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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
Marriage. In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years.It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased during the past 40 years.a)
Catheters again. The catheter company in Exercise 28 is reviewing its testing procedure.a) Suppose the significance level is changed to .Will the probability of a Type II error increase, decrease, or remain the same?b) What is meant by the power of the test the company conducts?c) Suppose the
TV safety revisited. The manufacturer of the metal TV stands in Exercise 27 is thinking of revising its safety test.a) If the company s lawyers are worried about being sued for selling an unsafe product, should they increase or decrease the value of ? Explain.b) In this context, what is meant by
Catheters. During an angiogram, heart problems can be examined via a small tube (a catheter) threaded into the heart from a vein in the patient s leg. It s important that the company that manufactures the catheter maintain a diameter of 2.00 mm. (The standard deviation is quite small.) Each day,
TV safety. The manufacturer of a metal stand for home TV sets must be sure that its product will not fail under the weight of the TV. Since some larger sets weigh nearly 300 pounds, the company s safety inspectors have set a standard of ensuring that the stands can support an average of over 500
Golf balls. The United States Golf Association (USGA)sets performance standards for golf balls. For example, the initial velocity of the ball may not exceed 250 feet per second when measured by an apparatus approved by the USGA. Suppose a manufacturer introduces a new kind of ball and provides a
Pizza. A researcher tests whether the mean cholesterol level among those who eat frozen pizza exceeds the value considered to indicate a health risk. She gets a P-value of 0.07. Explain in this context what the 7% represents.
Step-By-Step, 2nd look. This chapter s Step-By-Steps looked at the speeds of cars traveling on Triphammer Road in Ithaca, New York. We first found a 90% confidence interval for the mean speed to be miles per hour. Later, based on a P-value of 0.136, we failed to reject the null hypothesis that the
For Example, 2nd look. This chapter s For Examples looked at mirex contamination in farmed salmon. We first found a 95% confidence interval for the mean concentration to be 0.0834 to 0.0992 parts per million. Later we rejected the null hypothesis that the mean did not exceed the EPA s recommended
Late arrivals. Will your flight get you to your destination on time? The U.S. Bureau of Transportation Statistics reported the percentage of flights that were late each month from 1995 through 2006. Here s a histogram, along with some summary statistics:
Departures. What are the chances your flight will leave on time? The U.S. Bureau of Transportation Statistics of the Department of Transportation publishes information about airline performance. Here are a histogram and summary statistics for the percentage of flights departing on time each month
Better light. After his first attempt to determine the speed of light (described in Exercise 18), Michelson conducted an improved experiment. In 1897 he reported results of 100 trials with a mean of 852.4 and a standard deviation of 79.0.a) What is the standard error of the mean for these data?b)
Second dog. The nutrition lab in Exercise 17 tests the hot dogs again, this time using a sample of 60 reduced sodium frankfurters. The new sample produces a mean of 318 mg of sodium, and the standard deviation is 32 mg.a) Should this larger sample of hot dogs produce a more accurate estimate of the
Speed of light. In 1882 Michelson measured the speed of light (usually denoted c as in Einstein s famous equation ). His values are in km/sec and have 299,000 subtracted from them. He reported the results of 23 trials with a mean of 756.22 and a standard deviation of 107.12.a) Find a 95% confidence
Hot dogs. A nutrition laboratory tests 40 reduced sodium hot dogs, finding that the mean sodium content is 310 mg, with a standard deviation of 36 mg.a) Find a 95% confidence interval for the mean sodium content of this brand of hot dog.b) What assumptions have you made in this inference?Are the
Parking II. Suppose that, for budget planning purposes, the city in Exercise 14 needs a better estimate of the mean daily income from parking fees.a) Someone suggests that the city use its data to create a 95% confidence interval instead of the 90% interval first created. How would this interval be
Normal temperatures, part II. Consider again the statistics about human body temperature in Exercise 13.a) Would a 90% confidence interval be wider or narrower than the 98% confidence interval you calculated before? Explain. (You should not need to compute the new interval.)b) What are the
Parking. Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure
Normal temperature. The researcher described in Exercise 9 also measured the body temperatures of that randomly selected group of adults. The data he collected are summarized below. We wish to estimate the average (or normal ) temperature among the adult population.
