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Stats Data And Models (Subscription) 3rd Edition Richard D De Veaux, Paul D Velleman, David E Bock - Solutions
Anorexia, again. In Exercise 14 you used a confidence interval to examine the effectiveness of Prozac in treating anorexia nervosa. Suppose that instead you had conducted a hypothesis test. (Answer these questions without actually doing the test.)a) What hypotheses would you test?b) State a
Another ear infection. In Exercise 13 you used a confidence interval to examine the effectiveness of a vaccine against ear infections in babies. Suppose that instead you had conducted a hypothesis test. (Answer these questions without actually doing the test.)a) What hypotheses would you test?b)
Anorexia. The Journal of the American Medical Association reported on an experiment intended to see if the drug Prozac® could be used as a treatment for the eating disorder anorexia nervosa. The subjects, women being treated for anorexia, were randomly divided into two groups. Of the 49 who
Ear infections. A new vaccine was recently tested to see if it could prevent the painful and recurrent ear infections that many infants suffer from. The Lancet, a medical journal, reported a study in which babies about a year old were randomly divided into two groups. One group received
Carpal tunnel. The painful wrist condition called carpal tunnel syndrome can be treated with surgery or less invasive wrist splints. In September 2002, Time magazine reported on a study of 176 patients. Among the half that had surgery, 80% showed improvement after three months, but only 48% of
Pets. Researchers at the National Cancer Institute released the results of a study that investigated the effect of weed-killing herbicides on house pets. They examined 827 dogs from homes where an herbicide was used on a regular basis, diagnosing malignant lymphoma in 473 of them. Of the 130 dogs
Graduation. In October 2000 the U.S. Department of Commerce reported the results of a large-scale survey on high school graduation. Researchers contacted more than 25,000 Americans aged 24 years to see if they had finished high school; 84.9% of the 12,460 males and 88.1% of the 12,678 females
Arthritis. The Centers for Disease Control and Prevention reported a survey of randomly selected Americans age 65 and older, which found that 411 of 1012 men and 535 of 1062 women suffered from some form of arthritis.a) Are the assumptions and conditions necessary for inference satisfied?
Buy it again? A consumer magazine plans to poll car owners to see if they are happy enough with their vehicles that they would purchase the same model again.They’ll randomly select 450 owners of American-made cars and 450 owners of Japanese models. Obviously, the actual opinions of the entire
Gender gap. Apresidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They’ll randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. Obviously, the staff can’t know this, but
Regulating access. When a random sample of 935 parents were asked about rules in their homes, 77% said they had rules about the kinds of TV shows their children could watch. Among the 790 of those parents whose teenage children had Internet access, 85% had rules about the kinds of Internet sites
Revealing information. 886 randomly sampled teens were asked which of several personal items of information they thought it okay to share with someone they had just met. 44% said it was okay to share their e-mail addresses, but only 29% said they would give out their cell phone numbers. A
Origins. In a 1993 Gallup poll, 47% of the respondents agreed with the statement “God created human beings pretty much in their present form at one time within the last 10,000 years or so.” When Gallup asked the same question in 2001, only 45% of those respondents agreed. Is it reasonable to
Name recognition. Apolitical candidate runs a weeklong series of TV ads designed to attract public attention to his campaign. Polls taken before and after the ad campaign show some increase in the proportion of voters who now recognize this candidate’s name, with a P-value of 0.033.Is it
Science news. In 2007 a Pew survey asked 1447 Internet users about their sources of news and information about science. Among those who had broadband access at home, 34% said they would turn to the Internet for most EXERCISES of their science news. The report on this survey claims that this is not
Online social networking. The Parents & Teens 2006 Survey of 935 12- to 17-year-olds found that, among teens aged 15–17, girls were significantly more likely to have used social networking sites and online profiles.70% of the girls surveyed had used an online social network, compared to 54% of
Pottery. An artist experimenting with clay to create pottery with a special texture has been experiencing difficulty with these special pieces. About 40% break in the kiln during firing. Hoping to solve this problem, a ashe buys some more expensive clay from another supplier. She plans to make and
Did the player prove that he has improved?a) Suppose the player really is no better than before—still a 60% shooter. What’s the probability he can hit at least 9 of 10 shots anyway? (Hint: Use a Binomial model.)b) If that is what happened, now the coach thinks the player has improved when he
Hoops. A basketball player with a poor foul-shot record practices intensively during the off-season. He tells the coach that he has raised his proficiency from 60% to 80%.Dubious, the coach asks him to take 10 shots, and is surprised when the player hits 9 out of
Faulty or not? You are in charge of shipping computers to customers. You learn that a faulty disk drive was put into some of the machines. There’s a simple test you can perform, but it’s not perfect. All but 4% of the time, a good disk drive passes the test, but unfortunately, 35% of the bad
Two coins. In a drawer are two coins. They look the same, but one coin produces heads 90% of the time when spun while the other one produces heads only 30% of the time. You select one of the coins. You are allowed to spin it once and then must decide whether the coin is the 90%- or the 30%-head
Testing the ads. The company in Exercise 28 contacts 600 people selected at random, and only 133 remember the ad.a) Should the company renew the contract? Support your recommendation with an appropriate test.b) Explain what your P-value means in this context.
