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inferential statistics
Stats Modeling The World AP Edition Grades 9-12 3rd Edition David E. Bock, Paul F. Velleman, Richard D. De Veaux - Solutions
Super Bowl commercials. When spending large amounts to purchase advertising time, companies want to know what audience they ll reach. In January 2007, a poll asked 1008 American adults whether they planned to watch the upcoming Super Bowl. Men and women were asked separately whether they were
MS and vitamin D. 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
Heart attacks and height. 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
Standardized test scores. 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
More sampling methods. 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
Sampling methods. 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 accept Medicaid patients. We call the offices of 50 doctors randomly selected from local Yellow Page listings.b) We want to know
A fish story. 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
Quality control. 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 bottles of salsa, weighs the contents, and
Happy workers? A manufacturing company employs 14 project managers, 48 foremen, 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 danger
Accounting. 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
Fuel economy. 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 6 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
Arm length. 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
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. Anytime 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
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 favor
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 18-year-olds are old enough to vote
Playground, act two. The survey described in Exercise 24 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
Another ride. The survey of patrons waiting in line for the roller coaster in Exercise 23 asks whether they think it is worthwhile to wait a long time for the ride and whether they d like the amusement park to install still more roller coasters. What biases might cause a problem for this survey?
Banning ephedra. An online poll at a popular Web site 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
Wording the survey. Two members of the PTA committee in Exercises 19 and 20 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?326 CHAPTER 12 Sample Surveys
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
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 10th person on the
Fish. The U.S. Fish and Wildlife Service plans to study the kinds of fish being taken out of Saginaw Bay. To do that, they decide to randomly select 5 fishing boats at the end of a randomly chosen fishing day and to count the numbers and types of all the fish on those boats.a) What kind of design
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 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
Parent opinion, part 2. Let s revisit the school system described in Exercise 19. 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
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
Parent opinion, part
Another mistaken poll. Prior to the mayoral election discussed in Exercise 17, 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 to predict the winner in the upcoming mayoral election. Evening news viewers were invited to phone in their votes, with the results to be announced on the late-night news. Based on the phone calls, the station predicted that Amabo would win
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.
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.
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.
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.
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 residents they can find.
Researchers waited outside a bar they had randomly selected from a list of such establishments. They stopped every 10th person who came out of the bar and asked whether he or she thought drinking and driving was a serious problem.
The Gallup Poll interviewed 1007 randomly selected U.S.adults aged 18 and older, March 23 25, 2007. Gallup reports that when asked when (if ever) the effects of global warming will begin to happen, 60% of respondents said the effects had already begun. Only 11% thought that they would never happen.
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.
A question posted on the Lycos Web site on 18 June 2000 asked visitors to the site to say whether they thought that marijuana should be legally available for medicinal purposes. (www.lycos.com)
A business magazine mailed a questionnaire to the human resource directors of all Fortune 500 companies, and received responses from 23% of them. Those responding reported that they did not find that such surveys intruded significantly on their work day.
Gallup World. At its Web site (www.gallupworldpoll.com) the Gallup World Poll reports results of surveys conducted in various places around the world. At the end of one of these reports, they describe their methods, including explanations such as the following:
Gallup. At its Web site (www.galluppoll.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 1,008 national adults, aged 18 and older, conducted April 2 5,
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 40 players on the team.Each testing day can be considered a study of drug use in Major League
Emoticons. The Web site www.gamefaqs.com asked, as their question of the day to which visitors to the site were invited to respond, Do you ever use emoticons when you type online? Of the 87,262 respondents, 27% said that they did not use emoticons. ;-(a) What kind of sample was this?b) How much
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 200 contained 50 first-year students, 50 sophomores, 50 juniors, and 50 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
Tires. A tire manufacturer believes that the tread life of its snow tires can be described by a Normal model with mean of 32,000 miles and a standard deviation of 2500 miles. You buy four of these tires, hoping to drive them at least 30,000 miles. Estimate the chances that all four last at least
Admissions officers search the pile of envelopes, opening them at random to look for three applicants with SAT totals over 1800. How many envelopes do you think they will need to open?
Freshmen. A certain college estimates that the 3-score SAT total for students who apply for admission can be described by a Normal model with a mean of 1570 and a standard deviation of
Cell phones. A proud legislator claims that your state s new law against talking on a cell phone while driving has reduced cell phone use to less than 12% of all drivers. While waiting for your bus the next morning, you notice that 4 of the 10 people who drive by are using their cell phones. Does
Job discrimination? 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
Second team. Suppose the couples in Exercise 37 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?
Teammates. 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
The World Series. 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.
The hot hand. 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?
Parcheesi. 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?
Dice game. 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 in order to win. If you are 10 spaces away, how many turns might it take you to win?
A bigger family. 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?
The family. 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.
Find the ace. A new electronics store holds a contest to attract shoppers. Once an hour someone in the store is chosen at random to play the Music Game. 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 cards over one at a time,
Free groceries. 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
Blood donors. 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?
Basketball strategy. Late in a basketball game, the team that is behind often fouls someone in an attempt to get the ball back. Usually the opposing player will get to shoot foul shots one and one, meaning he gets a shot, and then a second shot only if he makes the first one.Suppose the opposing
Still learning? As in Exercise 25, 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.
