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Statistics The Art And Science Of Learning From Data 4th Global Edition Alan Agresti, Christine A. Franklin, Bernhard Klingenberg - Solutions
Club officers again In Exercise 4.15, 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
Security awareness training 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
Teaching and learning model A school district comprises 24 schools. The numbers of students in each of the schools are as follows:455 423 399 388 348 344 308 299 297 272 266 260 252 244 222 209 175 161 151 148 128 109 101 98 The district wants to implement an experimental teaching and learning
Pelvic girdle pain and sick leave The contingency table shows results from a Norwegian study about whether there was an association between pelvic girdle pain (PGP)and sick leave during pregnancy (Malmqvist et al., 2015).a. The study was retrospective. Explain what this means in the context of this
Smoking and lung cancer Refer to the smoking case-control study in Example 8. 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
Dream job and reality In 1995, 1000 teenagers participated in a survey. The respondents were asked about their dream jobs. Fifteen years later, a follow-up survey was conducted to see whether people were working in the jobs they wanted as teenagers or not. Was this study a retrospective study or a
Baseball under a full moon 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
Are two factors helpful? In 2014, a two-factor experiment was conducted in Eufaula city in Alabama (Omidire et al., 2015). It was designed to compare two fertilizers and to analyze whether yield results depend on crop type.The total yield (lbs/acre) of cucumber and okra harvested from plots
Which teaching method is more efficient? An experiment was designed to compare the efficiency of three types of teaching methods—traditional face-to-face instruction, hybrid (technology-mediated instruction) and completely online. A statistical course of three parts of comparable length was made
Effect of partner smoking in smoking cessation study Smokers may have a more difficult time quitting smoking if they live with a 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
Cell phones If you want to conduct a study with humans to see whether cell phone use makes brain cancer more likely, explain why an observational study is more realistic than an experiment.
Observational versus experimental study 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.
Unethical experimentation 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.
Spinal fluid proteins and Alzheimer’s 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,
Fear of drowning In 2015, the National Drowning Report published in Australia shows a drowning rate of 0.26 per 100,000 people in the Australian Capital Territory (ACT). A few days ago, you read about a teenager who drowned in the middle of the sea in the ACT.In deciding whether to go to the ACT
NCAA men’s basketball poll The last four teams of the Southeast region of the 2011 NCAA Men’s Basketball Tournament were Butler (located in Indiana), Brigham Young University (located in Utah), Florida, and Wisconsin. The sports website ESPN.com asked visitors of the site which team would win
Sampling your city’s citizens You are assigned to direct a study in your city to discover factors that are associated with good health. You decide to identify 50 citizens who have perfect health. Then, you measure explanatory variables for them that you think may be important such as good quality
Beware of online polls According to an online poll, 46%of Americans support Apple Inc.’s decision to oppose a federal court order demanding that it unlock a smartphone used by one of the culprits responsible for the San Bernardino terrorist attacks. Mention a lurking variable that could bias the
Comparing female and male students 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 elect a female president.a. Describe the steps for how you would
Second job for MPs An online poll was conducted asking respondents whether they thought members of parliament (MPs) should be allowed second jobs to boost their annual basic salary. The poll had two possible responses—“Yes, MPs should be allowed second jobs to avoid getting involved into
Obesity in metro areas 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 2010, reported that certain chronic conditions are more prevalent in the most obese
Voluntary sports polls In 2014, the Pittsburgh Penguins were ahead of the New York Rangers three games to one in the first round of the National Hockey League playoffs.ESPN.com conducted a voluntary, online poll that asked respondents to predict the outcomes of the rest of the series. Of all 1,094
Video games mindless? “Playing video games not so mindless.” This was the headline of a news report14 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
Physicians’ health study 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
Aspirin prevents heart attacks? 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 lower the rate of heart attacks. The physicians were randomly
Exercise and heart attacks Refer to Exercise 4.68. 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
Smoking and heart attacks Repeat the previous exercise, considering another potential confounding variable—whether the physicians smoked. The contingency table cross-classifies treatment group by smoking status. Smoking Status Treatment Never Past Current Total Aspirin 5,431 4,373 1,213 11,017
Aspirin, beta-carotene, and heart attacks 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 beta-carotene or placebo. Draw a table or a flow chart to portray the four
Bupropion and nicotine patch study results The subjects for the study described in Example 11 were evaluated for abstinence from cigarette smoking at the end of 12 months.The table shows the percentage in each group that were abstaining. Recall that margin of error and statistical significance are
Prefer M&Ms or Smarties? You want to conduct an experiment with your siblings to see whether they prefer M&Ms or Smarties candies.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.
