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bayesian statistics an introduction
Statistics Through Applications 2nd Edition Daren S Starnes, David S Moore, Dan Yates - Solutions
Drug improves coordination A drug is suspected of aff ecting the coordination of subjects. Th e drug can be administered in three ways: orally, by injection under the skin, or by injection into a vein. Th e potency of the drug probably depends on the method of administration as well as on the dose
Ugly french fries Few people want to eat discolored french fries. Potatoes are kept refrigerated before being cut for french fries to prevent spoiling and preserve fl avor. But immediate processing of cold potatoes causes discoloring due to complex chemical reactions. Th e potatoes must therefore
Meditation lowers anxiety An experiment that was publicized as showing that a meditation technique lowered the anxiety level of subjects was conducted as follows: Th e experimenter interviewed the subjects and assessed their levels of anxiety. Th e subjects then learned how to meditate and did so
Better air bags Car makers are interested in developing safer air bags that reduce injuries in collisions. An automobile manufacturer is trying to decide between two possible air bags for use in the company’s vehicles. Six reusable crash test dummies—large male, average male, small male, large
Data Exploration follow-up Refer to the Data Exploration (page 287) on standing and sitting pulse rates.(a) What statistical advantages did the class’s matched pairs design have over its completely randomized design?(b) In the matched pairs experiment, why did the class randomize who stood fi rst
Activity 6.2B follow-up Refer to the heart rate experiment from Activity 6.2B.(a) Why did we randomize the order in which each student used the two diff erent step heights?(b) Examine the class data from a diff erent angle. Do you see any evidence of a“learning eff ect” from the fi rst step
More rats In Exercise 6.12 (page 266), a nutritionist had 10 rats of each of two genetic strains. Th e eff ect of genetic strain can be controlled by treating the strains as blocks and randomly assigning 5 rats of each strain to Diet A. Th e remaining 5 rats of each strain receive Diet B.(a)
Doctors and nurses Nurse-practitioners are nurses with advanced qualifi cations who oft en act much like primary-care physicians. Are they as eff ective as doctors at treating patients with chronic conditions? An experiment was conducted with 1316 patients who had been diagnosed with asthma,
Comparing cancer treatments Th e progress of a type of cancer diff ers in women and men. A clinical experiment to compare three therapies for this cancer therefore treats sex as a blocking variable.(a) You have 500 male and 300 female patients who are willing to serve as subjects.Use a diagram to
In the cornfi eld An agriculture researcher wants to compare the yield of 5 corn varieties. Th e fi eld in which the experiment will be carried out increases in fertility from north to south. Th e researcher therefore divides the fi eld into 30 plots of equal size, arranged in 6 east-west rows of 5
Baking cakes A food company is preparing to market a new cake mix. It is important that the taste of the cake not be changed by small variations in baking time or temperature. In an experiment, cakes made from the mix are baked at 3008F, 3208F, or 3408F, and for 1 hour or for 1 hour and 15 minutes.
Clean clothes Which of two brands of laundry detergent—Brand A or Brand B—cleans clothes better? Does one brand work better in both hot and cold water? Let’s design an experiment to fi nd out. A basket containing 120 pieces of dirty laundry is available for the experiment.(a) Identify the
Dealing with cholesterol Clinical trials have shown that reducing blood cholesterol using either drugs or diet reduces heart attacks. Th e fi rst researchers followed their subjects for 5 to 7 years. In order to see results as quickly as possible, the subjects were chosen from the group at greatest
Diet and cancer Substances that cause cancer should not appear in our food. We don’t want to experiment on people to learn what substances cause cancer, so we experiment on rats instead. Th e rats are specially bred to have more tumors than humans do. Th ey are fed large doses of the test
Daytime running lights Canada requires that cars be equipped with“daytime running lights,” headlights that automatically come on at a low level when the car is started. Some manufacturers are now equipping cars sold in the United States with running lights. Will running lights reduce accidents
Testing a natural remedy Th e National Institutes of Health is at last sponsoring proper clinical trials of some natural remedies. In one study at Duke University, 330 patients with mild depression are enrolled in a trial to compare Saint-John’s-wort with a placebo and with Zoloft , a common
Activity 6.2A follow-up Refer to the Mozart Eff ect experiment from Activity 6.2A (page 273).(a) Was the experiment double-blind? Why is this important?(b) Did the experimental design take the placebo eff ect into account? Why is this important?(c) Why was the coin fl ip important in this
Ultrasound and birth weight In this study, researchers examined the eff ect of ultrasound on birth weight. Pregnant women participating in the study were randomly assigned one of two groups. Th e fi rst group of women received an ultrasound; the second group did not. When the subjects’ babies
Real-world problems Explain the diff erence between refusals, nonadherers, and dropouts in an experimental study. Why must researchers be concerned about these three groups?
