It 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 of breast cancer, while only 153 of 30,131 who had undergone screening died of breast cancer. 1. Do these results suggest that mammograms may be an effective screening tool to reduce breast cancer deaths? 2. If your conclusion is incorrect, what type of error have you committed?
> Is it a good idea to listen to music when studying for a big test? In a study conducted by some statistics students, 62 people were randomly assigned to listen to rap music, music by Mozart, or no music while attempting to memorize objects pictured on a
> Given the test results on golf tees described in Exercise 83 , is there evidence that balls hit off Stinger tees travel farther? Again, assume that 6 balls were hit off each tee and that the data were suitable for inference.
> Does it matter what kind of tee a golfer places the ball on? The company that manufactures Stinger tees claims that the thinner shaft and smaller head lessen resistance and drag, reducing spin and allowing the ball to travel farther. In August 2003, Golf
> In Exercise 81 , we looked at the times in two different heats for the 400-m women run from the 2012 Olympics. Unlike track events, swimming heats are not determined at random. Instead, swimmers are seeded so that better swimmers are placed in later heat
> In 2015 the Council of Europe published a report entitled The European School Survey Project on Alcohol and Other Drugs. (www.espad.org) Among other issues, the survey investigated the percentages of 16-year-olds who had used marijuana. Shown here are th
> In Olympic running events, preliminary heats are determined by random draw, so we should expect the abilities of runners in the various heats to be about the same, on average. Here are the times (in seconds) for the 400-m women run in the 2012 Olympics i
> Here some additional information about the Ontario crossing times presented in Exercise 79 . It is generally thought to be harder to swim across the lake from north to south. Indeed, this has been done only 5 times. Every one of those crossings was by a
> As we saw in Chapter 8, Exercise 46, between 1954 and 2016, swimmers have crossed Lake Ontario 62 times. Both women and men have made the crossing. Here are some plots (we’ve omitted a crossing by Vikki Keith, who swam a round trip nort
> Researchers randomly assigned participants either a tall, thin highball glass or a short, wide tumbler, each of which held 355 ml. Participants were asked to pour a shot (1.5 oz=44.3 ml) into their glass. Did the
> Researchers investigated how the size of a bowl affects how much ice cream people tend to scoop when serving themselves.12 At an ice cream social, people were randomly given either a 17-oz or a 34-oz bowl (both large enough that they would not be filled
> You are a consultant to the marketing department of a business preparing to launch an ad campaign for a new product. The company can afford to run ads during one TV show, and has decided not to sponsor a show with sexual content. You read the study descr
> The Journal of Applied Psychology reported on a study that examined whether the content of TV shows influenced the ability of viewers to recall brand names of items featured in the commercials. The researchers randomly assigned volunteers to watch one of
> Having done poorly on their math final exams in June, six students repeat the course in summer school, then take another exam in August. If we consider these students representative of all students who might attend this summer school in other years, expl
> A company institutes an exercise break for its workers to see if this will improve job satisfaction, as measured by a questionnaire that assesses workers satisfaction. Scores for 10 randomly selected workers before and after implementation of the exercis
> Recall from Chapter 7, Exercise 75 , that data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per million
> Two researchers measured the pH (a scale on which a value of 7 is neutral and values below 7 are acidic) of water collected from rain and snow over a 6-month period in Allegheny County, Pennsylvania: 4.57 5.62 4.12 5.29 4.64 4.31 4.30 4.39 4.45 5.67 4.39
> American League baseball teams play their games with the designated hitter rule, meaning that pitchers do not bat. The league believes that replacing the pitcher, traditionally a weak hitter, with another player in the batting order produces more runs an
> Does ginkgo biloba enhance memory? In an experiment to find out, subjects were assigned randomly to take ginkgo biloba supplements or a placebo. Their memory was tested to see whether it improved. The numbers reported are the number of items recalled bef
> Are men or women at higher risk for having high cholesterol? The answer may surprise you. Use the data in Framingham. 1. Make boxplots comparing the cholesterol levels of men and women. 2. Does it seem convincing from the boxplots that one gender has hig
> In Chapter 6, Exercise 25, we looked at collected samples of water from streams in the Adirondack Mountains to investigate the effects of acid rain. Researchers measured the pH (acidity) of the water and classified the streams with respect to the kind of
> An educator believes that new reading activities for elementary school children will improve reading comprehension scores. She randomly assigns third graders to an eight-week program in which some will use these activities and others will experience trad
> Some archaeologists theorize that ancient Egyptians interbred with several different immigrant populations over thousands of years. To see if there is any indication of changes in body structure that might have resulted, they measured 30 skulls of male E
> The data below show the sugar content (as a percentage of weight) of several national brands of children and adults cereals. Create and interpret a 95% confidence interval for the difference in mean sugar content. Be sure to check the necessary assumptio
> The house sales we looked at in Exercise 63 also listed whether the home was new construction or not. Find and interpret a 95% confidence interval for how much more an agent can expect to sell a new home for. (From technology, df=197.8.) Here are the sum
> How much extra is having a waterfront property worth? A student took a random sample of 170 recently sold properties in Upstate New York to examine the question. Here are her summaries and boxplots of the two groups of prices: Construct and interpret a 9
> A researcher wanted to see whether there is a significant difference in resting pulse rates for men and women. The data she collected are displayed in the boxplots and summarized below. 1. What do the boxplots suggest about differences between male and f
> Students were given the assignment to make a histogram of the data on bird counts reported in Exercise 48. One student submitted the following display: 1. Comment on this graph. 2. Create your own histogram of the data.