Comparing gas brands The marketing department of a major oil company wants to investigate whether cars get better mileage using its 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
Samples not equally likely in a cluster sample? 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.
Nursing homes You plan to sample residents of registered nursing homes in your county. You obtain a list of all 97 nursing homes in the county, and randomly select five of them. You obtain lists of residents from those five homes and interview all the residents in each home.a. Are the nursing homes
Multistage health survey 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
Marijuana and schizophrenia Many research studies 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 individuals who smoke
Family disruption and age at menarche In 2013, a study was conducted in New Zealand. Information was used from a community sample of full sister pairs. This study examined menarcheal age in a group comprising age discrepant biologically disrupted/father absent sister pairs, and a matched control
Cell phone use Using the Internet, find a study about cell phone use and its potential risk when used by drivers of automobiles.a. Was the study an experiment or an observational study?b. Identify the response and explanatory variables.c. Describe any randomization or control conducted in the study
Read a medical journal Go to a website for an online medical journal, such as British Medical Journal(www.bmj.com). Pick an article in a recent issue.a. Was the study an experiment or an observational study?b. Identify the response variable and the primary explanatory variable(s).c. Describe any
Internet poll Find an example of results of an Internet poll. Do you trust the results of the poll? If not, explain why not.
Search for an observational study Find an example of an observational study from a newspaper, journal, the Internet, or some other medium.a. Identify the explanatory and response variables and the population of interest.b. What type of observational study was conducted?Describe how the data were
Search for an experimental study Find an example of a randomized experiment from a newspaper, journal, the Internet, or some other media.a. Identify the explanatory and response variables.b. What were the treatments? What were the experimental units?c. How were the experimental units assigned to
Judging sampling design 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 whether they believe government expenditures should be reduced by cutting social programs. Based on 1434 votes, the
More poor sampling designs 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 to graduate. She lists all of the first-period classes. Then, using a
Age for legal alcohol 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
Quota sampling 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
Smoking and heart attacks A Reuters story (April 2, 2003)reported that “The number of heart attack victims fell by almost 60% at one hospital six months after a smoke-free ordinance went into effect in the area (Helena, Montana), a study showed, reinforcing concerns about second-hand smoke.”