Testing a natural remedy Although the law doesn’t require it, we decide to subject Dr. Moore’s Old Indiana Extract to a clinical trial. We hope to show that the extract reduces pain from arthritis. Sixty patients suff ering from arthritis and needing pain relief are available. We will give a
Emergency room care An article in a medical journal reports on an experiment to see if injecting an oxygen-carrying fl uid in addition to performing standard emergency room procedures would help patients in shock from loss of blood. Th e article describes the experiment as a “randomized,
Medical news When it was found that hydroxyurea reduced the symptoms of sickle-cell anemia, the National Institutes of Health released a medical bulletin. Th e bulletin said, “Th ese fi ndings are the results of data analyzed from the Multicenter Study of Hydroxyurea in Sickle Cell Anemia (MSH),
Acupuncture and pregnancy A study sought to determine if the ancient Chinese art of acupuncture could help infertile women become pregnant.13 One hundred sixty healthy women undergoing treatment with artifi cial insemination were recruited for the study. Half of the subjects were randomly assigned
More statistics majors A university’s statistics department wants to attract more majors. It prepares two advertising brochures. Brochure A stresses the intellectual excitement of statistics. Brochure B stresses how much more money statisticians make. Which will be more attractive to fi rst-year
Clumsy men? A doctor at a veterans hospital examines all of the patient records over a 9-year period and fi nds that twice as many men as women fell out of their hospital beds during their stay. Th is is put forward as evidence that men are clumsier than women.(a) Is this an experiment or an
Healthy nurses? Th e Nurses’ Health Study has surveyed a sample of over 100,000 female registered nurses every 2 years since 1976. Beginning in 1980, the study asked questions about diet, including alcohol consumption. Aft er looking at all deaths among these nurses, the researchers concluded:
Learning about markets, II Refer to the previous exercise.(a) Outline a better design for an experiment to compare the two methods of learning about economic markets. What do you suggest as a response variable?Use the diagrams in Figures 6.2 (page 263) and 6.3 (page 264) as models.(b) Use Table B,
Learning about markets, I An economics teacher wonders if playing market games online will help students understand how markets set prices. You suggest an experiment: have some students use the online games, while others talk about markets in small group discussions. Th e course has two sections of
What a headache! Doctors identify “chronic tension–type headaches”as headaches that occur almost daily for at least six months. Can antidepressant medications or stress management training reduce the number and severity of these headaches? Are both together more effective than either alone?