Driving test. 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
Play the winner? Another strategy for beating the lottery is the reverse of the system described in Exercise 23.Simulate the simplified lottery described in Exercise 21.Each time, bet the number that just turned up. The Web site suggests that this method should do worse. Does it?Play many games and
It evens out in the end. The beat the lottery Web site of Exercise 21 notes that in the long run we expect each value to turn up about the same number of times.That leads to their recommended betting strategy. First, watch the lottery for a while, recording all the winners.Then bet the value that
Play many games. What proportion of the time do you win?
Random is as random does. The beat the lottery Web site discussed in Exercise 21 suggests that because lottery numbers are random, it is better to select your bet randomly. For the same simple lottery in Exercise 21 (random values from 0 to 9), generate each bet by choosing a separate random value
Beat the lottery. Many states run lotteries to raise money. A Web site advertises that it knows how to increase YOUR chances of Winning the Lottery. They offer several systems and criticize others as foolish. One system is called Lucky Numbers. People who play the Lucky Numbers system just pick a
Lucky guessing? A friend of yours who took the multiple choice quiz in Exercise 19 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
Multiple choice. 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? Your simulation should use at least 20 runs.
Cereal, again. Suppose you really want the Tiger Woods picture. How many boxes of cereal do you need to buy to be pretty sure of getting at least one? Your simulation should use at least 10 runs.
Cereal. In the chapter s example, 20% of the cereal boxes contained a picture of Tiger Woods, 30% David Beckham, and the rest Serena Williams. Suppose you 3 5 atriple 4 5 ahome run 0 5 an out 1 5 asingle 2 5 adouble buy five boxes of cereal. Estimate the probability that you end up with a complete
Two pair, or three of a kind? 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
Election. 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
Another wrong conclusion. After simulating the spread of a disease, a researcher wrote, 24% of the people contracted the disease. What should the correct conclusion be?
Wrong conclusion. A Statistics student properly simulated the length of checkout lines in a grocery store and then reported, The average length of the line will be 3.2 people. What s wrong with this conclusion?
More bad simulations. Explain why each of the following simulations fails to model the real situation properly: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
Bad simulations. Explain why each of the following simulations fails to model the real situation properly:a) Use a random integer from 0 through 9 to represent the number of heads that appear when 9 coins are tossed.b) A basketball player takes a foul shot. Look at a random digit, using an odd
Play it again, Sam. In Exercise 8 you imagined playing the lottery by using random digits to decide what numbers to play. Is this a particularly good or bad strategy? Explain.
Play the lottery. Some people play state-run lotteries by always playing the same favorite lucky number.Assuming that the lottery is truly random, is this strategy better, worse, or the same as choosing different numbers for each play? Explain.
Get rich. 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
Geography. 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 kid gets. Here are the
Colorblind. By some estimates, about 10% of all males have some color perception defect, most commonly red green colorblindness. How would you assign random numbers to conduct a simulation based on this statistic?
Birth defects. The American College of Obstetricians and Gynecologists says that out of every 100 babies born in the United States, 3 have some kind of major birth defect. How would you assign random numbers to conduct a simulation based on this statistic?
Games. 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 lottery. 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.
Casino. A casino claims that its electronic video roulette machine is truly random. What should that claim mean?
Coin toss. Is a coin flip random? Why or why not, in your opinion?
Least squares. Consider the four points (12,800),(24,680), (36,740), and (48,660). The line of best fit is. Use these data to explain what least squares means.
Chips. A start-up company has developed an improved electronic chip for use in laboratory equipment. The company needs to project the manufacturing cost, so it develops a spreadsheet model that takes into account the purchase of production equipment, overhead, raw materials, depreciation,
Down the drain. Most water tanks have a drain plug so that the tank may be emptied when it s to be moved or repaired. How long it takes a certain size of tank to drain depends on the size of the plug, as shown in the table.Create a model.
Profit. How are a company s profits related to its sales?Let s examine data from 71 large U.S. corporations. All amounts are in millions of dollars.a) Here are histograms of Profits and Sales and histograms of the logarithms of Profits and Sales. Why are the re-expressed data better for regression?
Vehicle weights. The Minnesota Department of Transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed weigh-in-motion scale. After installation of the scale, a study was conducted to find out whether the scale s
Williams vs. Texas. Here are the average weights of the football team for the University of Texas for various years in the 20th century
Models. Find the predicted value of y, using each model for .a)b)c)
Football weights. The Sears Cup was established in 1993 to honor institutions that maintain a broad-based athletic program, achieving success in many sports, both men s and women s. Since its Division III inception in 1995, the cup has been won by Williams College in every year except one. Their
Tobacco and alcohol. Are people who use tobacco products more likely to consume alcohol? Here are data on household spending (in pounds) taken by the British Government on 11 regions in Great Britain. Do tobacco and alcohol spending appear to be related? What questions do you have about these data?
Gasoline. Since clean-air regulations have dictated the use of unleaded gasoline, the supply of leaded gas in New York state has diminished. The table below was given on the August 2001 New York State Math B exam, a statewide achievement test for high school students.
The table and graph show the number of minutes the kids stayed at the table and the number of calories they consumed.
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