Issues in clinical trials A randomized clinical trial is planned for AIDS patients to investigate whether a new treatment provides improved survival over the current standard treatment. It is not known whether it will be better or worse.a. Why do researchers use randomization in such experiments
Compare smokers with nonsmokers Example 8 and Table 4.2 described a case-control study on smoking and lung cancer. Explain carefully why it is not sensible to use the study’s proportion of smokers who had lung cancer(that is, 688> 1688 + 6502) and proportion of nonsmokers who had lung cancer 121>
Is a vaccine effective? A vaccine is claimed to be effective in preventing a rare disease that occurs in about one of every 100,000 people. Explain why a randomized clinical trial comparing 100 people who get the vaccine to 100 people who do not get it is unlikely to be worth doing. Explain how you
Distinguish helping and hindering among infants Researchers at Yale University’s Infant Cognition Center were interested in determining whether infants had the ability to distinguish between the actions of helping and hindering. Each infant in the study was shown two videos. One video included a
Distinguish helping and hindering among infants, continued In the previous exercise, we considered how showing each baby in the study the two videos in the same order might create a bias. In fact, of the 16 babies in the study, half were shown the videos in one order while the other half was shown
Distinguish helping and hindering among infants, continued 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
Multiple choice: What’s a simple random sample?A simple random sample of size n is one in whicha. Every nth member is selected from the population.b. Each possible sample of size n has the same chance of being selected.c. There is exactly the same proportion of women in the sample as is in the
Multiple choice: Be skeptical of medical studies? An analysis of published medical studies about heart attacks(Crossen, 1994, p. 168) noted that in the studies having randomization and strong controls for bias, the new therapy provided improved treatment 9% of the time. In studies without
Multiple choice: Opinion and question wording A recent General Social Survey asked subjects whether they supported legalized abortion in each of seven circumstances.The percentage who supported legalization varied between 44.6% (if the woman is not married) to 88.6% (if the woman’s health is
Multiple choice: Campaign funding When the Yankelovich polling organization asked, “Should laws be passed to eliminate all possibilities of special interests giving huge sums of money to candidates?” 80% of the sample answered yes. When they posed the question,“Should laws be passed to
Multiple choice: Emotional health survey An Internet poll conducted in the United Kingdom by Netdoctor.co.uk asked individuals to respond to an “emotional health survey”(see www.hfienberg.com/clips/pollspiked.htm). There were 400 volunteer respondents. Based on the results, the British
Multiple choice: Sexual harassment In 1995 in the United Kingdom, the Equality Code used by the legal profession added a section to make members more aware of sexual harassment. It states that “research for the Bar found that over 40 percent of female junior tenants said they had encountered
Multiple choice: Effect of response categories A study(N. Schwarz et al., Public Opinion Quarterly, vol. 49, 1985, p. 388) asked German adults how many hours a day they spend watching TV on a typical day. When the possible responses were the six categories (up to 12 hour, 12 to 1 hour, 1 to 112
Systematic sampling 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, skipping 100 names to get the next subject, skipping another 100 names to get the next subject, and so on.This is called a
Complex multistage GSS sample Go to the website for the GSS, on Documentation and then click 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, and (c) simple random sampling.
Mean family size 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). (Hint: When you sample individuals, explain why you are
Capture–recapture 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
Munchie capture–recapture Your class can use the capture–recapture method described in the previous exercise to estimate the number of goldfish in a bag of Cheddar Goldfish. Pour the Cheddar Goldfish into a paper bag, which represents the pond. Sample 10 of them. For this initial sample, use
Activity: Sampling the states This activity illustrates how sampling bias can result when you use a nonrandom sample, even if you attempt to make it representative:You are in a geography class, discussing center and variability for several characteristics of the states in the contiguous United
2.133 Political conservatism and liberalism Where do Americans tend to fall on the conservative–liberal political spectrum? The General Social Survey asks, “I’m going to show you a seven-point scale on which the political views that people might hold are arranged from extremely liberal, point
2.131 Youth unemployment by gender The side-by-side box plots below show the unemployment rate among 15- to 24-year-olds in 28 European nations for each gender. The two outliers shown for each box plot refer to the same countries, Greece and Spain. Write a short paragraph comparing the distribution
2.129 Controlling asthma A study of 13 children suffering from asthma (Clinical and Experimental Allergy, vol. 20, pp. 429–432, 1990) compared single inhaled doses of formoterol(F) and salbutamol (S). Each child was evaluated using both medications. The outcome measured was the child’s peak
