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Statistics The Art And Science Of Learning From Data 3rd Edition Alan Agresti, Christine A. Franklin - Solutions
For Table 3.6 on the 50 states and D.C., the figure below shows the relationship between the murder rate and the percentage of single-parent families.a. For D.C., the percentage of single-parent families = 44.7 and the murder rate = 41.8. Identify D.C. on the scatter plot, and explain the effect
For the U.S. Statewide Crime data file on the text CD, let y = violent crime rate and x = percent with a college education. a. Construct a scatter plot. Identify any points that you think may be influential in a regression analysis. b. Fit the regression line using all 51 observations. Interpret
Repeat the previous exercise using x = percent with at least a high school education. This shows that an outlier is not especially influential if its x -value is not relatively large or small. a. Construct a scatter plot. Identify any points that you think may be influential in a regression
For the U.S. Statewide Crime data file on the text CD, using MINITAB to analyze y = violent crime rate and x = urbanization (percentage of the residents living in metropolitan areas) gives the results shown:The regression equation is violent = 36.0 + 5.93 urban a. Using the five-number summary of
Access the HS Graduation Rates file on the text CD, which contains statewide data on x = high school graduation rate and y = percentage of individuals without health insurance. a. Construct a scatter plot. Describe the relationship. b. Find the correlation. Interpret. c. Find the regression
In recent election years, political scientists have analyzed whether a gender gap exists in political beliefs and party identification. The table shows data collected from the 2004 General Social Survey on gender and party identification (ID).a. Identify the response and explanatory variables. b.
Example 11 discussed how the winning height in the Olympic high jump changed over time. Using the High Jump data file on the text CD, MINITAB reports Women_Meters = 10.9 0.00650 Year_Women for predicting the women’s winning height (in meters) using the year number. a. Predict the winning
A survey of adults revealed a positive correlation between the height of the subjects and their income in the previous year. a. Explain how gender could be a potential lurking variable that could be responsible for this association. b. If gender had actually been one of the variables measured in
For United Nations data from several countries, there is a strong negative correlation between the birth rate and the per capita television ownership. a. Does this imply that having higher television ownership causes a country to have a lower birth rate? b. Identify a lurking variable that could
An Associated Press story (February 15, 2002) quoted a study at the University of California at San Diego that reported, based on a nationwide survey, that those who averaged at least 8 hours sleep a night were 12% more likely to die within six years than those who averaged 6.5 to 7.5 hours of
Marilyn vos Savant writes a column for Parade magazine to which readers send questions, often puzzlers or questions with a twist. In the April 28, 1996, column, a reader asked, “A company decided to expand, so it opened a factory generating 455 jobs. For the 70 white-collar positions, 200 males
You have done a regression analysis for the catalog sales company you work for, using monthly data for the last year on y = total sales in the month and x = number of catalogs mailed in preceding month. You are asked to prepare a 200-word summary of what regression does under the heading
An Associated Press story (August 25, 1998) about the lack of fluoride in most of the water supply in Utah quoted antifluoride activist Norma Sommer as claiming that fluoride may be responsible for AIDS, since the water supply in San Francisco is heavily fluoridated and that city has an unusually
Consider the cell phone Study 3 described in Example 1. a. Identify the response variable and the explanatory variable. b. Was this an observational study or an experiment? Explain why.
During a baseball game between the Boston Brouhahas and the Minnesota Meddlers, the broadcaster mentions that the away team has won “13 consecutive meetings between the two teams played on nights with a full moon.” a. Is the broadcaster’s comment based on observational or experimental
Fourteen of the 16 infants in the Yale study elected to play with a toy resembling the helpful figure as opposed to one resembling the hindering figure. Is this convincing evidence that infants tend to prefer the helpful figure? Use the Simulating the Probability of Head with a Fair Coin applet to
a. Find the approximate margin of error when n = 1.b. Show the two possible percentage outcomes you can get with a single observation. Explain why the result in part a means that with only a single observation, you have essentially no information about the population percentage.c. How large a
A researcher wants to select 1% of the 10,000 subjects from the sampling frame. She selects subjects by picking one of the first 100 on the list at random, and then skipping 100 names to get the next subject, skipping another 100 names to get the next subject, and so on. This is called a systematic
Go to the Web site for the GSS, www.norc.org/GSS+Website/, click on Documentation, and then click on Sampling Design and Weighting. There you will see described the complex multistage design of the GSS. Explain how the GSS uses (a) Clustering. (b) Stratification. (c) Simple random sampling.