> A man who moves to a new city sees that there are two routes he could take to work. A neighbor who has lived there a long time tells him Route A will average 5 minutes faster than Route B. The man decides to experiment. Each day, he flips a coin to deter
> The study of the new CPMP Mathematics methodology described in Exercise 57 also tested students abilities to solve word problems. This table shows how the CPMP and traditional groups performed. (The df are 590.049.) What do you conclude?
> During the study described in Exercise 57 , students in both CPMP and traditional classes took another algebra test that did not allow them to use calculators. The table below shows the results. Are the mean scores of the two groups significantly differe
> In Exercises 49 and 50, Chapter 4, we looked at data from an experiment to determine whether visual information about an image helped people see the image in 3D. 2-Sample t-Interval  for  μ1 μ2Conf level=90%   df=70μ(NV)−μ(VV) interval:(0.5
> The Core Plus Mathematics Project (CPMP) is an innovative approach to teaching Mathematics that engages students in group investigations and mathematical modeling. After field tests in 36 high schools over a three-year period, researchers compared the pe
> In Exercise 54, we saw a 98% confidence interval of (40, 22) minutes for μTop μFront the difference in time it takes top-loading and front-loading washers to do a load of clothes. Explain why you think each of the following statements is true or false:
> In Exercise 53 , we saw a 90% confidence interval of (6.5, 1.4) grams for μMeat−μBeef the difference in mean fat content for meat vs. all-beef hot dogs. Explain why you think each of the following statements is true or false: 1. If I eat a meat hot d
> The Consumer Reports article described in Exercise 52 continued their investigation of washing machines. One of the variables the article reported was “cycle time,†the number of minutes it took each machine to wash a load of clothes. Among the machin
> The Consumer Reports article described in Exercise 51 also listed the fat content (in grams) for samples of beef and meat hot dogs. The resulting 90% confidence interval for μMeat μBeef is (6.5, 1.4). 1. The endpoints of this confidence interval are ne
> In the June 2007 issue, Consumer Reports also examined the relative merits of top-loading and front-loading washing machines, testing samples of several different brands of each type. Suppose the study tested the null hypothesis that top- and front-loadi
> Students were asked to make a histogram of the number of home runs Alex Rodriguez hit from 1994 to 2016 (see Exercise 73). One student submitted the following display: 1. Comment on this graph. 2. Create your own histogram of the data.
> In the July 2007 issue, Consumer Reports examined the calorie content of two kinds of hot dogs: meat (usually a mixture of pork, turkey, and chicken) and all beef. The researchers purchased samples of several different brands. The meat hot dogs averaged
> The global survey we learned about in Exercise 49 also asked respondents how they felt about the statement 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 somew
> 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
> Recently, 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.
> In the same article from Exercise 46 , Time magazine, reporting on a survey of men 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 9
> A Time magazine article about a survey of men attitudes reported that 11 of 161 black respondents and 20 of 358 Latino respondents responded Yes to the question Are you a stay-at-home dad? How big is the difference in proportions in the two populations?
> Political pundits talk about the bounce that a presidential candidate gets after his party convention. In the past 40 years, it has averaged about 6 percentage points. Just before the 2004 Democratic convention, Rasmussen Reports polled 1500 likely voter
> 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
> 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
> In 2001, the conclusion of the study outlined in Exercise 41 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, co
> The following data give the numbers of hurricanes classified as major hurricanes in the Atlantic Ocean each year from 1944 through 2013 (www.nhc.noaa.gov/data/): 3, 3, 1, 2, 4, 3, 8, 5, 3, 4, 2, 6, 2, 2, 5, 2, 2, 7, 1, 2, 6, 1, 3, 1, 0, 5, 2, 1, 0, 1, 2,
> 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.
> 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 World Trade Center on the weight of babies. Researchers found that 8% of 182 babies born to mothers who
> A study published in the Archives of General Psychiatry examined the impact of depression on a patient ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4
> A Vermont study published 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 questi
> In Exercise 34 , 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.) 1. What hypotheses wo
> In Exercise 33 , 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.) 1. What hypoth
> 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
> 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. O
> Data collected in 2015 by the Behavioral Risk Factor Surveillance System revealed that in the state of New Jersey, 27.3% of whites and 47.2% of blacks were cigarette smokers. Suppose these proportions were based on samples of 3607 whites and 485 blacks.