Does job training work? A state institutes a job-training program for manufacturing workers who lose their jobs. Aft er fi ve years, the state reviews how well the program works. Critics claim that, because the state’s unemployment rate for manufacturing workers was 6% when the program began and
Signifi cant doesn’t mean important Suppose we’re testing a new antibacterial cream, “Formulation NS.” We know from previous research that, with no medication, the mean healing time (defi ned as the time for the scab to fall off ) is 7.6 days.We make a small cut on the inner forearm of 25
Family dinners and better grades? Does eating dinner with their families improve students’ academic performance? According to an ABC News article,“Teenagers who eat with their families at least fi ve times a week are more likely to get better grades in school.”10 Th is fi nding was based on
TV harms children Observational studies suggest that children who watch many hours of television get lower grades in school and are more likely to commit crimes than those who watch less TV. Explain clearly why these studies do not show that watching TV causes these harmful eff ects. In particular,
Prayer and meditation You read in a magazine that “nonphysical treatments such as meditation and prayer have been shown to be eff ective in controlled scientifi c studies for such ailments as high blood pressure, insomnia, ulcers, and asthma.” Explain in simple language what the article means
Statistical signifi cance, II Th e fi nancial aid offi ce of a university asks a sample of students about their employment and earnings. Th e report says that “for academic year earnings, a signifi cant diff erence was found between the sexes, with men earning more on the average. No signifi cant
Statistical signifi cance, I A randomized comparative experiment examines whether a calcium supplement in the diet reduces the blood pressure of healthy men.Th e subjects receive either a calcium supplement or a placebo for 12 weeks. Th e researchers conclude that “the blood pressure of the
Randomization at work To demonstrate how randomization reduces confounding, consider the following situation. A nutrition experimenter intends to compare the weight gain of newly weaned male rats fed Diet A with that of rats fed Diet B. To do this, she will feed each diet to 10 rats. She has
Learning on the Web Th e discussion following Example 6.1 (page 259)notes that the Nova Southeastern University study doesn’t tell us much about Web versus classroom learning because the students who chose the Web version were much better prepared. Describe the design of an experiment to get
Healthy turkeys Turkeys raised commercially for food are oft en fed the antibiotic salinomycin to prevent infections from spreading among the birds.Salinomycin can damage the birds’ internal organs, especially the pancreas. A researcher believes that adding vitamin E to the diet may prevent
Internet phone calls It is possible to use a computer to make telephone calls over the Internet. How will the cost aff ect the behavior of users of this service?You will off er the service to all 200 rooms in a college dormitory. Some rooms will pay a fl at rate. Others will pay higher rates at
Aspirin and heart attacks, II Refer to the previous exercise. Discuss how each of the three principles of experimental design was addressed in the Physicians’ Health Study.
Aspirin and heart attacks, I Can aspirin help prevent heart attacks? Th e Physicians’ Health Study, a large medical experiment involving 22,071 male physicians, attempted to answer this question. One randomly selected group of 11,037 physicians took an aspirin every second day, while the rest
Do placebos really work? Researchers in Japan conducted an experiment on 13 individuals who were extremely allergic to poison ivy. On one arm, each subject was rubbed with a poison ivy leaf and told the leaf was harmless. On the other arm, each subject was rubbed with a harmless leaf and told it
Activity 6.1 follow-up(a) Identify the subjects, treatments, and explanatory and response variables in the therapeutic touch experiment.(b) Aft er Emily’s results were published, therapeutic touch practitioners argued that her results were not valid. Discuss one or two arguments they might have
Vitamin C and colds Last year only 10% of a group of adult men did not have a cold at some time during the winter. Th is year all the men in the group took 1 gram of vitamin C each day, and 20% had no colds. A writer claims that this shows that vitamin C helps prevent colds. Explain why this
Nursing your baby An article in a women’s magazine says that women who nurse their babies feel warmer and more receptive toward the infants than mothers who bottle-feed. Th e author concludes that nursing has desirable eff ects on the mother’s attitude toward the child. But women choose whether
Public housing A study of the eff ect of living in public housing on family stability in low-income households was carried out as follows: A list of applicants accepted for public housing was obtained, together with a list of families who applied but were rejected by the housing authorities. A
On sale A researcher wants to study the eff ect of price promotions on consumers’ expectations. Th e researcher makes up two diff erent histories of the store price of a video game for the past year. Students in an economics course view one or the other price history on a computer. Some students
Steroids in baseball A 2008 New York Times article on public opinion about steroid use in baseball discussed the results of a sample survey. Th e survey found that 34% of adults think that at least half of Major League Baseball (MLB) players “use steroids to enhance their athletic performance.”
