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intro stats
Intro Stats 4th International Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions
Tomatoes finis What factors might confound the results of the experiment in Exercise 4?
Confounded tips For the experiment of Exercise 3, name some confounding variables that might influence the experiment’s results?
Blocking tomatoes To obtain enough plants for the tomato experiment of Exercise 4, experimenters have to purchase plants from two different garden centers.They then randomly assign the plants from each garden center to all three fertilizer treatments. Is the experiment blocked? Is that a good idea?
Block that tip 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
Tomatoes again For the experiment of Exercise 4, discuss variables that could be controlled or that could not be controlled. Is the experiment randomized and replicated?
Tips again For the experiment of Exercise 3, name some variables the driver did or should have controlled. Was the experiment randomized and replicated?
Tomatoes again For the experiment of Exercise 4, discuss variables that could be controlled or that could not be controlled. Is the experiment randomized and replicated?
Tips again For the experiment of Exercise 3, name some variables the driver did or should have controlled. Was the experiment randomized and replicated?
Tomatoes II For the experiment described in Exercise 4, name the factor and its levels. How might the response be measured?
Tips II For the experiment described in Exercise 3, list the factor, the levels, and the response variable.
Tomatoes You want to compare the tastiness and juiciness of tomatoes grown with three amounts of a new fertilizer: none, half the recommended amount, and the full recommended amount. You allocate 6 tomato plants to receive each amount of fertilizer, assigning them at random. What are the
Tips A pizza delivery driver, always trying to increase tips, runs an experiment on his next 40 deliveries. He flips a coin to decide whether or not to call a customer from his mobile phone when he is five minutes away, hoping this slight bump in customer service will lead to a slight bump in tips.
E-commerce 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.
Steroids 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,
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 Pages 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 jars of salsa, weighs the contents, and
Happy workers? 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
40. 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
39. 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 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
38. 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
37. 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
36. 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 p.m., and interview whoever answers, anticipating contacts with at least 200 people.a) Why is it difficult to
35. 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
34. 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
33. 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
32. 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
31. 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
30. 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
29. 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
28. 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
27. Parent opinion, part 2 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
26. Parent opinion, part 1 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
25. 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
24. Mistaken poll 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
23. Milk samples 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.
22. Snack foods 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.
21. 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 10% of the cars they stop.
20. Soil samples 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.
19. Mayoral race 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.
18. Social life 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.”
17. 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 20% of those responding reported cures or substantial improvement in their condition.
16. 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 July
15. 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
14. 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
13. 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
12. 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
11. 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
10. 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?
9. 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?”
8. 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
7. 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
6. 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 7. Is this a simple random sample?
5. Sampling students 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
4. 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.
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
2. 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 24,000 employees. They contacted a random sample of employees and asked them about their job satisfaction, obtaining 437 completed
1. Texas A&M 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 ?
44. Smartphones 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
43. 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.
42. Second team 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?
41. 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
40. 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.
39. 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?
38. 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?
37. 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 to win. If you are 10 spaces away, how many turns might it take you to win?
36. 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?
35. 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.
34. Find the ace 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,
33. 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
32. 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?
31. Basketball strategy 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-andone situation.
30. Still learning? 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.
29. 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
28. Play the winner? Another strategy for beating the lottery is the reverse of the system described in Exercise 27.Simulate the simplified lottery described in Exercise 25.Each time, bet the number that just turned up. The website suggests that this method should do worse. Does it?Play many games
27. It evens out in the end The “beat the lottery” website of Exercise 25 notes that in the long run we expect each value to turn up about the same number of times. That leads to their recommended strategy. First, watch the lottery for a while, recording the winners. Then bet the value that has
26. Random is as random does The “beat the lottery”website discussed in Exercise 25 suggests that because lottery numbers are random, it is better to select your bet randomly. For the same simple lottery in Exercise 25(random values from 0 to 9), generate each bet by choosing a separate random
25. Beat the lottery Many states run lotteries to raise money.A website 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
24. Lucky guessing? 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
23. 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? Use at least 20 trials.
22. Cereal, again 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.
21. Cereal 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. 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
19. 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
18. 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?
17. 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?
16. More bad simulations 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
15. 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 when 9 coins are tossed.b) A basketball player takes a foul shot. Look at a random digit, using an odd digit to
14. Play it again, Sam In Exercise 12, you imagined playing the lottery by using random digits to decide what numbers to play. Is this a particularly good or bad strategy?Explain.
13. Play the lottery Some people play state-run lotteries by always playing the same favorite “lucky” numbers.Assuming that the lottery is truly random, is this strategy better, worse, or the same as choosing different numbers for each play? Explain.
12. 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
11. 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 student gets. Here
10. 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 percentage?
9. 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 proportion?
8. 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.
7. 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.
6. Response variable, take two For the burger joint contest described in Exercise 4, how will you combine components to model a trial? What is the response variable?
5. Response variable For the board game described in Exercise 3, how will you combine components to model a trial? What is the response variable?
4. More components 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 received. You will simulate to estimate how many purchases you will need to collect the entire set to win a free meal. Identify the
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