> Alex Rodriguez (known to fans as A-Rod) was the youngest player ever to hit 500 home runs. Here is a stem-and-leaf display of the number of home runs hit by A-Rod during the 1994 2016 seasons. Describe the distribution, mentioning its shape and any unusu
> 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. Recently, The New England Journal of Medicine published results of some
> The painful wrist condition called carpal tunnel syndrome can be treated with surgery or, less invasively, with wrist splints. Recently, Time magazine reported on a study of 176 patients. Among the half that had surgery, 80% showed improvement after thre
> 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 lym
> 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,
> 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. 1. Are the assumptions and conditions necessary
> 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 randomly select 450 owners of American-made cars and 450 owners of Japanese models. Obviously, the actual
> A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. Obviously, the sta
> 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
> Eight hundred eighty-six randomly sampled teens were asked which of several personal items of information they thought it ok to share with someone they had just met. Forty-four percent said it was ok to share their e-mail addresses, but only 29% said the
> At the end of 2013, the Pew Project for Excellence in Journalism investigated where people are getting their news. In the study 22% of people 1829 years old said they still read newspapers as one of their sources of news, while only 18% of people 3049 sa
> In Exercise 70, you examined the number of games played by hockey great Wayne Gretzky during his 20-year career in the NHL. 1. Would you use the median or the mean to describe the center of this distribution? Why? 2. Find the median. 3. Without actually
> In September 2013, the Pew Internet and American Life Project surveyed American adults on their Facebook use. It found that 64% visited the site on a daily basis, up from 51% in 2010. What does it mean to say that the difference in proportions is signifi
> In Chapter 18 we saw data from samples of farmed salmon and examined the mirex content. The EPA sets a limit of 0.08 ppm as a maximum safe value. We performed a bootstrap on these data, drawing 10,000 resamples. Here is the resulting histogram of bootstr
> Exercise 53 of Chapter 18 asked for a Student t-based test of the hypothesis that every bag of Chips Ahoy! cookies had at least 1000 chips. Here is a histogram of 10,000 bootstrapped means based on the sample of packages in the data file. What P-value wo
> 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
> 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
> You are in charge of shipping computers to customers. You learn that a faulty chip was put into some of the machines. There a simple test you can perform, but it not perfect. All but 4% of the time, a good chip passes the test, but unfortunately, 35% of
> 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 co
> The catheter company in Exercise 40 is reviewing its testing procedure. 1. Suppose the significance level is changed to α=0.01. Will the probability of a Type II error increase, decrease, or remain the same? 2. What is meant by the power of the test the
> The manufacturer of the metal TV stands in Exercise 39 is thinking of revising its safety test. 1. If the company lawyers are worried about being sued for selling an unsafe product, should they increase or decrease the value of α? Explain. 2. In this co
> During an angiogram, heart problems can be examined via a small tube (a catheter) threaded into the heart from a vein in the patient leg. It important that the company that manufactures the catheter maintain a diameter of 2.00 mm. (The standard deviation
> The stem-and-leaf display shows populations of the 50 states, in millions of people, according to the 2010 census. 1. From the stem-and-leaf display, find the median and the interquartile range. 2. Write a few sentences describing this distribution.
> 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 safety inspectors have set a standard of ensuring that the stands can s
> The company in Exercise 36 contacts 600 people selected at random, and only 133 remember the ad. 1. Should the company renew the contract? Support your recommendation with an appropriate test. 2. Explain what your P-value means in this context.
> Software, part II 203 students signed up for the Stats course in Exercise 35 . They used the software suggested by the salesman, and scored an average of 108 points on the final with a standard deviation of 8.7 points. 1. Should the professor spend the m
> 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 product. The radio station conducts a random phone
> A statistics professor has observed that for several years students score an average of 105 points out of 150 on the semester exam. A salesman suggests that he try a statistics software package that gets students more involved with computers, predicting
> 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. 1. Is this
> 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 hiring practices are discriminatory? 1. Is this a one-tailed or a
> Consider again the task of the quality control inspectors in Exercise 30 . 1. In this context, what is meant by the power of the test the inspectors conduct? 2. They are currently testing 5 items each hour. Someone has proposed that they test 10 instead.
> As in Exercise 29 , state regulators are checking up on repair shops to see if they are certifying vehicles that do not meet pollution standards. 1. In this context, what is meant by the power of the test the regulators are conducting? 2. Will the power
> 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
> During his 20 seasons in the NHL, Wayne Gretzky scored 50% more points than anyone who ever played professional hockey. He accomplished this amazing feat while playing in 280 fewer games than Gordie Howe, the previous record holder. Here are the number o
> Recent concern with the rise in global temperatures has focused attention on the level of carbon dioxide (CO2) in the atmosphere. The National Oceanic and Atmospheric Administration (NOAA) records the CO2 levels in the atmosphere atop the Mauna Loa volca
> 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
> Testing for Alzheimer 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
> In 2015, the U.S. Census Bureau reported that 62.2% of American families owned their homes the lowest rate in 20 years. 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
> Consider again the points-based spam filter described in Exercise 24 . 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-ma
> Exercise 23 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 financial condition fail to add up to a minimum cutoff score set by the bank will
> 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. T
> 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 income level, cre
