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Statistics The Art And Science Of Learning From Data 4th Global Edition Alan Agresti, Christine A. Franklin, Bernhard Klingenberg - Solutions
What’s wrong with regression? Explain what’s wrong with the way regression is used in each of the following examples:a. Winning times in the Boston marathon (at www.bostonmarathon.org) have followed a straight-line decreasing trend from 160 minutes in 1927 (when the race was first run at the
Education causes crime? The table shows a small data set that has a pattern somewhat like that in Figure 3.22 in Example 14. As in that example, education is measured as the percentage of adult residents who have at least a high school degree. Using software,a. Construct a data file with columns
Death penalty and race The table shows results of whether the death penalty was imposed in murder trials in Florida between 1976 and 1987. For instance, the death penalty was given in 53 out of 467 cases in which a white defendant had a white victim.a. First, consider only those cases in which the
NAEP scores In 2015, eighth-grade math scores on the National Assessment of Educational Progress had a mean of 283.56 in Maryland compared to a mean of 284.37 in Connecticut (Source: http://nces.ed.gov/nationsreportcard/naepdata/dataset.aspx).a. Identify the response variable and the explanatory
Diabetes and breast cancer In 2015, an article published in the journal Breast Cancer Research and Treatment examined the impact of diabetes on the stages of breast cancer. The study concluded that diabetes is associated with advanced stages of breast cancer in patients and this could be a reason
Choose explanatory and response variables For the following pairs of variables, identify the response variable and the explanatory variable.a. Number of weeks of gestation and weight of an infant at birth.b. Preferred smartphone operating system (iOS, Android, Windows Mobile, etc) and gender.c.
Graphing data For each case in the previous exercise,a. Indicate whether each variable is quantitative or categorical.b. Describe the type of graph that could best be used to portray the results.
Life after death for males and females In a recent General Social Survey, respondents answered the question,“Do you believe in a life after death?” The table shows the responses cross-tabulated with gender.a. Construct a table of conditional proportions.b. Summarize results. Is there much
God and happiness Go to the GSS website sda.berkeley.edu/GSS; click GSS, with No Weight as the default weight selection; type GOD for the row variable, HAPPY for the column variable; and YEAR(2014) for the Selection Filter, then click Run the Table.a. Report the contingency table of counts.b.
Jobs and income A report on the best jobs in 2015 shows salaries related to jobs in the following table:a. Identify the response variable. Is it quantitative or categorical?b. Identify the explanatory variable. Is it quantitative or categorical?c. Explain how a bar graph could summarize the data.
Bacteria in ground turkey Consumer Reports magazine(June 2013) reported purchasing samples of ground turkey from different brands to test for the presence of bacteria.The table below shows the number of samples that tested positive for Enterococcus bacteria for packages that claimed no use of
Women managers in the work force The following sideby-side bar graph appeared in a 2003 issue of the Monthly Labor Review about women as managers in the work force. The graph summarized the percentage of managers in different occupations who were women, for the years 1972 and 2002.a. Consider the
RateMyProfessor.com The website RateMyProfessors.com13 reported a correlation of 0.62 between the quality rating of the professor (on a simple 1 to 5 scale with higher values representing higher quality) and the rating of how easy a grader the professor is. This correlation is based on ratings of
Women in government and economic life The OECD(Organization for Economic Cooperation and Development) consists of advanced, industrialized countries that accept the principles of representative democracy and a free market economy. For the nations outside of Europe that are in the OECD, the table
African droughts and dust Is there a relationship between the amount of dust carried over large areas of the Atlantic and the Caribbean and the amount of rainfall in African regions? In an article (by J. M. Prospero and P. J. Lamb, Science, vol. 302, 2003, pp. 1024–1027) the following
Crime rate and urbanization For the data in Example 14 on crime in Florida, the regression line between y = crime rate (number of crimes per 1000 people)and x = percentage living in an urban environment is yn = 24.5+ 0.56x.a. Using the slope, find the difference in predicted crime rates between
Gestational period and life expectancy revisited The data in the Animals file on the book’s website holds observations on the average longevity (in years) and gestational period(in days) for a variety of animals. Exercise 3.52 showed the scatterplot together with the regression equation with
Gas consumption and temperature A study was performed in Duke University to predict the monthly natural gas consumption in North Carolina as a function of the average monthly temperature. Residential gas consumptions were recorded from January 2009 to June 2015 and temperature measures were
Predicting college GPA An admissions officer claims that at his college the regression equation yn = 0.5 + 7x approximates the relationship between y = college GPA and x = high school GPA, both measured on a fourpoint scale.a. Sketch this equation between x = 0 and 4, labeling the x- and y-axes. Is
College GPA high school GPA Refer to the previous exercise. Suppose the regression equation is yn = x.Identify the y-intercept and slope. Interpret the line in context.