Credit card charges. A credit card company takes a random sample of 100 cardholders to see how much they charged on their card last month. A histogram and boxplot are as follows:
CEO compensation. A sample of 20 CEOs from the Forbes 500 shows total annual compensations ranging from a minimum of $0.1 to $62.24 million. The average for these 20 CEOs is $7.946 million. The histogram and boxplot are as follows:Based on these data, a computer program found that a 95% confidence
Crawling. Data collected by child development scientists produced this confidence interval for the average age(in weeks) at which babies begin to crawl:t-Interval for m 29.202 , m(age) , 31.844(95.00% Confidence):a) Explain carefully what the software output means.b) What is the margin of error for
Pulse rates. A medical researcher measured the pulse rates (beats per minute) of a sample of randomly selected adults and found the following Student s t-based confidence interval:With 95.00% Confidence, 70.887604 , m(Pulse) , 74.497011a) Explain carefully what the software output means.b) What s
Rain. Based on meteorological data for the past century, a local TV weather forecaster estimates that the region s average winter snowfall is 23", with a margin of error of 62 inches. Assuming he used a 95% confidence interval, how should viewers interpret this news? Comment on each of these
Meal plan. After surveying students at Dartmouth College, a campus organization calculated that a 95%confidence interval for the mean cost of food for one term(of three in the Dartmouth trimester calendar) is ($1102,$1290). Now the organization is trying to write its report and is considering the
Teachers. Software analysis of the salaries of a random sample of 288 Nevada teachers produced the confidence interval shown below. Which conclusion is correct?What s wrong with the others?t-Interval for m: with 90.00% Confidence, 38944 , m(TchPay) , 42893a) If we took many random samples of Nevada
Cattle. Livestock are given a special feed supplement to see if it will promote weight gain. Researchers report that the 77 cows studied gained an average of 56 pounds, and that a 95% confidence interval for the mean weight gain this supplement produces has a margin of error of pounds. Some
t-models, part IV (last one!). Describe how the critical value of t for a 95% confidence interval changes as the number of degrees of freedom increases.
t-models, part III. Describe how the shape, center, and spread of t-models change as the number of degrees of freedom increases.
t-models, part II. Using the t tables, software, or a calculator, estimatea) the critical value of t for a 95% confidence interval with df = 7.b) the critical value of t for a 99% confidence interval with df = 102.c) the P-value for with 41 degrees of freedom.d) the P-value for with 12 degrees of
t-models, part I. Using the t tables, software, or a calculator, estimatea) the critical value of t for a 90% confidence interval with df = 17.b) the critical value of t for a 98% confidence interval with df = 88.c) the P-value for with 4 degrees of freedom.d) the P-value for with 22 degrees of
Dropouts. One study comparing various treatments for the eating disorder anorexia nervosa initially enlisted 198 subjects, but found overall that 105 failed to complete their assigned treatment programs. Construct and interpret an appropriate confidence interval. Discuss any reservations you have
NIMBY. In March 2007, the Gallup Poll split a sample of 1003 randomly selected U.S. adults into two groups at random. Half of the respondents were asked, Overall, do you strongly favor, somewhat favor, somewhat oppose, or strongly oppose the use of nuclear energy as one of the ways to provide
Name recognition, part II. The advertising company described in Exercise 37 is thinking about signing a WNBA star to an endorsement deal. In its poll, 27% of the respondents could identify her.a) Fans who never took Statistics can t understand why the company did not offer this WNBA player an
Name recognition. An advertising agency won t sign an athlete to do product endorsements unless it is sure the person is known to more than 25% of its target audience. The agency always conducts a poll of 500 people to investigate the athlete s name recognition before offering a contract. Then it
Grade inflation. In 1996, 20% of the students at a major university had an overall grade point average of 3.5 or higher (on a scale of 4.0). In 2000, a random sample of 1100 student records found that 25% had a GPA of 3.5 or higher. Is this evidence of grade inflation?
Approval 2007. Of all the post World War II presidents, Richard Nixon had the highest disapproval rating near the end of his presidency. His disapproval rating peaked at 66% in July 1974, just before he resigned. In May 2007, George W. Bush s disapproval rating was 63%, according to a Gallup poll
Power. We are replicating an experiment. How will each of the following changes affect the power of our test? Indicate whether it will increase, decrease, or remain the same, assuming that all other aspects of the situation remain unchanged.a) We increase the number of subjects from 40 to 100.b) We
Fried PCs. A computer company recently experienced a disastrous fire that ruined some of its inventory. Unfortunately, during the panic of the fire, some of the damaged computers were sent to another warehouse, where they were mixed with undamaged computers. The engineer responsible for quality
Safety. Observers in Texas watched children at play in eight communities. Of the 814 children seen biking, roller skating, or skateboarding, only 14% wore a helmet.a) Create and interpret a 95% confidence interval.b) What concerns do you have about this study that might make your confidence
Preemies. Among 242 Cleveland-area children born prematurely at low birth weights between 1977 and 1979, only 74% graduated from high school. Among a comparison group of 233 children of normal birth weight, 83%were high school graduates. ( Outcomes in Young Adulthood for Very-Low-Birth-Weight
Errors. An auto parts company advertises that its special oil additive will make the engine run smoother, cleaner, longer, with fewer repairs. An independent laboratory decides to test part of this claim. It arranges to use a taxicab company s fleet of cars. The cars are randomly divided into two
Alcohol abuse. Growing concern about binge drinking among college students has prompted one large state university to conduct a survey to assess the size of the problem on its campus. The university plans to randomly select students and ask how many have been drunk during the past week. If the
Teen smoking 2006. The Centers for Disease Control and Prevention say that about 23% of teenagers smoke tobacco (down from a high of 38% in 1997). A college has 522 students in its freshman class. Is it likely that more than 30% of them are smokers? Explain.