They used the software suggested by the salesman, and only 11 dropped out of the course.a) Should the professor spend the money for this software? Support your recommendation with an appropriate test.b) Explain what your P-value means in this context.
Dropouts, part II. Initially, 203 students signed up for the Stats course in Exercise
Ads. A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than 20% of the residents of the city have heard the ad and recognize the company’s product.The radio station conducts a random phone survey of 400 people.a) What are the
Dropouts. A Statistics professor has observed that for several years about 13% of the students who initially enroll in his Introductory Statistics course withdraw before the end of the semester. A salesman suggests that he try a statistics software package that gets students more involved with
How would this affect the power of the test? Explain.
Stop signs. Highway safety engineers test new road signs, hoping that increased reflectivity will make them more visible to drivers. Volunteers drive through a test course with several of the new- and old-style signs and rate which kind shows up the best.a) Is this a one-tailed or a two-tailed
Equal opportunity? A company is sued for job discrimination because only 19% of the newly hired candidates were minorities when 27% of all applicants were minorities. Is this strong evidence that the company’s hiring practices are discriminatory?a) Is this a one-tailed or a two-tailed test?
Production. Consider again the task of the quality control inspectors in Exercise 22.a) In this context, what is meant by the power of the test the inspectors conduct?b) They are currently testing 5 items each hour. Someone has proposed that they test 10 instead. What are the advantages and
Cars, again. As in Exercise 21, state regulators are checking up on repair shops to see if they are certifying vehicles that do not meet pollution standards.a) In this context, what is meant by the power of the test the regulators are conducting?b) Will the power be greater if they test 20 or 40
Quality control. Production managers on an assembly line must monitor the output to be sure that the level of defective products remains small. They periodically inspect a random sample of the items produced. If they find a significant increase in the proportion of items that must be rejected, they
Testing cars. Aclean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample of cars that a suspect repair
Alzheimer’s. Testing for Alzheimer’s disease can be a long and expensive process, consisting of lengthy tests and medical diagnosis. A group of researchers (Solomon et al., 1998) devised a 7-minute test to serve as a quick screen for the disease for use in the general population of senior
Homeowners 2005. In 2005 the U.S. Census Bureau reported that 68.9% of American families owned their homes. Census data reveal that the ownership rate in one small city is much lower. The city council is debating a plan to offer tax breaks to first-time home buyers in order to encourage people to
When the points assigned to various components of an e-mail exceed the cutoff value you’ve set, the filter rejects its null hypothesis (that the message is real) and diverts that e-mail to a junk mailbox.a) In this context, what is meant by the power of the test?b) What could you do to increase
More spam. Consider again the points-based spam filter described in Exercise
Second loan. Exercise 15 describes the loan score method a bank uses to decide which applicants it will lend money.Only if the total points awarded for various aspects of an applicant’s financial condition fail to add up to a minimum cutoff score set by the bank will the loan be denied.a) In this
Is that analogous to choosing a higher or lower value of for a hypothesis test? Explain.d) What impact does this change in the cutoff value have on the chance of each type of error?