Salary and employee satisfaction In 2015, a study was conducted among a sample of 221,000 users of the website www.glassdoor.com. It explored the link between salary (in dollars)and employee satisfaction (measured on a rating scale of 0 to 100). According to their model, if an employee
Car weight and gas hogs: The table shows a short excerpt from the Car Weight and Mileage data file on the book’s website. That file lists several 2004 model cars with automatic transmission and their x = weight(in pounds) and y = mileage (miles per gallon of gas).The prediction equation is yn =
Predicting Internet use from cell phone use We now use data from the Human Development data file on cell phone use and Internet use for 39 countries.a. The MINITAB output below shows a scatterplot.Describe it in terms of (i) identifying the response variable and the explanatory variable, (ii)
Income depends on education? For a study of counties in Florida, the table shows part of a printout for the regression analysis relating y = median income (thousands of dollars) to x = percent of residents with at least a high school education.a. County A has 10% more of its residents than County B
Fertility and GDP Refer to the Human Development data file on the book’s website. Use x = GDP and y = fertility (mean number of children per adult woman).a. Construct a scatterplot and indicate whether regression seems appropriate.b. Find the correlation and the regression equation.c. With x =
Women working and birth rate Using data from several nations, a regression analysis of y = crude birth rate (number of births per 1000 population size)on women’s economic activity (female labor force as a percentage of the male labor force) yielded the equation yn = 36.3- 0.30x and a correlation
Education and income The regression equation for a sample of 100 people relating x = years of education and y = annual income (in dollars) is yn = -20,000 + 4000x, and the correlation equals 0.50. The standard deviations were2.0 for education and 16,000 for annual income.a. Show how to find the
Income in euros Refer to the previous exercise. Results in the regression equation yn = -20,000 + 4000x for y = annual income were translated to units of euros at a time when the exchange rate was $1.25 per euro.a. Find the intercept of the regression equation.(Hint: What does 20,000 dollars equal
Changing units for cereal data Refer to the Cereal data file on the book’s website, with x = sugar 1g2 and y = sodium 1mg2, for which yn = 169 - 0.25x.a. Convert the sugar measurements to mg and calculate the line obtained from regressing sodium (mg) on sugar (mg). Which statistics change and
Murder and single-parent families 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
Violent crime and college education For the U.S.Statewide Crime data file on the book’s website, let y = violent crime rate and x = percent with a college education.a. Construct a scatterplot. Identify any points that you think may be influential in a regression analysis.b. Fit the regression
Violent crime and high school education 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.
Crime and urbanization For the U.S. Statewide Crime data file on the book’s website, using MINITAB to analyze y = violent crime rate and x = urbanization(percentage of the residents living in metropolitan areas)gives the results shown:a. Using the five-number summary of positions, sketch a box
High school graduation rates and health insurance Access the HS Graduation Rates file on the book’s website, which contains statewide data on x = high school graduation rate and y = percentage of individuals without health insurance.a. Construct a scatterplot. Describe the relationship.b. Find
Women’s Olympic high jumps Example 11 discussed how the winning height in the Olympic high jump changed over time. Using the High Jump data file on the book’s website, we get (see also Figure 3.16)Women_Meters = -10.94 + 0.0065 (Year_Women)for predicting the women’s winning height (in
IQ and shoe size A survey of elementary school students revealed a positive correlation between the shoe size of the subjects and their GPA in the previous year.a. Explain how age could be a potential lurking variable that could be responsible for this association.b. If age had actually been one of
More TV watching goes with fewer babies? 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.