2.126 Who was Roger Maris? Roger Maris, who spent most of his professional baseball career with the New York Yankees, held the record for the most home runs in one season (61) from 1961 until 1998, when the record was broken by Mark McGwire. Maris played in the major leagues from 1957 to 1968. The
2.123 SAT scores The U.S. statewide average total SAT scores math + reading + writing for 2010 are summarized in the box plot. These SAT scores are out of a possible 2400.(Data available on the book’s website.)a. Explain how the box plot gives you information about the distribution shape.b. Using
2.117 NASDAQ stock prices The data values below represent the closing prices of the 20 most actively traded stocks on the NASDAQ Stock Exchange (rounded to the nearest dollar) on May 2, 2014.a. Sketch a dot plot or construct a stem-and-leaf plot.b. Find the median, the first quartile, and the third
2.116 Cereal sugar values Revisit the sugar data for breakfast cereals that are given in Example 4.a. Interpret the box plot in the figure (MINITAB output) by giving approximate values for the five-number summary.b. What does the box of the box plot suggest about possible skew?c. The mean is 8.75
2.112 Hurricane damage The histogram shows the distribution of the damage (in billion dollars) of the 30 most costly hurricanes hitting the U.S. mainland between 1900 and 2010. (Numbers are inflation adjusted and in 2010 dollars). The data are available in the Hurricane file on the book’s
2.108 Central Park monthly temperatures The MINITAB graph below uses dot plots to compare the distributions of the Central Park temperatures from 1869–2010 for the months of January and July.a. Describe the shape of each of the two distributions.b. Estimate the balance point for each of the two
2.99 Sandwiches and protein Listed in the table below are the prices of six-inch Subway sandwiches at a particular franchise and the number of grams of protein contained in each sandwich.a. Construct a stem-and-leaf plot of the protein amounts in the various sandwiches.b. What is the advantage(s)
2.98 Match the histogram Match each lettered histogram with one of the following descriptions: Skewed to the left, bimodal, symmetric, skewed to the right. 15 25 35 45 35 45 55 65 75 85 95 15 25 35 45 55 65 75 85 95 a b
2.97 Newspaper reading Exercise 2.24 gave results for the number of times a week a person reads a daily newspaper for a sample of 36 students at the University of Georgia.The frequency table is shown below.a. Construct a dot plot of the data.b. Construct a stem-and-leaf plot of the data. Identify
2.95 Number of siblings In a survey administered to members of an entertainment club, the results obtained for the question “How many siblings do you have?” werea. What is the sample size in this study?b. Which is the most appropriate graph to summarize the data—dot plot, stem-and-leaf plot,
2.94 Chad voting problems The 2000 U.S. presidential election had various problems in Florida. One was overvotes—people mistakenly voting for more than one presidential candidate. (There were multiple minor-party candidates.) There were 110,000 overvote ballots, with Al Gore marked on 84,197 and
2.92 Young non-citizens in the U.S. The table shows the number of 18- to 24-year-old noncitizens living in the United States between 2010 and 2012.a. Is Region of Birth quantitative or categorical? Show how to summarize results by adding a column of percentages to the table.b. Which of the
2.88 Federal government spending Explain what is wrong with the following pie chart, which depicts the federal government breakdown by category for 2010. Education (1%) Interest on national debt (5%) Medicaid (8%) Medicare (13%) Federal Spending for 2010 Other (18%) Social Security (20%) Defense
2.87 BBC license fee Explain what is wrong with the time plot shown of the annual license fee paid by British subjects for watching BBC programs. (Source: Evening Standard, November 29, 2006.) Licence fee increases () 150 140 130 120 110 100 90 At 1.8% above inflation fee will be 185 by 2013
2.86 Terrorism and war in Iraq In 2004, a college newspaper reported results of a survey of students taken on campus. One question asked was, “Do you think going to war with Iraq has made Americans safer from terrorism, or not?” The figure shows the way the magazine reported results.a. Explain
2.85 Enrollment trends Examples 18 and 19 presented graphs showing the total student enrollment at a U.S. university between 2004 and 2012 and the data for STEM major enrollment during that same time period. The data are repeated here.a. Construct a graph for only STEM major enrollments over this
2.84 Market share for food sales The pie chart shown was displayed in an article in The Scotsman newspaper(January 15, 2005) to show the market share of different supermarkets in Scotland.a. Pie charts can be tricky to draw correctly. Identify two problems with this chart.b. From looking at the
2.82 CO2 comparison The vertical side-by-side box plots shown below compare per capita carbon dioxide emissions in 2011 for many Central and South American and European nations. (Data available on the book’s website. Source: www.eia.gov)a. Give the approximate value of carbon dioxide emissions
2.75 Energy statistics The Energy Information Administration records per capita consumption of energy by country. The box plot below shows 2011 per capita energy consumption(in millions of BTUs) for 36 OECD countries, with a mean of 195 and a standard deviation of 120. Iceland had the largest per
2.72 Central Park temperature distribution revisited Exercise 2.26 showed a histogram for the distribution of Central Park annual average temperatures. The box plot for these data is shown here.a. If this distribution is skewed, would you expect it to be skewed to the right or to the left?