Spam. Spam filters try to sort your e-mails, deciding which are real messages and which are unwanted. One method used is a point system. The filter reads each incoming e-mail and assigns points to the sender, the subject, key words in the message, and so on. The higher the point total, the more
Loans. Before lending someone money, banks must decide whether they believe the applicant will repay the loan. One strategy used is a point system. Loan officers assess information about the applicant, totaling points they award for the person’s income level, credit history, current debt burden,
Fans. A survey of 81 randomly selected people standing in line to enter a football game found that 73 of them were home team fans.a) Explain why we cannot use this information to construct a confidence interval for the proportion of all people at the game who are fans of the home team.b) Construct
Dogs. Canine hip dysplasia is a degenerative disease that causes pain in many dogs. Sometimes advanced warning signs appear in puppies as young as 6 months.A veterinarian checked 42 puppies whose owners brought them to a vaccination clinic, and she found 5 with early hip dysplasia. She considers
Superdads. The Spike network commissioned a telephone poll of randomly sampled U.S. men. Of the 712 respondents who had children, 22% said “yes” to the question “Are you a stay-at-home dad?” (Time, August 23, 2004).a) To help market commercial time, Spike wants an accurate estimate of the
Approval 2007. In May 2007, George W. Bush’s approval rating stood at 30% according to a CBS News/New York Times national survey of 1125 randomly selected adults.a) Make a 95% confidence interval for his approval rating by all U.S. adults.b) Based on the confidence interval, test the null
Is the Euro fair? Soon after the Euro was introduced as currency in Europe, it was widely reported that someone had spun a Euro coin 250 times and gotten heads 140 times. We wish to test a hypothesis about the fairness of spinning the coin.a) Estimate the true proportion of heads. Use a 95%
Success. In August 2004, Time magazine reported the results of a random telephone poll commissioned by the Spike network. Of the 1302 men who responded, only 39 said that their most important measure of success was their work.a) Estimate the percentage of all American males who measure success
Significant again? Anew reading program may reduce the number of elementary school students who read below grade level. The company that developed this program supplied materials and teacher training for a large-scale test involving nearly 8500 children in several different school districts.
Significant? Public health officials believe that 90% of children have been vaccinated against measles. Arandom survey of medical records at many schools across the country found that, among more than 13,000 children, only 89.4% had been vaccinated. Astatistician would reject the 90% hypothesis
Alpha, again. Environmentalists concerned about the impact of high-frequency radio transmissions on birds found that there was no evidence of a higher mortality rate among hatchlings in nests near cell towers. They based this conclusion on a test using Would they have made the same decision at ?
Alpha. A researcher developing scanners to search for hidden weapons at airports has concluded that a new device is significantly better than the current scanner. He made this decision based on a test using Would he have made the same decision at ? How about? Explain.
Another P-value. Have harsher penalties and ad campaigns increased seat-belt use among drivers and passengers? Observations of commuter traffic failed to find evidence of a significant change compared with three years ago. Explain what the study’s P-value of 0.17 means in this context.
P-value. A medical researcher tested a new treatment for poison ivy against the traditional ointment. He concluded that the new treatment is more effective.Explain what the P-value of 0.047 means in this context.
Which alternative? In each of the following situations, is the alternative hypothesis one-sided or two-sided?What are the hypotheses?a) A college dining service conducts a survey to see if students prefer plastic or metal cutlery.b) In recent years, 10% of college juniors have applied for study
One sided or two? In each of the following situations, is the alternative hypothesis one-sided or two-sided? What are the hypotheses?a) A business student conducts a taste test to see whether students prefer Diet Coke or Diet Pepsi.b) PepsiCo recently reformulated Diet Pepsi in an attempt to appeal
AP Stats. The College Board reported that 60% of all students who took the 2006 AP Statistics exam earned scores of 3 or higher. One teacher wondered if the performance of her school was different. She believed that year’s students to be typical of those who will take AP Stats at that school and
John Wayne. Like a lot of other Americans, John Wayne died of cancer. But is there more to this story? In 1955 Wayne was in Utah shooting the film The Conqueror.Across the state line, in Nevada, the United States military was testing atomic bombs. Radioactive fallout from those tests drifted across
TV ads. A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads. The goal of the company is that over 40% of the public recognize its brand name
Lost luggage. An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 90% is recovered and delivered to its owner within 24 hours. A consumer group that surveyed a large number of air
Acid rain. A study of the effects of acid rain on trees in the Hopkins Forest shows that 25 of 100 trees sampled exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recent Environmetrics article on the average proportion of damaged trees in the
Dropouts. Some people are concerned that new tougher standards and high-stakes tests adopted in many states have driven up the high school dropout rate. The National Center for Education Statistics reported that the high school dropout rate for the year 2004 was 10.3%. One school district whose
Jury. Census data for a certain county show that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty and only 9 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection system? Explain.