More coffee protects from cancer? In February 2015, a new study published in the Journal of the National Cancer Institute shows people who regularly drink coffee have a lower chance of developing skin cancer. Based on this study, individuals drinking four or more cups of coffee a day had 20 percent
Ask Marilyn 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,
NL baseball team ERA and number of wins Is a baseball team’s earned run average 1ERA = the average number of earned runs they give up per game2 a good predictor of the number of wins that a team has for a season? The data for the National League teams in 2010 are available in the NL Team
Time studying and GPA Is there a relationship between the amount of time a student studies and a student’s GPA? Access the Georgia Student Survey file on the book’s website or use your class data to explore this question using appropriate graphical and numerical methods.Write a brief report
Warming in Newnan, Georgia Access the Newnan GA Temp’s file on the book’s website, which contains data on average annual temperatures for Newnan, Georgia, during the 20th century. Fit a regression line to these temperatures and interpret the trend. Compare the trend to the trend found in
Regression for dummies 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
Fluoride and AIDS 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
Fish fights Alzheimer’s An AP story (July 22, 2003) described a study conducted over four years by Dr. Martha Morris and others from Chicago’s Rush-Presbyterian-St. Luke’s Medical Center involving 815 Chicago residents aged 65 and older (Archives of Neurology, July 21, 2003). Those who
Dogs make you healthier A study published in the British Journal of Health Psychology (D. Wells, vol.12, 2007, pp. 145–156) found that dog owners are physically healthier than cat owners. The author of the study was quoted as saying, “It is possible that dogs can directly promote our well being
Multiple choice: Correlate GPA and GRE In a study of graduate students who took the Graduate Record Exam (GRE), the Educational Testing Service reported a correlation of 0.37 between undergraduate grade point average (GPA) and the graduate first year GPA.14 This means thata. As undergraduate GPA
Multiple choice: Properties of r Which of the following is not a property of r?a. r is always between -1 and 1.b. r depends on which of the two variables is designated as the response variable.c. r measures the strength of the linear relationship between x and y.d. r does not depend on the units of
Multiple choice: Interpreting r One can interpret r = 0.30 asa. a weak, positive associationb. 30% of the time yn = yc. yn changes 0.30 units for every one-unit increase in xd. a stronger association than two variables with r = -0.70
Multiple choice: Correct statement about r Which one of the following statements is correct?a. The correlation is always the same as the slope of the regression line.b. The mean of the residuals from the least-squares regression line is 0 only when r = 0.c. The correlation is the percentage of
Multiple choice: Describing association between categorical variables You can summarize the data for two categorical variables x and y bya. drawing a scatterplot of the x- and y-values.b. constructing a contingency table for the x- and y-values.c. calculating the correlation between x and y.d.
Multiple choice: Slope and correlation The slope of the regression equation and the correlation are similar in the sense thata. they do not depend on the units of measurement.b. they both must fall between -1 and +1.c. they both have the same sign.d. neither can be affected by severe regression
Multiple choice: Interpretation of r2 An r2 measure of 0.85 implies thata. the correlation between x and y equals 0.85.b. for a one-unit increase in x, we predict y to increase by 85%.c. 85% of the response variable y can be explained by the linear relationship between x and y.d. 85% of the
True or false The variables y = annual income (thousands of dollars), x1 = number of years of education, and x2 = number of years experience in job are measured for all the employees having city-funded jobs in Knoxville, Tennessee. Suppose that the following regression equations and correlations
Correlation doesn’t depend on units Suppose you convert y = income from British pounds to dollars, and suppose a pound equals 2.00 dollars.a. Explain why the y values double, the mean of y doubles, the deviations 1y - y2 double, and the standard deviation sy doubles.b. Using the formula for
When correlation slope Consider the formula b = r1sy>sx2 that expresses the slope in terms of the correlation. Suppose the data are equally spread out for each variable. That is, suppose the data satisfy sx = sy.Show that the correlation and the slope are the same.(In practice, the standard
Center of the data Consider the formula a = y - bx for the y-intercept.a. Show that y = a + bx. Explain why this means that the predicted value of the response variable is yn = y when x = x.b. Show that an alternative way of expressing the regression model is as 1yn - y2 = b1x - x2. Interpret this
Final exam “regresses toward mean” of midterm Let y = final exam score and x = midterm exam score.Suppose that the correlation is 0.70 and that the standard deviation is the same for each set of scores.a. Using part b of the previous exercise and the relation between the slope and correlation,
Analyze your data Refer to the data file the class created in Activity 3 in Chapter 1. For variables chosen by your instructor, conduct a regression and correlation analysis. Prepare a one-page report summarizing your analyses, interpreting your findings.
Activity: Effect of moving a point The Explore Linear Regression web app accessible at the book’s website lets you add and delete points on a scatterplot. The regression line is automatically calculated for the points you provide.a. Select the option “Draw Own” and add 5 points to the empty
Activity: Guess the correlation The Guess the Correlation web app accessible at the book’s website allows you to guess the correlation r with randomly generated data points. How close are your guesses to the actual correlation of the points? Find the correlation between your guesses and the
Cell phones 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.
High blood pressure and binge drinking 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
Low-fat versus low-carb diet? One hundred forty-eight men and women without heart disease or diabetes enrolled in a study. Half of the subjects were randomly assigned to a low-carb diet 1640 g>d2, and the others were given a low-fat diet (630% of daily energy intake from total fat).Subjects on the
Experiments versus observational studies 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.
