and take samples of the milk to test for contamination. If the milk is found to contain dirt, antibiotics, or other foreign matter, the milk will be destroyed and the farm reinspected until purity is restored. Identify the following items (if possible). If
A local TV station conducted a "Pulse-Poll" 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% of the vote. They
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% of the vote. The
In a large city school system with 20 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 plan. Listed below are
Let's revisit the school system described in Exercise 26. 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
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 17 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 churches at
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 10th person on the line for the roller
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 and students be held
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 ephedra is
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 18-year-olds are old enough to vote and to serve in
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 P.M., and interview whoever answers, anticipating contacts with at least 200 people. a) Why is it difficult to use a simple
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 changed over time?
How long is your arm compared with your hand size? Put your right thumb at your left shoulder bone, stretch your hand open wide, and extend your hand down your arm. Put your thumb at the place where your little finger is, and extend down the arm again. Repeat this a third time. Now your little
Occasionally, when I fill my car with gas, I figure out how many miles per gallon my car got. I wrote down those results after six fill-ups in the past few months. Overall, it appears my car gets 28.8 miles per gallon. a) What statistic have I calculated? b) What is the parameter I'm trying to
Between quarterly audits, a company likes to check on its accounting procedures to address any problems before they become serious. The accounting staff processes payments on about 120 orders each day. The next day, the supervisor rechecks 10 of the transactions to be sure they were processed
A manufacturing company employs 14 project managers, 48 supervisors, and 377 laborers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a sample of employees every month.a) Do you see any potential danger
Sammy's Salsa, a small local company, produces 20 cases of salsa a day. Each case contains 12 jars and is imprinted with a code indicating the date and batch number. To help maintain consistency, at the end of each day, Sammy selects three jars of salsa, weighs the contents, and tastes the product.
Concerned about reports of discolored scales on fish caught downstream from a newly sited chemical plant, scientists set up a field station in a shoreline public park. For one week, they asked fishermen there to bring any fish they caught to the field station for a brief inspection. At the end of
Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. a) We want to know what percentage of local doctors accepts Medicaid patients. We call the offices of 50 doctors randomly selected from local Yellow Pages listings. b) We want to know what
Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. a) We want to know if there is neighborhood support to turn a vacant lot into a playground. We spend a Saturday afternoon going door-to-door in the neighborhood, asking people to sign a
A professor teaching a large lecture class of 350 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 everyone had an equal
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 sophomores, 200 juniors,
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 those employed for more than 10
What problems do you see with asking the following question of students? "Are you the first member of your family to seek higher education?"
The 1990s and early 2000s could be considered the steroids era in Major League Baseball, as many players have admitted to using the drug to increase performance on the field. If a sports writer wanted to compare home run totals from the steroids era to an earlier decade, say the 1960s, explain why
If the tomato taster doesn't know how the tomatoes have been treated, is the experiment single or double-blind? How might the blinding be improved further?
The driver of Exercise 3 wants to know about tipping in general. So he recruits several other drivers to participate in the experiment. Each driver randomly decides whether to phone customers before delivery and records the tip percentage. Is this experiment blocked? Is that a good idea?
For his Statistics class experiment, researcher J. Gilbert decided to study how parents' income affects children's performance on standardized tests like the SAT. He proposed to collect information from a random sample of test takers and examine the relationship between parental income and SAT
Researchers who examined health records of thousands of males found that men who died of myocardial infarction (heart attack) tended to be shorter than men who did not.a) Is this an experiment? If not, what kind of study is it?b) Is it correct to conclude that shorter men are at higher risk of
Multiple sclerosis (MS) is an autoimmune disease that strikes more often the farther people live from the equator. Could vitamin D—which most people get from the sun's ultraviolet rays—be a factor? Researchers compared vitamin D levels in blood samples from 150 U.S. military personnel who have
When spending large amounts to purchase advertising time, companies want to know what audience they'll reach. In January 2011, a poll asked 1008 American adults whether they planned to watch the upcoming Super Bowl. Men and women were asked separately whether they were looking forward more to the
Researchers studied the herb black cohosh as a treatment for hot flashes caused by menopause. They randomly assigned 351 women aged 45 to 55 who reported at least two hot flashes a day to one of five groups: (1) black cohosh, (2) a multiherb supplement with black cohosh, (3) the multiherb
A business student conjectures that the Internet caused companies to become more profitable, since many transactions previously handled "face-to-face" could now be completed online. The student compares earnings from a sample of companies from the 1980s to a sample from the 2000s. Explain why this
Coffee stations in offices often just ask users to leave money in a tray to pay for their coffee, but many people cheat. Researchers at Newcastle University replaced the picture of flowers on the wall behind the coffee station with a picture of staring eyes. They found that the average contribution
Over a 4-month period, among 30 people with bipolar disorder, patients who were given a high dose (10 g/day) of omega-3 fats from fish oil improved more than those given a placebo. Read each brief report of statistical research, and identify a) Whether it was an observational study or an
Among a group of disabled women aged 65 and older who were tracked for several years, those who had a vitamin B12 deficiency were twice as likely to suffer severe depression as those who did not.Read each brief report of statistical research, and identifya) Whether it was an observational study or
In a test of roughly 200 men and women, those with moderately high blood pressure (averaging 164/89 mm Hg) did worse on tests of memory and reaction time than those with normal blood pressure.Read each brief report of statistical research, and identifya) Whether it was an observational study or an

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