You’d like to estimate the mean size of families in your community. Explain why you’ll tend to get a smaller sample mean if you sample n families than if you sample n individuals (asking them to report their family size). (When you sample individuals, explain why you are more likely to sample a
Biologists and naturalists often use sampling to estimate sizes of populations, such as deer or fish, for which a census is impossible. Capture€“recapture is one method for doing this. A biologist wants to count the deer population in a certain region. She captures 50 deer, tags each, and then
A nationwide census is conducted in the United States every 10 years. a. Give at least two reasons why the United States takes a census only every 10 years. b. What are reasons for taking the census at all?
A campus club consists of five officers: president (P), vice president (V), secretary (S), treasurer (T), and activity coordinator (A). The club can select two officers to travel to New Orleans for a conference; for fairness, they decide to make the selection at random. In essence, they are
In Example 4, a random drawing was held to select the winners of the football tickets. Organizers randomly chose two numbers from a collection of slips of paper numbered 1 through 60. Using the Table of Random Digits, begin the selection process at line 10. Which individuals did you choose? Repeat
Use the Random Numbers applet on the text CD or use software to (a) answer the previous exercise and (b) select a simple random sample of three students out of a class of 500 students.
Use the Random Numbers applet on the text CD to select 10 of the 60 school district accounts described in Example 5. Explain how you did this, and identify the accounts to be sampled.
Use either software or a statistical calculator to select 10 of the 60 school district accounts described in Example 5. Explain how you did this, and identify the accounts to be sampled.
A local telephone directory has 50,000 names, 100 per page for 500 pages. Explaining how you found and used random numbers, select 10 numbers to identify subjects for a simple random sample of 10 names.
Many studies have demonstrated that high blood pressure increases the risk of developing heart disease or having a stroke. It is also safe to say that the health risks associated with binge drinking far outweigh any benefits. A study published in Heath Magazine in 2010 suggested that a combination
The following table shows the result of the 2008 presidential election along with the vote predicted by several organizations in the days before the election. The sample sizes were typically about 1000 to 2000 people. The percentages for each poll do not sum to 100 because of voters who indicated
The Gallup poll in Example 6 reported that during March 2011, 60% of Americans favored offshore drilling as a means of reducing U.S. dependence on foreign oil. The poll was based on the responses of n = 1021 individuals, and resulted in a margin of error of approximately 3%. Find the approximate
Some southern states in the United States have wrestled with the issue of a state flag that is sensitive to African Americans and not divisive. Suppose a survey asks, “Do you oppose the present state flag that contains the Confederate symbol, a symbol of past slavery in the South and a flag
A February 2, 2003, Atlanta Journal Constitution article about the bleak job market for graduating MBA students described an opinion survey conducted by a graduate student at a major state university. The student polled 1500 executive recruiters, asking their opinions on the industry’s most
More than 75% of Americans answer yes when asked, “Do you favor cracking down against illegal gun sales?” but more than 75% say no when asked, “Would you favor a law giving police the power to decide who may own a firearm?” a. Which statistic would someone who opposes gun control prefer to
An Internet survey of 545 Hong Kong residents suggested that close daily monitoring of volatile financial affairs may not be good for your mental health (J. Social and Clinical Psychology 2002: 21: 116–128). Subjects who felt that their financial future was out of control had the poorest overall
This was the headline of a New York Times article (May 19, 2003) about the Gowanus Canal in Brooklyn, which had become infamous for its contamination from sewage and industrial waste. Scientists and Army Corps of Engineers technicians used augurs, drills, and a split-spoon, which sucks up the muck
In August 2006, a trade group for liquor retailers put out a press release with the headline, “Millions of Kids Buy Internet Alcohol, Landmark Survey Reveals.” Further details revealed that in an Internet survey of 1001 teenagers, 2.1% reported that they had bought alcohol online. In such a
A few studies published in 2007 claimed health benefits from eating dark chocolate or drinking cocoa. One study found much lower rates of death due to cancer among the Kuna Indians, who live in the San Blas islands of Panama and drink cocoa as their main beverage, compared to residents of mainland
A story titled “Personals, Sex Sites Changing the Rules of Love” at www.msnbc.msn.com reported results of a study about oanline dating by the MSNBC network. The study used online responses of 15,246 people. Of those who responded, three fourths were men and about two thirds had at least a
A newspaper designs a survey to estimate the proportion of the population willing to invest in the stock market. It takes a list of the 1000 people who have subscribed to the paper the longest and sends each of them a questionnaire that asks, “Given the extremely volatile performance of the stock