Tobacco prevention campaigns A study published by www.tobaccofreekids.org concluded that prevention campaigns organized by tobacco companies were ineffective at best and even worked to encourage kids to smoke.Nevertheless, tobacco companies spent $9.6 billion on such prevention campaigns in 2012 in
Hormone therapy and heart 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
Children of mothers with remitted depression A 2016 study (http://europepmc.org/abstract/med/26451509) investigated parallels between affect recognition in mothers with remitted depression and their children. They examined two groups—a group of remitted depressed mothers and a group of healthy
Breast-cancer screening A study published in 2010 in the New England Journal of Medicine discusses a breast-cancer screening 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
Experiment or observe? Explain whether an experiment or an observational study would be more appropriate to investigate the following:a. Whether caffeine has an effect on long-term memory.b. Whether multitasking in class affects the grades of business students.c. Whether studying abroad tends to be
Baseball under a full moon 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
Seat belt anecdote Andy once heard about a car crash victim who died because he was pinned in the wreckage by a seat belt he could not undo. As a result, Andy refuses to wear a seat belt when he rides in a car. How would you explain to Andy the fallacy behind relying on this anecdotal evidence?
Job opportunity in New York City Tina’s mother is extremely proud that her daughter has a great job offer from a prestigious company located in Manhattan. However, she expresses concern when she learns that, based on statistics collected from 2003 through 2015, 494 homicides on average are
What’s more to blame for obesity? In a study published in the July 7, 2014, edition of the American Journal of Medicine, it was suggested that lack of exercise contributed more to weight gain than eating too much. The study examined the current exercise habits and caloric intake of a sample of
Census every 10 years? A nationwide census is conducted in the United States every 10 years.a. Give at least two reasons the United States takes a census only every 10 years.b. What are reasons for taking the census at all?c. The most commonly discussed characteristic learned from a census is the
Choosing officers 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,
Simple random sample of students In Example 4, a random drawing was held to select the winners of the football tickets. Organizers randomly chose numbers, using the computer to generate the sample randomly. Choose another sample by using either the Random Numbers web app from the book’s website,
Auditing accounts—app Use an app or computer program 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.
Sampling from a directory 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.
Bias due to interviewer gender A social scientist in a less developed country studied the effect of the gender of the interviewer in a survey administrated to male respondents.The survey addressed the question of women’s participation in politics. Half the subjects were surveyed by males and the
Charity walk A nonprofit organization surveyed its members for their opinion regarding an upcoming charity walk. The survey asked, “We are considering a shift of our preannounced location to a new one this year.Would you be willing to walk from the new location if it meant that many more teenage
Instructor ratings The website www.ratemyprofessors.com provides students an opportunity to view ratings for instructors at their universities. A group of students planning to register for a statistics course in the upcoming semester are trying to identify the instructors who receive the highest
Gun control 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
Sexual harassment on the Internet In his statistics course project, a student stated “Millions of Internet users engaged in online activities of sexual harassment”. This conclusion was based on a survey administrated through different social media networks, in which 2% of the respondents
Cheating spouses and bias In a survey conducted by vouchercloud.net and reported in the Palm Beach Post, it was found that of 2645 people who had participated in an extramarital affair, the average amount spent per month on the affair was $444. (Source:
Drug use by athletes In 2015, the outgoing president of the International Association of Athletics Federations(IAAF) claimed “99% of athletes are clean”(www.irishexaminer.com). However, based on a survey administered online, a sports reporter concluded that only 30% of athletics fans agreed
Identify the bias 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
Types of bias Give an example of a survey that would suffer froma. Sampling bias due to the sampling designb. Sampling bias due to undercoveragec. Response biasd. Nonresponse bias
Smoking affects lung cancer? 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 ever to smoke. Fifty years from now, you will analyze whether
Never leave home without duct tape 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
More duct tape 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
Fertilizers An agricultural field experiment was conducted by Bo D. Pettersson in the Nordic Research Circle for Biodynamic Farming in Järna, Sweden, which began in 1958 and lasted until 1990. The field experiment included eight different fertilizer treatments with a primary focus on aspects of
Facebook study During the one-week period of January 11–18, 2012, Facebook conducted an experiment to research whether emotional states can be transferred to others via emotional contagion. Facebook users were randomly selected to be part of two parallel studies in which Facebook manipulated the
Texting while driving Texting while driving is dangerous and causes injuries and fatalities. A team of researchers studied whether typing text messages, reading them, or a combination of both, while driving affect eye movements, stimulus detection, reaction time, collisions, lane positioning, speed
Pain reduction medication 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
Pain reduction medication, continued Consider the same setting as that of Exercise 4.37. 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.
Pain reduction medication, yet again Revisit the setting of Exercise 4.37. Suppose that in addition to the participants being blinded, the researchers responsible for recording the results of the study are also blinded. Why does it matter whether the researchers know which participants receive
Colds and vitamin C 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
Reducing high blood pressure A pharmaceutical company has developed a new drug for treating high blood pressure. The company would like to compare the drug’s 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
Student loan debt 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
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