Crohn s disease. In 2002 the medical journal The Lancet reported that 335 of 573 patients suffering from Crohn s disease responded positively to injections of the arthritisfighting drug infliximab.a) Create a 95% confidence interval for the effectiveness of this drug.b) Interpret your interval in
Cigarettes 2006. In 1999 the Centers for Disease Control and Prevention estimated that about 34.8% of high school students smoked cigarettes. They established a national health goal of reducing that figure to 16% by the year 2010. To that end, they hoped to achieve a reduction to 20% by 2006. In
Language. Neurological research has shown that in about 80% of people language abilities reside in the brain s left side. Another 10% display right-brain language centers, and the remaining 10% have two-sided language control. (The latter two groups are mainly lefthanders.) (Science News, 161, no.
Cheating. A Rutgers University study released in 2002 found that many high school students cheat on tests. The researchers surveyed a random sample of 4500 high school students nationwide; 74% of them said they had cheated at least once.a) Create a 90% confidence interval for the level of cheating
Largemouth bass. Organizers of a fishing tournament believe that the lake holds a sizable population of largemouth bass. They assume that the weights of these fish have a model that is skewed to the right with a mean of 3.5 pounds and a standard deviation of 2.2 pounds.a) Explain why a skewed model
Perfect pitch. A recent study of perfect pitch tested 2700 students in American music conservatories. It found that 7% of non-Asian and 32% of Asian students have perfect pitch. A test of the difference in proportions resulted in a P-value ofa) What are the researchers null and alternative
Teen deaths. Traffic accidents are the leading cause of death among people aged 15 to 20. In May 2002, the National Highway Traffic Safety Administration reported that even though only 6.8% of licensed drivers are between 15 and 20 years old, they were involved in 14.3% of all fatal crashes.
Enough eggs? One of the important issues for poultry farmers is the production rate the percentage of days on which a given hen actually lays an egg. Ideally, that would be 100% (an egg every day), but realistically, hens tend to lay eggs on about 3 of every 4 days. ISA Babcock wants to advertise
Polling disclaimer. A newspaper article that reported the results of an election poll included the following explanation:The Associated Press poll on the 2000 presidential campaign is based on telephone interviews with 798 randomly selected registered voters from all states except Alaska and
Eggs. The ISA Babcock Company supplies poultry farmers with hens, advertising that a mature B300 Layer produces eggs with a mean weight of 60.7 grams. Suppose that egg weights follow a Normal model with standard deviation 3.1 grams.a) What fraction of the eggs produced by these hens weigh more than
Eclampsia. Refer again to the research summarized in Exercise 16. Is there any evidence that when eclampsia does occur, the magnesium sulfide treatment may help prevent the woman s death?a) Write an appropriate hypothesis.b) Check the assumptions and conditions.c) Find the P-value of the test.d)
Eclampsia. It s estimated that 50,000 pregnant women worldwide die each year of eclampsia, a condition involving elevated blood pressure and seizures. A research team from 175 hospitals in 33 countries investigated the effectiveness of magnesium sulfate in preventing the occurrence of eclampsia in
Twins. There is some indication in medical literature that doctors may have become more aggressive in inducing labor or doing preterm cesarean sections when a woman is carrying twins. Records at a large hospital show that, of the 43 sets of twins born in 1990, 20 were delivered before the 37th week
Free throws 2007. During the 2006 2007 NBA season, Kyle Korver led the league by making 191 of 209 free throws, for a success rate of 91.39%. But Matt Carroll was close behind, with 188 of 208 (90.39%).a) Find a 95% confidence interval for the difference in their free throw percentages.b) Based on
Archery. A champion archer can generally hit the bull s-eye 80% of the time. Suppose she shoots 200 arrows during competition. Let represent the percentage of bull s-eyes she gets (the sample proportion).a) What are the mean and standard deviation of the sampling distribution model for ?b) Is a
Vitamin D. In July 2002 the American Journal of Clinical Nutrition reported that 42% of 1546 African-American women studied had vitamin D deficiency. The data came from a national nutrition study conducted by the Centers for Disease Control and Prevention in Atlanta.a) Do these data meet the
Bimodal. We are sampling randomly from a distribution known to be bimodal.a) As our sample size increases, what s the expected shape of the sample s distribution?b) What s the expected value of our sample s mean?Does the size of the sample matter?c) How is the variability of this sample s mean