Give an example of a survey that would suffer from a. Sampling bias due to the sampling design b. Sampling bias due to under coverage c. Response bias d. Non-response bias
You would like to investigate whether smokers are more likely than nonsmokers to get lung cancer. From the students in your class, you pick half at random to smoke a pack of cigarettes each day and half not to ever smoke. Fifty years from now, you will analyze whether more smokers than nonsmokers
There have been anecdotal reports of the ability of duct tape to remove warts. In an experiment conducted at the Madigan Army Medical Center in the state of Washington (Archives of Pediatric and Adolescent Medicine 2002; 156: 971–974), 51 patients between the ages of 3 and 22 were randomly
In a follow-up study, 103 patients in the Netherlands having warts were randomly assigned to use duct tape or a placebo, which was a ring covered by tape so that the wart itself was kept clear (Arch. Pediat. Adoles. Med. 2006; 160: 1121–1125). a. Identify the response variable, the explanatory
A New York Times article (March 12, 2006) described two studies in which subjects who had recently had a heart attack were randomly assigned to one of four treatments: placebo and three different doses of vitamin B. In each study, after years of study, the differences among the proportions having a
A study published in 2010 in The New England Journal of Medicine investigated the effect of financial incentives on smoking cessation. As part of the study, 878 employees of a company, all of whom were smokers, were randomly assigned to one of two treatment groups. One group (442 employees) was to
A randomized experiment investigates whether an herbal treatment is better than a placebo in treating subjects suffering from depression. Unknown to the researchers, the herbal treatment has no effect: Subjects have the same score on a rating scale for depression (for which higher scores represent
Consider an experiment being designed to study the effectiveness of an experimental pain reduction medication. The plan includes recruiting 100 individuals suffering from moderate to severe pain to participate. One half of the group will be assigned to take the actual experimental drug, and the
When either type of study is feasible, an experiment is usually preferred over an observational study. Explain why, using an example to illustrate. Also explain why it is not always possible for researchers to carry out a study in an experimental framework. Give an example of such a situation.
Consider the same setting as that of Exercise 4.39. Of the 100 participants, 45 are male and 55 are female. During the design of the study, one member of the research team suggests that all males be given the active drug and all females be given the placebo. Another member of the team wants to
For some time there has been debate about whether regular large doses of vitamin C reduce the chance of getting a common cold. a. Explain how you could design an experiment to test this. Describe all parts of the experiment, including (i) what the treatments are, (ii) how you assign subjects to the
A pharmaceutical company has developed a new drug for treating high blood pressure. They would like to compare its effects to those of the most popular drug currently on the market. Two hundred volunteers with a history of high blood pressure and who are currently not on medication are recruited to
A researcher wants to compare student loan debt for students who attend four-year public universities with those who attend four-year private universities. She plans to take a random sample of 100 recent graduates of public universities and 100 recent graduates of private universities. Which type
In Exercise 4.14, two officers were to be selected to attend a conference in New Orleans. Three of the officers are female and two are male. It is decided to send one female and one male to the convention. a. Labeling the officers as 1, 2, 3, 4, 5, where 4 and 5 are male, draw a stratified random
Of 400 employees at a company, 25% work in production, 40% work in sales and marketing, and 35% work in new product development. As part of a security awareness training program, the group overseeing implementation of the program will randomly choose a sample of 20 employees to begin the training;
A school district comprises 24 schools. The numbers of students in each of the schools are as follows:The district wants to implement an experimental teaching and learning model for approximately 20% of the 6057 students in the district. Administrators want to choose the 20% randomly, but they will
The contingency table shows results from the German study about whether there was an association between mobile phone use and eye cancer (Stang et al., 2001).a. The study was retrospective. Explain what this means.b. Explain what is meant by cases and controls in the headings of the table.c. What
Refer to the smoking case-control study in Example 9. Since subjects were not matched according to all possible lurking variables, a cigarette company can argue that this study does not prove a causal link between smoking and lung cancer. Explain this logic, using diet as the lurking variable.
Example 3 discussed a study comparing high schools that tested for drugs with high schools that did not test for drugs, finding similar levels of student drug use in each. State a potential lurking variable that could affect the results of such a study. Describe what the effect could be.