Women executives. Acompany is criticized because only 13 of 43 people in executive-level positions are women. The company explains that although this proportion is lower than it might wish, it’s not surprising given that only 40% of all its employees are women. What do you think? Test an
Seeds. A garden center wants to store leftover packets of vegetable seeds for sale the following spring, but the center is concerned that the seeds may not germinate at the same rate a year later. The manager finds a packet of last year’s green bean seeds and plants them as a test.Although the
WebZine. Amagazine is considering the launch of an online edition. The magazine plans to go ahead only if it’s convinced that more than 25% of current readers would subscribe. The magazine contacted a simple random sample of 500 current subscribers, and 137 of those surveyed expressed interest.
Football 2006. During the 2006 season, the home team won 136 of the 240 regular-season National Football League games. Is this strong evidence of a home field advantage in professional football? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and
Twins. In 2001 a national vital statistics report indicated that about 3% of all births produced twins. Is the rate of twin births the same among very young mothers? Data from a large city hospital found that only 7 sets of twins were born to 469 teenage girls. Test an appropriate hypothesis and
Scratch and dent. An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling them the appliances get damaged. Even though the damage may be minor, the company must sell those machines at drastically reduced prices. The company
Pollution. A company with a fleet of 150 cars found that the emissions systems of 7 out of the 22 they tested failed to meet pollution control guidelines. Is this strong evidence that more than 20% of the fleet might be out of compliance? Test an appropriate hypothesis and state your conclusion. Be
Med School. According to the Association of American Medical Colleges, only 46% of medical school applicants were admitted to a medical school in the fall of 2006.5 Upon hearing this, the trustees of Striving College expressed concern that only 77 of the 180 students in their class of 2006 who
Law School. According to the Law School Admission Council, in the fall of 2006, 63% of law school applicants were accepted to some law school.4 The training program LSATisfaction claims that 163 of the 240 students trained in 2006 were admitted to law school. You can safely consider these trainees
Take the offer, part II. In Exercise 16 in Chapter 19 you learned that First USA, a major credit card company, is planning a new offer for their current cardholders. First USA will give double airline miles on purchases for the next 6 months if the cardholder goes online and registers for this
Contributions, please, part II. In Exercise 15 of Chapter 19 you learned that the Paralyzed Veterans of America is a philanthropic organization that relies on contributions.They send free mailing labels and greeting cards to potential donors on their list and ask for a voluntary contribution. To
Educated mothers. The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996, 31%of students reported that their mothers had graduated from college. In 2000,
Absentees. The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996, 34% of students had not been absent from school even once during the previous month. In the
Abnormalities. In the 1980s it was generally believed that congenital abnormalities affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384
Dowsing. In a rural area, only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by“dowsing”—using a forked stick to indicate where the well should be drilled. You check with 80 of his customers and find
Got milk? In November 2001, the Ag Globe Trotter newsletter reported that 90% of adults drink milk. Aregional farmers’ organization planning a new marketing campaign across its multicounty area polls a random sample of 750 adults living there. In this sample, 657 people said that they drink milk.
Cell phones. Many people have trouble setting up all the features of their cell phones, so a company has developed what it hopes will be easier instructions. The goal is to have at least 96% of customers succeed. The company tests the new system on 200 people, of whom 188 were successful. Is this
Candy. Someone hands you a box of a dozen chocolate-covered candies, telling you that half are vanilla creams and the other half peanut butter. You pick candies at random and discover the first three you eat are all vanilla.a) If there really were 6 vanilla and 6 peanut butter candies in the box,
He cheats! A friend of yours claims that when he tosses a coin he can control the outcome. You are skeptical and want him to prove it. He tosses the coin, and you call heads; it’s tails. You try again and lose again.a) Do two losses in a row convince you that he really can control the toss?