Death penalty 2006. In May of 2006, the Gallup Organization asked a random sample of 537 American adults this question:If you could choose between the following two approaches, which do you think is the better penalty for murder, the death penalty or life imprisonment, with absolutely no
News sources. In May of 2000, the Pew Research Foundation sampled 1593 respondents and asked how they obtain news. In Pew s report, 33% of respondents say that they now obtain news from the Internet at least once a week.a) Pew reports a margin of error of for this result.Explain what the margin of
Dice. When one die is rolled, the number of spots showing has a mean of 3.5 and a standard deviation of 1.7. Suppose you roll 10 dice. What s the approximate probability that your total is between 30 and 40 (that is, the average for the 10 dice is between 3 and 4)? Specify the model you use and the
Scrabble. Using a computer to play many simulated games of Scrabble, researcher Charles Robinove found that the letter A occurred in 54% of the hands. This study had a margin of error of . (Chance, 15, no. 1[2002])a) Explain what the margin of error means in this context.b) Why might the margin of
Surgery and germs. Joseph Lister (for whom Listerine is named!) was a British physician who was interested in the role of bacteria in human infections. He suspected that germs were involved in transmitting infection, so he tried using carbolic acid as an operating room disinfectant. In 75
Leaky gas tanks. Nationwide, it is estimated that 40%of service stations have gas tanks that leak to some extent. A new program in California is designed to lessen the prevalence of these leaks. We want to assess the effectiveness of the program by seeing if the percentage of service stations whose
Polling 2004. In the 2004 U.S. presidential election, the official results showed that George W. Bush received 50.7% of the vote and John Kerry received 48.3%. Ralph Nader, running as a third-party candidate, picked up only 0.4%. After the election, there was much discussion about exit polls, which
Birth days. During a 2-month period in 2002, 72 babies were born at the Tompkins Community Hospital in upstate New York. The table shows how many babies were born on each day of the week.a) If births are uniformly distributed across all days of the week, how many would you expect on each day?b)
Colorblind. Medical literature says that about 8% of males are colorblind. A university s introductory psychology course is taught in a large lecture hall. Among the students, there are 325 males. Each semester when the professor discusses visual perception, he shows the class a test for
Herbal cancer. A report in the New England Journal of Medicine (June 6, 2000) notes growing evidence that the herb Aristolochia fangchi can cause urinary tract cancer in those who take it. Suppose you are asked to design an experiment to study this claim. Imagine that you have data on urinary tract
Fast food. The global survey we learned about in Exercise 41 also asked respondents how they felt about the statement I try to avoid eating fast foods. The random sample of 800 included 411 people 35 years old or younger, and of those, 197 agreed (completely or somewhat) with the statement. Of the
Food preference. GfK Roper Consulting gathers information on consumer preferences around the world to help companies monitor attitudes about health, food, and healthcare products. They asked people in many different cultures how they felt about the following statement:I have a strong preference for
Computer gaming. Who plays online or electronic games? A survey in 2006 found that 69% of 223 boys aged 12 14 said they played computer or console games like Xbox or PlayStation . . . or games online. Of 248 boys aged 15 17, only 62% played these games. Is this evidence of a real age-based
Online activity checks. Are more parents checking up on their teen s online activities? A Pew survey in 2004 found that 33% of 868 randomly sampled teens said that their parents checked to see what Web sites they visited.In 2006 the same question posed to 811 teens found 41%reporting such checks.
Retention rates. In 2004 the testing company ACT, Inc., reported on the percentage of first-year students at 4-year colleges who return for a second year. Their sample of 1139 students in private colleges showed a 74.9%retention rate, while the rate was 71.9% for the sample of 505 students at
Intentional walk. During the 2004 baseball season, San Francisco Giants slugger Barry Bonds was such a dangerous hitter that many teams simply chose to walk him rather than throw him a pitch he could hit. Just before a series of games in New York, an analyst advised the Mets that they should pitch
Carbs. In July of 2004, the Gallup Poll asked 1005 U.S.adults if they actively try to avoid carbohydrates in their diet. That number increased to 27% from 20% in a similar 2002 poll. Is this a statistically significant increase? Explain.