Exercise 4.10 mentioned that the away team has won 13 consecutive games played between the Boston Brouhahas and Minnesota Meddlers during full moons. This is a statement based on retrospective observational data. a. Many databases are huge, including those containing sports statistics. If you had
A two-factor experiment designed to compare two diets and to analyze whether results depend on gender randomly assigns 20 men and 20 women to the two diets, 10 of each to each diet. After three months the sample mean weight losses are as shown in the table.a. Identify the two factors (explanatory
A study (Psychosomatic Medicine 2002; 64: 593–603) claimed that people who consume caffeine regularly may experience higher stress and higher blood pressure. In the experiment, 47 regular coffee drinkers consumed 500 milligrams of caffeine in a pill form (equivalent to four 8-oz cups) during one
An experiment is being designed to compare relief from hay fever symptoms given by a low dose of a drug, a high dose of the drug, and a placebo. Each subject who suffers from hay fever and volunteers for the study is observed on three separate days, with a different treatment used each day. There
Smokers may have a more difficult time quitting smoking if they live with another smoker. How can an experiment explore this possibility in a study to compare bupropion with placebo? Suppose the researchers split the subjects into two groups: those who live with another smoker, and those who do not
If you want to conduct a study with humans to see if cell phone use makes brain cancer more likely, explain why an observational study is more realistic than an experiment.
Without using technical language, explain the difference between observational and experimental studies to someone who has not studied statistics. Illustrate with an example, using it also to explain the possible weaknesses of an observational study.
Give an example of a scientific question of interest for which it would be unethical to conduct an experiment. Explain how you could instead conduct an observational study.
A research study published in 2010 in the Archives of Neurology investigated the relationship between the results of a spinal fluid test and the presence of Alzheimer’s disease. The study included 114 patients with normal memories, 200 with memory problems, and 102 with Alzheimer’s disease.
Since 1976 the Nurses’ Health Study has followed more than 100,000 nurses. Every two years, the nurses fill out a questionnaire about their habits and their health. Results from this study indicated that postmenopausal women have a reduced risk of heart disease if they take a hormone replacement
The Gallup U.S. Employment poll reported on March 15, 2011, a national unemployment rate of 10.4%. (Data from www.gallup.com/poll/125639/Gallup_Daily_Workforce.aspx.)a. Gallup claims that the margin of error of the poll is +/– 0.7 percentage points. Estimate approximately on how many responses
Your friend reads about a study in an epidemiology journal that estimates that the chance is 15 out of 1 million that a teacher who works for 30 years in a school with typical asbestos levels gets cancer from asbestos. However, she also knows about a teacher who died recently who may have had
The last four teams of the Southeast region of the 2011 NCAA Mens Basketball Tournament were Butler (located in Indiana), Brigham Young University (located in Utah), Florida, and Wisconsin. The sports Web site espn.com asked visitors of the site which team would win the Southeast
You are assigned to direct a study on your campus to discover factors that are associated with strong academic performance. You decide to identify 20 students, who have perfect GPAs of 4.0, and then measure explanatory variables for them that you think may be important, such as high school GPA and
An Internet survey at a newspaper Web site reports that only 14% of respondents believe in gun control. Mention a lurking variable that could bias the results of such an online survey, and explain how it could affect the results.
You plan to sample from the 3500 undergraduate students who are enrolled at the University of Rochester to compare the proportions of female and male students who would like to see the United States have a female president. a. Describe the steps for how you would proceed, if you plan a simple
A large southern university had problems with 17 football players being disciplined for team rule violations, arrest charges, and possible NCAA violations. The online Atlanta Journal Constitution ran a poll with the question, Has the football coach lost control over his
A Gallup poll tracks obesity in the United States for the most and least obese metro areas in the United States. The poll, based on more than 200,000 responses between January and December of 2010, reported that certain chronic conditions are more prevalent in the most obese metro areas. The table
In fall 1995, the BBC in Britain requested viewers to call the network and indicate their favorite poem. Of 7500 callers, more than twice as many voted for Rudyard Kipling’s If than for any other poem. The BBC then reported that this was the clear favorite. a. Since any person could call, was
“Playing video games not so mindless.” This was the headline of a CNN news report 16 about a study that concluded that young adults who regularly play video games demonstrated better visual skills than young adults who do not play regularly. Sixteen young men volunteered to take a series of
In a study by Swedish researchers (Occupational and Environmental Medicine 2002, 59:517– 522), 2410 women who had worked as hairdressers and given birth to children were compared to 3462 women from the general population who had given birth. The hairdressers had a slightly higher percentage of
Read about the first Physicians’ Health Study at phs.bwh.harvard.edu. a. Explain whether it was (i) an experiment or an observational study and (ii) a retrospective or prospective study. b. Identify the response variable and the explanatory variable(s), and summarize results.