Life and Internet A poll of 586 adults who used the Internet in the past week were asked whether “the Internet has made your life much better, somewhat better, somewhat worse, much worse, or has it not aff ected your life either way.” In all, 152 of the 586 said “much better.”26(a) What is
The Harris Poll Here is the language used by the Harris Poll to explain the accuracy of its results: “In theory, with a sample of this size, one can say with 95 percent certainty that the results have a statistical precision of plus or minus 3 percentage points of what they would be if the entire
Should he go or stay? In December 1998, the House of Representatives impeached President Clinton, the fi rst step in removing him from offi ce. Th e Senate then conducted a trial and found the president not guilty. Here are two opinion poll questions asked aft er the House had acted:What do you
Bigger samples, please Explain in your own words the advantages of bigger random samples in a sample survey.
Planning a survey of students Th e student government plans to ask a random sample of students at a large high school about their priorities for improving the school newspaper. A school counselor provides a list of the 3500 students at the school to serve as a sampling frame.(a) How would you
TV commercials Th e noted scientist Dr. Iconu wanted to investigate attitudes toward television advertising among American college students. He decided to use a sample of 100 students. Students in freshman psychology (PSY 001) are required to serve as subjects for experimental work. Dr. Iconu
We don’t like one-way streets Highway planners decided to make a main street in West Lafayette, Indiana, a one-way street. Th e Lafayette Journal and Courier took a one-day poll by inviting readers to call a telephone number to record their comments.Th e next day, the paper reported:Journal and
Dress code? Th e principal has asked your statistics class to carry out a survey of student opinion about a proposed dress code. Th e class decides to choose four of its members at random to meet with the principal. Th e class list appears below. Choose an SRS of 4 using Table B, beginning at line
Baseball tickets Suppose you want to know the average amount of money spent by the fans attending opening day for the Cleveland Indians baseball season.You get permission from the team’s management to conduct a survey at the stadium, but they will not allow you to bother the fans in the club
Survey time! Return to Activity 5.3 (page 236). Once your teacher has approved your survey design plan, go ahead and carry it out. Write a brief report summarizing the results. Follow the four-step statistical problem-solving process (page 19).
What kind of error? Each of the following is a source of error in a sample survey. Label each as sampling error or nonsampling error, and explain your answers.(a) Th e telephone directory is used as a sampling frame.(b) Th e person cannot be contacted in fi ve calls.(c) Interviewers choose people
Telling the truth? Many people don’t give honest answers to questions about illegal or sensitive issues. One study divided a large group of adults into thirds at random. All were asked if they had ever used cocaine. Th e fi rst group was interviewed by telephone: 21% said “Yes.” In the group
Did you vote? When the Current Population Survey asked the adults in its sample of 50,000 households if they voted in the most recent presidential election, 54% said they had. In fact, only 49% of the adult population voted in that election.(a) Use the quick method to estimate the margin of error
TV ratings Th e method of collecting the data can infl uence the accuracy of sample results. Th e following methods have been used to collect data on television viewing in a sample household:(a) Diary method. Th e household keeps a diary of all programs watched and who watched them for a week, then
Multistage sampling Th e previous exercise gives part of the description of a sample survey from the Wall Street Journal.(a) It appears that the sample was taken in several stages. Why can we say this?(b) Th e fi rst stage no doubt used a stratifi ed sample, though the Journal does not say this.