Cars. A survey investigating whether the proportion of today’s high school seniors who own their own cars is higher than it was a decade ago finds a P-value of 0.017.Is it reasonable to conclude that more high schoolers have cars? Explain.
Relief. A company’s old antacid formula provided relief for 70% of the people who used it. The company tests a new formula to see if it is better and gets a P-value of 0.27. Is it reasonable to conclude that the new formula and the old one are equally effective? Explain.
We don’t believe that claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns out to be 0.03. Which conclusion is appropriate? Explain.a) There’s a 3% chance that the die is fair.b) There’s a 97% chance that the die is fair.c) There’s a 3% chance that a loaded
Dice. The seller of a loaded die claims that it will favor the outcome
Negatives. After the political ad campaign described in Exercise 1a, pollsters check the governor’s negatives.They test the hypothesis that the ads produced no change against the alternative that the negatives are now below 30% and find a P-value of 0.22. Which conclusion is appropriate?
More hypotheses. Write the null and alternative hypotheses you would use to test each situation.a) In the 1950s only about 40% of high school graduates went on to college. Has the percentage changed?b) 20% of cars of a certain model have needed costly transmission work after being driven between
Hypotheses. Write the null and alternative hypotheses you would use to test each of the following situations:a) A governor is concerned about his “negatives”—the percentage of state residents who express disapproval of his job performance. His political committee pays for a series of TV ads,
Amendment. ATV news reporter says that a proposed constitutional amendment is likely to win approval in the upcoming election because a poll of 1505 likely voters indicated that 52% would vote in favor. The reporter goes on to say that the margin of error for this poll was 3%.a) Explain why the
Approval rating. A newspaper reports that the governor’s approval rating stands at 65%. The article adds that the poll is based on a random sample of 972 adults and has a margin of error of 2.5%. What level of confidence did the pollsters use?
Another pilot study. During routine screening, a doctor notices that 22% of her adult patients show higher than normal levels of glucose in their blood—a possible warning signal for diabetes. Hearing this, some medical researchers decide to conduct a large-scale study, hoping to estimate the
Pilot study. A state’s environmental agency worries that many cars may be violating clean air emissions standards. The agency hopes to check a sample of vehicles in order to estimate that percentage with a margin of error of 3% and 90% confidence. To gauge the size of the problem, the agency
Better hiring info. Editors of the business report in Exercise 30 are willing to accept a margin of error of 4%but want 99% confidence. How many randomly selected employers will they need to contact?
Graduation, again. As in Exercise 29, we hope to estimate the percentage of adults aged 25 to 30 who never graduated from high school. What sample size would allow us to increase our confidence level to 95%while reducing the margin of error to only 2%?
Hiring. In preparing a report on the economy, we need to estimate the percentage of businesses that plan to hire additional employees in the next 60 days.a) How many randomly selected employers must we contact in order to create an estimate in which we are 98% confident with a margin of error of
Graduation. It’s believed that as many as 25% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group.a) How many of this younger age group must we survey in order to estimate the proportion of non-grads to within 6% with 90%
Pregnancy, II. The San Diego reproductive clinic in Exercise 24 wants to publish updated information on its success rate.a) The clinic wants to cut the stated margin of error in half. How many patients’ results must be used?b) Do you have any concerns about this sample? Explain.
Deer ticks. Wildlife biologists inspect 153 deer taken by hunters and find 32 of them carrying ticks that test positive for Lyme disease.a) Create a 90% confidence interval for the percentage of deer that may carry such ticks.b) If the scientists want to cut the margin of error in half, how many
Back to campus, again. In 2004 ACT, Inc., reported that 74% of 1644 randomly selected college freshmen returned to college the next year. The study was stratified by type of college—public or private. The retention rates were 71.9% among 505 students enrolled in public colleges and 74.9% among
Payments. In a May 2007 Experian/Gallup Personal Credit Index poll of 1008 U.S. adults aged 18 and over, 8% of respondents said they were very uncomfortable with their ability to make their monthly payments on their current debt during the next three months. Amore detailed poll surveyed 1288
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