During the 1980s approximately 22,000 physicians over the age of 40 agreed to participate in a long-term study called the Physicians’ Health Study. One question investigated was whether aspirin helps to lower the rate of heart attacks. The physicians were randomly assigned to take aspirin or take
Refer to Exercise 4.71. One potential confounding variable was the amount of exercise the physicians got. The randomization should have balanced the treatment groups on exercise. The contingency table shows the relationship between whether the physician exercised vigorously and the treatments.a.
Repeat the previous exercise, considering another potential confounding variablewhether the physicians smoked. The contingency table cross-classifies treatment group by smoking status.a. Find the conditional proportions (recall Section 3.1) in the categories of this potential confounder
In the study discussed in the previous three exercises, this completely randomized study actually used two factors: whether received aspirin or placebo and whether received betacarotene or placebo. Draw a table or a flow chart to portray the four treatments for this study.
The subjects for the study described in Example 12 were evaluated for abstinence from cigarette smoking at the end of 12 months. The table shows the percentage in each group that were abstaining.a. Find the approximate margin of error for the abstinence percentage in each group. Explain what a
You want to conduct an experiment with your class to see if students prefer Coke or Pepsi. a. Explain how you could do this, incorporating ideas of blinding and randomization, (i) with a completely randomized design and (ii) with a matched pairs design. b. Which design would you prefer? Why?
The marketing department of a major oil company wants to investigate whether cars get better mileage using their gas (Brand A) than from an independent one (Brand B) that has cheaper prices. The department has 20 cars available for the study. a. Identify the response variable, the explanatory
In a cluster random sample with equal-sized clusters, every subject has the same chance of selection. However, the sample is not a simple random sample. Explain why not.
You plan to sample residents of registered nursing homes in your county. You obtain a list of all 97 nursing homes in the county, which you number from 01 to 97. Using random numbers, you choose five of the nursing homes. You obtain lists of residents from those five homes and interview all the
A study published in 2010 in the New England Journal of Medicine discusses a breastcancerscreening program that began in Norway in 1996 and was expanded geographically through 2005. Women in the study were offered mammography screening every two years. The goal of the study was to compare incidence
A researcher wants to study regional differences in dental care. He takes a multistage sample by dividing the United States into four regions, taking a simple random sample of ten schools in each region, randomly sampling three classrooms in each school, and interviewing all students in those
Studies show that marijuana is extremely popular among individuals who suffer from psychotic disorders such as schizophrenia. A recent study published in the British Journal of Psychiatry followed 80 marijuana smokers, 42 who had schizophrenia. Over the course of six days, the participants were
Many research studies such as the one discussed in Exercise 4.82 focus on a link between marijuana use and psychotic disorders such as schizophrenia. Studies have found that people with schizophrenia are twice as likely to smoke marijuana as those without the disorder. Data also suggest that
Excessive cumulative exposure to ovarian hormones is believed to cause breast cancer. A study (New England J. Medic. 2003; 348: 2313–2322) used information from 1811 pairs of female twins, one or both of whom had breast cancer. Paired twins were compared with respect to age at puberty, when
Explain whether an experiment or an observational study would be more appropriate to investigate the following: a. Whether or not smoking has an effect on coronary heart disease b. Whether or not higher SAT scores tend to be positively associated with higher college GPAs c. Whether or not a special
In each of the following situations, summarize negative aspects of the sample design. a. A newspaper asks readers to vote at its Internet site to determine if they believe government expenditures should be reduced by cutting social programs. Based on 1434 votes, the newspaper reports that 93% of
Repeat the previous exercise for the following scenarios: a. A principal in a large high school wants to sample student attitudes toward a proposal that seniors must pass a general achievement test in order to graduate. She lists all of the first-period classes. Then, using a random number table,
You want to investigate the opinions students at your school have about whether the age for legal drinking of alcohol should be 18. a. Write a question to ask about this in a sample survey in such a way that results would be biased. Explain why it would be biased. b. Now write an alternative
An interviewer stands at a street corner and conducts interviews until obtaining a quota in various groups representing the relative sizes of the groups in the population. For instance, the quota might be 50 factory workers, 100 housewives, 60 elderly people, 30 Hispanics, and so forth. This is
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