Sensitive men. In August 2004, Time magazine, reporting on a survey of men s attitudes, noted that Young men are more comfortable than older men talking about their problems. The survey reported that 80 of 129 surveyed 18- to 24-year-old men and 98 of 184 25- to 34-yearold men said they were
Stay-at-home dads. In August 2004, a Time magazine article about a survey of men s attitudes reported that 11 of 161 black respondents and 20 of 358 Latino respondents responded Yes to the question Are you a stay-athome dad? How big is the difference in proportions in the two populations?a)
Convention bounce. Political pundits talk about the bounce that a presidential candidate gets after his party s convention. In the last forty years, it has averaged about 6 percentage points. Just before the 2004 Democratic convention, Rasmussen Reports polled 1500 likely voters at random and found
Gender gap. Candidates for political office realize that different levels of support among men and women may be a crucial factor in determining the outcome of an election.One candidate finds that 52% of 473 men polled say they will vote for him, but only 45% of the 522 women in the poll express
Pain. Researchers comparing the effectiveness of two pain medications randomly selected a group of patients who had been complaining of a certain kind of joint pain.They randomly divided these people into two groups, then administered the pain killers. Of the 112 people in the group who received
Mammograms redux. In 2001, the conclusion of the study outlined in Exercise 29 was questioned. A new 9-year study was conducted in Sweden, comparing 21,088 women who had mammograms with 21,195 who did not. Of the women who underwent screening, 63 died of breast cancer, compared to 66 deaths among
Mammograms. It s widely believed that regular mammogram screening may detect breast cancer early, resulting in fewer deaths from that disease. One study that investigated this issue over a period of 18 years was published during the 1970s. Among 30,565 women who had never had mammograms, 196 died
Shopping. A survey of 430 randomly chosen adults found that 21% of the 222 men and 18% of the 208 women had purchased books online.a) Is there evidence that men are more likely than women to make online purchases of books? Test an appropriate hypothesis and state your conclusion in context.b) If
Twins. In 2001, one county reported that, among 3132 white women who had babies, 94 were multiple births.There were also 20 multiple births to 606 black women.Does this indicate any racial difference in the likelihood of multiple births?a) Test an appropriate hypothesis and state your conclusion.b)
Retirement. The Employee Benefit Research Institute reports that 27% of males anticipate having enough money to live comfortably in retirement, but only 18%of females express that confidence. If these results were based on samples of 200 people of each sex, would you consider this strong evidence
Politics and sex. One month before the election, a poll of 630 randomly selected voters showed 54% planning to vote for a certain candidate. A week later it became known that he had had an extramarital affair, and a new poll showed only 51% of 1010 voters supporting him. Do these results indicate a
Birthweight. In 2003 the Journal of the American Medical Association reported a study examining the possible impact of air pollution caused by the 9/11 attack on New York s World Trade Center on the weight of babies. Researchers found that 8% of 182 babies born to mothers who were exposed to heavy
Pregnancy. In 1998, a San Diego reproductive clinic reported 42 live births to 157 women under the age of 38, but only 7 live births for 89 clients aged 38 and older. Is this strong evidence of a difference in the effectiveness of the clinic s methods for older women?a) Test an appropriate
Depression revisited. Consider again the study of the association between depression and cardiac disease survivability in Exercise 20.a) Create a 95% confidence interval for the difference in survival rates.b) Interpret your interval in this context.c) Carefully explain what 95% confidence means.
Teen smoking, part II. Consider again the Vermont study discussed in Exercise 19.a) Create a 95% confidence interval for the difference in the proportion of children who may smoke and have approving parents and those who may smoke and have disapproving parents.b) Interpret your interval in this
Depression. A study published in the Archives of General Psychiatry in March 2001 examined the impact of depression on a patient s ability to survive cardiac disease.Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361
Teen smoking, part I. A Vermont study published in December 2001 by the American Academy of Pediatrics examined parental influence on teenagers decisions to smoke. A group of students who had never smoked were questioned about their parents attitudes toward smoking. These students were questioned
Anorexia again. In Exercise 16 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.)
Another ear infection. In Exercise 15 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
War. In September 2002, a Gallup Poll found major differences of opinion based on political affiliation over whether Congress should give President Bush authority to take military action in Iraq. Overall, about 50% of the 1010 respondents were in favor, with a margin of error of . Opinion differed
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