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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
Politics. A poll checking on the level of public support for proposed antiterrorist legislation reported that 68%of the respondents were in favor. The pollsters reported a sampling error of . When the responses were broken down by party affiliation, support was 2% higher among Republican
Race and smoking 2005. In 2005 the New Jersey Adult Tobacco Survey found that 22.5% of 464 blacks surveyed said that they smoked cigarettes while 18.3% of 2449 white respondents reported smoking.a) Create a 90% confidence interval for the difference in the percentage of smokers between black and
Prostate cancer. There has been debate among doctors over whether surgery can prolong life among men suffering from prostate cancer, a type of cancer that typically develops and spreads very slowly. In the summer of 2003, The New England Journal of Medicine published results of some Scandinavian
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. A presidential 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
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 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 the
Global warming. A survey by the Pew Research Center for the People & the Press, conducted January 10 15, 2007 among 1708 Americans, found 55% saying that global warming is a problem that requires immediate government action. Pew reports that this is a decline from the previously established level
Little League. In a 1999 2000 longitudinal study of youth baseball, researchers found that 26% of 298 young pitchers complained of elbow pain after pitching.a) Create a 90% confidence interval for the percentage of young players who may develop elbow pain after pitching.b) A coach claims that only
Fire safety. A city law requires all buildings to have a fire safety inspection at least once every three years. Concerned that some of these inspections are not being done, the mayor orders a survey to see what fraction of the city s buildings may be out of compliance. Results for the sample
Survey. A company has surveyed a stratified sample of its employees to find out how many might take advantage of a program to help people stop smoking. You may assume that the sampling strategy was properly random and that the data-gathering methodology avoided biases. The table below shows the
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, she buys some more expensive clay from another supplier. She plans to make and
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 10. Did the player prove that he
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 disk
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 26 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 carefully what your P-value means in this context.
Dropouts, part II. Initially, 203 students signed up for the Stats course in Exercise 25. 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)
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
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?
Production. Consider again the task of the quality control inspectors in Exercise 20.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 each hour instead.What are the advantages
Cars again. As in Exercise 19, 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. A clean 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. Recently, 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
More spam. Consider again the points-based spam filter described in Exercise 14. 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
Second loan. Exercise 13 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
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,
Superdads. The Spike network commissioned a telephone poll of randomly sampled U.S. men. Of the 712 P 5 0.011 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 true
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? A new 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. A random survey of medical records at many schools across the country found that, among more than 13,000 children, only 89.4% had been vaccinated. A statistician 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 has tested a new treatment for poison ivy against the traditional ointment. He concludes that the new treatment, with a P-value of 0.047, is more effective. Explain what the P-value 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 wants to know if students prefer plastic or metal cutlery. They conduct a survey to find out.b) In recent years, 10% of college juniors
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 and
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 travelers
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 may drive 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. A company 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. A magazine 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
Satisfaction. A company hopes to improve customer satisfaction, setting as a goal no more than 5% negative comments. A random survey of 350 customers found only 10 with complaints.a) Create a 95% confidence interval for the true level of dissatisfaction among customers.b) Does this provide evidence
Smoking 2004. National data in the 1960s showed that about 44% of the adult population had never smoked cigarettes. In 2004 a national health survey interviewed a random sample of 881 adults and found that 54.6% had never been smokers.a) Create a 95% confidence interval for the proportion of adults
Take the offer, part II. In Exercise 19.16 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 offer. To test
Contributions, please, part II. In Exercise 19.15 you learned that the Paralyzed Veterans of America is a philanthropic organization that relies on contributions.
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 2000
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 that 27
Got milk? In November 2001, the Ag Globe Trotter newsletter reported that 90% of adults drink milk. A regional 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 chocolatecovered candies, telling you that half are vanilla creams and the other half peanut butter. You pick candies at random and discover that the first three you eat are all vanilla.a) If there really were 6 vanilla and 6 peanut butter candies in the
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? Explain.
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.
Name recognition. A political 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
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 conclude
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 die
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? Explain.a)
More hypotheses. Write the null and alternative hypotheses you would use to test each of the following situations.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
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, hoping
Amendment. A TV 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 first
Better hiring info. Editors of the business report in Exercise 36 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 35, 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 26 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
Legal Music. A random sample of 168 students were asked how many songs were in their digital music library and what fraction of them were legally purchased. Overall, they reported having a total of 117,079 songs, of which 23.1% were legal. The music industry would like a good estimate of the
Another payment. Exercise 29 described an Experian/Gallup poll of 1008 adults which found that 8% of them were worried about their ability to make their monthly payments. A more detailed poll surveyed 1288 adults, reporting similar overall results and also noting differences among four age groups:
Back to campus again. The ACT, Inc., study described in Exercise 28 was actually 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 1139 students enrolled in private colleges.a) Will the 95% confidence
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. Find a 95% confidence interval for the
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