Critiquing a poll Th e Wall Street Journal published an article on attitudes toward the Social Security system based on a sample survey. It found, for example, that 36% of people aged 18 to 34 expected Social Security to pay nothing at all when they retire. News articles tend to be brief in
Women engineers About 20% of the engineering students at a large university are women. Th e school plans to poll a sample of 200 engineering students about the quality of student life.(a) If an SRS of size 200 is selected, about how many women do you expect to fi nd in the sample?(b) If the poll
A stratifi ed sample A university has 2000 male and 500 female faculty members. Th e university president wants to poll the opinions of a random sample of faculty members. In order to give adequate attention to female faculty opinion, the president decides to choose a stratifi ed random sample of
Systematic random sample Th e fi nal stage in a multistage sample must choose 5 of the 500 addresses in a neighborhood. You have a list of the 500 addresses in geographical order. To choose a systematic random sample, proceed as follows:Step 1. Choose 1 of the fi rst 100 addresses on the list at
Bad survey questions Write your own examples of bad sample survey questions.(a) Write a biased question designed to get one answer rather than another.(b) Write a question that is confusing, so that it is hard to answer.
Closed versus open questions Two basic types of questions are closed questions and open questions. A closed question asks the subject for one or more of a fi xed set of responses. An open question allows the subject to answer in his or her own words. Th e interviewer writes down the responses and
Wording of questions A New York Times/CBS News Poll asked a random sample of Americans about abortion: “Do you think there should be an amendment to the Constitution prohibiting abortions, or shouldn’t there be such an amendment?” Th e same people were later asked, “Do you believe there
Genetically modifi ed foods An article in the journal Science looks at diff erences in attitudes toward genetically modifi ed foods in Europe and the United States. Th is calls for sample surveys. Th e European survey chose a sample of 1000 adults in each of 17 European countries. Here’s part of
Scholar-athletes To ask about their future plans, you want to interview 10 students at your high school who have received athletic scholarships to attend college. Because you believe there may be large diff erences among athletes in diff erent sports, you decide to interview a stratifi ed random
A sampling paradox? Example 5.19 compares two SRSs—of a university’s undergraduate and graduate students. Th e sample of undergraduates contains a smaller fraction of the population, 1 out of 90, versus 1 out of 15 for graduate students. Yet sampling 1 out of 90 undergraduates gives a smaller
Activity 5.3 follow-up Return to the survey your team constructed in Activity 5.3 (page 236). Discuss how your design protects against(a) sampling errors.(b) nonsampling errors.
Internet users now Who uses the Internet more today—males or females?Find a report of a recent survey that you believe provides accurate information on this question. Print the article if possible. Be sure to record all source information.Write a brief report following the four-step statistical
Polling students A high school chooses an SRS of 100 students from the school’s attendance list to interview about student life. If it selected two SRSs of 100 students at the same time, the two samples would give somewhat diff erent results. Is this variation a source of sampling error or of
Internet users then A survey of Internet users in 1995 found that males outnumbered females by nearly 2 to 1. Th is was a surprise, because earlier surveys had put the ratio of men to women closer to 9 to 1. Later in the article we fi nd this information:Detailed surveys were sent to more than
What kind of error? Which of the following are sources of sampling error and which are sources of nonsampling error? Explain your answers.(a) Th e subject lies about past drug use.(b) A typing error is made in recording the data.(c) Data are gathered by asking people to mail in a coupon printed in
Not in the margin of error A recent Gallup Poll found that 68% of adult Americans favor teaching creationism along with evolution in public schools. Th e Gallup press release says:For results based on samples of this size, one can say with 95 percent confi dence that the maximum error attributable
Simulating summer employment Random digits can be used to simulate the results of random sampling. Suppose that you are drawing simple random samples of size 25 from a large number of college students and that 20% of the students are unemployed during the summer. To simulate this SRS, let 25
Video gaming In a 2006 poll, 40% of American adults surveyed said that they play computer or video games. Of those who played such games, 10% reported playing for 10 or more hours per week. According to the Associated Press, “Th e results are taken from a poll of 3,024 adults, including 1,046 who
Protecting teens Th e previous exercise describes a sample survey of 1070 teens, with margin of error 63% for 95% confi dence.(a) An agency that is responsible for protecting children thinks that 95% confi -dence is not enough. Th ey want to be 99% confi dent. How would the margin of error for 99%
Teens on the Net A poll of 1070 teens aged 13 to 17 fi nds that 742 have received personal messages online from people they don’t know. Th e announced margin of error for this result is plus or minus 3 percentage points. Th e news report does not give the confi dence level, but you can be quite
Explaining confi dence A student reads that we are 95% confi dent that the average score of young men on the quantitative part of the National Assessment of Educational Progress is 267.8 to 276.2. Asked to explain the meaning of this statement, the student says, “95% of all young men have scores
Find the margin of error Exercise 5.38 (page 228) describes a sample survey of 61,239 adults living in Ontario. About what is the margin of error for conclusions having 95% confi dence about the entire adult population of Ontario?Show your work.
