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 population of senior citizens. A patient who tested positive would then go through the more expensive battery of tests and medical diagnosis. The authors reported a false-positive rate of 4% and a false-negative rate of 8%. 1. Put this in the context of a hypothesis test. What are the null and alternative hypotheses? 2. What would a Type I error mean? 3. What would a Type II error mean? 4. Which is worse here, a Type I or Type II error? Explain. 5. What is the power of this test?
> 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,
> 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 n
> 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
> 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
> 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
> 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 wi
> In June 2010, a random poll of 800 working men found that 9% had taken on a second job to help pay the bills. (www.careerbuilder.com) 1. Estimate the true percentage of men that are taking on second jobs by constructing a 95% confidence interval. 2. A pu
> In January 2014, 16 gas stations in eastern Wisconsin posted these prices for a gallon of regular gasoline: 1. Make a stem-and-leaf display of these gas prices. Use split stems; for example, use two 3.2 stems one for prices between $3.20 and $3.24 and th
> In January 2016, at the end of his time in office, President Obama approval rating stood at 57% in Gallup daily tracking poll of 1500 randomly surveyed U.S. adults. (www.gallup.com/poll/113980/gallup-daily-obama-job-approval.aspx) 1. Make a 95% confidenc
> 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. 1. Estimate the true proportion
> Yahoo surveyed 2400 U.S. men. 1224 of the men identified themselves as the primary grocery shopper in their household. 1. Estimate the percentage of all American males who identify themselves as the primary grocery shopper. Use a 98% confidence interval.
> 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 α=0.05. Would
> 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 α=0.05. Would he have made the same decision at α=0.
> 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 P-value of 0.17 means in
> 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.
> According to www.marketingcharts.com/, the average 18–24-year old has 649 Facebook friends. The student who collected the survey data in Student survey wanted to test if the mean number is higher at his school. Using his data, test an appropriate hypot
> Here are the data from the researcher studying the reaction times of rats from Chapter 17, Exercise 61. Recall that he has a requirement that the maze take about a minute to complete on average. 1. Plot the data. Do you think the conditions are satisfied
> As we saw in Chapter 17, Exercise 60, Consumer Reports tested 11 brands of vanilla yogurt and found these numbers of calories per serving: 1. Check the assumptions and conditions. 2. A diet guide claims that you will get an average of 120 calories from a
> A meteorologist preparing a talk about global warming compiled a list of weekly low temperatures (in degrees Fahrenheit) he observed at his southern Florida home last year. The coldest temperature for any week was 36°F, but he inadvertently recorded the
> As we learned in Chapter 17, Exercise 59, in 1998, as an advertising campaign, the Nabisco Company announced a 1000 Chips Challenge, claiming that every 18-ounce bag of their Chips Ahoy! cookies contained at least 1000 chocolate chips. Dedicated statisti
> From Chapter 17, Exercise 58, Bjork Larsen was trying to decide whether to use a new racing wax for cross-country skis. He decided that the wax would be worth the price if he could average less than 55 seconds on a course he knew well, so he planned to s
> In Chapter 17, Exercise 57 we saw that Yvon Hopps ran an experiment to determine optimum power and time settings for microwave popcorn. His goal was to find a combination of power and time that would deliver high-quality popcorn with less than 10% of the
> We saw in Chapter 17, Exercise 56 that some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5. 1. Do
> Recall from Chapter 17, Exercise 55 that students investigated the packaging of potato chips. They purchased 6 bags of Lay Ruffles marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (i
> The technology committee of Chapter 17, Exercise 42 wants to perform a test to see if the mean amount of time students are spending in the lab has increased from 55 minutes. Here are the data from a random sample of 12 students. 1. Plot the data. Are any
> The researcher from Chapter 17, Exercise 39 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.
> The nutrition lab in Chapter 17, Exercise 38 tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for reduced sodium franks. The mean sodium content for the sample was 322.0 mg with a standard dev
> From the measurements of body temperature in Chapter 17, Exercise 29, you created a confidence interval for the true mean body temperature of healthy adults. 1. 98.6°F is commonly assumed to be normal. Set up the null and alternative hypothese
> The College Board reported that 60.3% of all students who took the 2016 AP Statistics exam earned scores of 3 or higher. One teacher wondered if the performance of her school was better. She believed that year students to be typical of those who will tak
> The histogram shows total gross earnings (in millions of dollars) of the top 200 major release movies in 2015. (Data extracted from Movies_06-15) An industry publication reports that the typical movie makes $23.2 million, but a watchdog group concerned w
> 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 fall
> 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 t
> An airline 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 la
> 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 propor
> 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 2014 was 6
> 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 jur
> 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 not a surprising value given that only 40% of all its employees are women. Wha
> 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 green bean seeds and pla
> A magazine is considering the launch of an online edition. The magazine plans to go ahead only if it convinced that more than 25% of current readers would subscribe. The magazine contacted a Simple Random Sample of 500 current subscribers, and 137 of tho
> During the first 15 weeks of the 2016 season, the home team won 137 of the 238 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 conclu
> Exercise 64 looked at distances PGA golfers can hit the ball. The standard deviation of these average drive distances is 11.2 yards, and the quartiles are Q1=282.05 yards and Q3=294.5 yards. 1. Write a sentence or two describing the spread in distances b
> 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
> 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 re
> 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 hypoth
> We saw in Chapter 16, Exercise 36 that First USA tested the effectiveness of a double miles campaign by recently sending out offers to a random sample of 50,000 cardholders. Of those, 1184 registered for the promotion. Even though this is nearly a 2.4% r
> We learned in Chapter 16, Exercise 35 that the Paralyzed Veterans of America recently sent letters to a random sample of 100,000 potential donors and received 4781 donations. They’ve had a contribution rate of 5% in past campaigns, but a staff member wor
> 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 fro
> 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 dur
> In the 1980s, it was generally believed that congenital abnormalities affected about 5% of the nation 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.
> 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