2.63 Youth unemployment In recent years, many European nations have suffered from relatively high youth unemployment.For the 28 EU nations, the table below shows the unemployment rate among 15- to 24-year-olds in 2013, also available as a file on the book’s website. (Source:World Bank). If you
2.55 Shape of cigarette taxes A recent summary for the distribution of cigarette taxes (in cents) among the 50 states and Washington, D.C., in the United States reported xQ = 73 and s = 48. Based on these values, do you think that this distribution is bell shaped? If so, why? If not, why not, and
2.52 Histograms and standard deviation The figure shows histograms for three samples, each with sample size n = 100.a. Which sample has the (i) largest and (ii) smallest standard deviation?b. To which sample(s) is the empirical rule relevant? Why? 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7
2.44 Knowing homicide victims The table summarizes responses of 4383 subjects in a recent General Social Survey to the question, “Within the past 12 months, how many people have you known personally that were victims of homicide?”a. To find the mean, it is necessary to give a score to the “4
2.43 Marriage statistics for 20–24-year-olds The table in the next column shows the number of times 20–24-year-old U.S. residents have been married, based on a Bureau of the Census report from 2004. The frequencies are actually thousands of people. For instance, 8,418,000 men never married, but
2.41 European fertility The European fertility rates (mean number of children per adult woman) from Exercise 2.18 are shown again in the table.a. Find the median of the fertility rates. Interpret.b. Find the mean of the fertility rates. Interpret.c. For each woman, the number of children is a whole
2.36 Center of plots The figure shows dot plots for three sample data sets.a. For which, if any, data sets would you expect the mean and the median to be the same? Explain why.b. For which, if any, data sets would you expect the mean and the median to differ? Which would be larger, the mean or the
2.35 Cereal sodium The dot plot shows the cereal sodium values from Example 4. What aspect of the distribution causes the mean to be less than the median? Dot Plot of Sodium Values for 20 Breakfast Cereals mean = 167 median = 180 0 50 100 150 200 250 300 350 Sodium (mg)
2.27 Is whooping cough close to being eradicated? In the first half of the 20th century, whooping cough was a frequently occurring bacterial infection that often resulted in death, especially among young children. A vaccination for whooping cough was developed in the 1940s. How effective has the
2.26 Central Park temperatures The first figure shows a histogram of the Central Park, New York, annual average temperatures from 1869 to 2012.a. Describe the shape of the distribution.b. What information can the time plot above show that a histogram cannot provide?c. What information does the
2.25 Blossom widths A data set (available at the book’s website) analyzed by the famous statistician R. A. Fisher consisted of measurements of different varieties of iris blossoms. Histograms representing the widths of the petals of the two species, Iris setosa and Iris versicolor, are on the
2.24 How often do students read the newspaper? Question 14 on the class survey (Activity 3 in Chapter 1) asked,“Estimate the number of times a week, on average, that you read a daily newspaper.”a. Is this variable continuous or discrete? Explain.b. The histogram shown gives results of this
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