Left ies According to “Real Facts” at Snapple.com, 13% of adults are left -handed. At a math teacher’s conference, 16% of those attending were left -handed.5.48 Single-sex classes In an experiment to test the eff ectiveness of single-sex classrooms, girls assigned at random to a coeducational
Presidential polls California has about four times as many voters as Ohio, but both are very important states for the outcome of any presidential election.One national polling organization plans to take surveys of 1000 randomly selected voters in each of these two states on the day before the
Strike three A survey is conducted in Chicago (population 2,800,000) using random digit dialing equipment that places calls at random to residential phones, both listed and unlisted. Th e purpose of the survey is to determine the percent of Chicagoans who support the “three strikes and you’re
Is there a heaven? A news article reports that in a recent opinion poll, 81%of a sample of 1003 adults said they believe there is a heaven.(a) Use the quick method to estimate the margin of error for a sample of this size.(b) Make a confi dence statement about the percent of all adults who believe
Polling men and women Th e sample survey described in Exercise 5.42 interviewed 472 randomly selected men as well as 1025 women. Th e poll announced a margin of error of 63 percentage points for 95% confi dence in conclusions about women. Th e margin of error for results concerning men was 65
Polling women Many years ago, a New York Times Poll on women’s issues interviewed 1025 women randomly selected from the United States, excluding Alaska and Hawaii. One question was “Many women have better jobs and more opportunities than they did 20 years ago. Do you think women had to give up
The Current Population Survey Though opinion polls usually make 95% confidence statements, some sample surveys use other confidence levels.The monthly unemployment rate, for example, is based on the Current Population Survey of about 50,000 households. The margin of error in the unemployment rate
Find the margin of error Example 5.12 tells us that Gallup asked 501 teenagers whether they approved of legal gambling; 52% said they did. Use the quick method to estimate the margin of error for conclusions about all teenagers. How does your result compare with Gallup’s margin of error quoted in
Take a bigger sample A student is planning a project on student attitudes toward part-time work while attending school. She develops a questionnaire and plans to ask 25 randomly selected students to fi ll it out. Her statistics teacher approves the questionnaire but suggests that the sample size be
Canada’s national health care Th e Ministry of Health in the Canadian province of Ontario wants to know whether the national health care system is achieving its goals in the province. Much information about health care comes from patient records, but that source doesn’t allow us to compare
A sampling simulation Let us illustrate sampling variability in a small sample from a small population. Ten of the 25 club members listed below are female. Th eir names are marked with asterisks in the list. Th e club chooses 5 members at random to receive free trips to the national convention.(a)
Predict the election Just before a presidential election, a national opinion poll increases the size of its weekly sample from the usual 1500 people to 4000 people.(a) Does the larger random sample reduce the bias of the poll result? Explain.(b) Does it reduce the variability of the result? Explain.
No hands! Students from Hunter College in New York City carried out an observational study of driver behaviors at 50 diff erent intersections. Of the 3120 drivers they observed, 23% were talking on cell phones.8(a) In national surveys of driver behavior, well over half of those surveyed admit that
Sampling variability In thinking about Gallup’s sample of size 1523, we asked, “Could it happen that one random sample finds that 57% of adults recently bought a lottery ticket and a second random sample finds that only 37% had done so?” Look at Figure 5.6 (page 224), which shows the results
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