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Statistics The Art And Science Of Learning From Data 3rd Edition Alan Agresti, Christine A. Franklin - Solutions

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 graph without inspecting the
Examples 19 and 20 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 period. Describe the
In 2004, a college newspaper reported results of a survey of students taken on campus. One question asked was, €œDo 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
A 2011 Roper Center survey asked: “If you were making up the budget for the federal government this year (2011), would you increase spending, decrease spending, or keep spending the same for financial aid for college students?” Of those surveyed, 44% said to increase spending, 16% said to
Identify each of the following variables as categorical or quantitative. a. Number of children in family b. Amount of time in football game before first points scored c. College major (English, history, chemistry,) d. Type of music (rock, jazz, classical, folk, and other)
Which of the following variables are continuous, when the measurements are as precise as possible? a. Age of mother b. Number of children in a family c. Cooking time for preparing dinner d. Latitude and longitude of a city e. Population size of a city
The table shows the number (in millions) of the foreign-born population of the United States in 2004, by place of birth. Foreign-Born Population in the United States Place of Birth Number (in Millions) Europe............ 4.7 Caribbean.......... 3.3 Central America........ 12.9 South
A recent survey 9 asked 1200 university students in China to pick the personality trait that most defines a person as “cool.” The possible responses allowed, and the percentage making each, were individualistic and innovative (47%), stylish (13.5%), dynamic and capable (9.5%), easygoing and
The 2000 U.S. presidential election had various problems in Florida. One was €œover votes€€”people mistakenly voting for more than one presidential candidate. (There were multiple minor party candidates.) There were 110,000 over vote ballots, with Al Gore marked on
For the question €œHow many children have you ever had?€ in the 2008 General SocialSurvey, the results werea. Which is the most appropriate graph to display the data€”dot plot, stem-and-leaf plot, or histogram? Why? b. Based on sketching or using software to construct
Exercise 2.25 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 the stems and the
Match each lettered histogram with one of the following descriptions: Skewed to the left, symmetric and bimodal, symmetric and unimodal, skewed to the right.
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) of using the stem-and-leaf
For the following pairs of variables, which more naturally is the response variable and which is the explanatory variable? a. College grade point average (GPA) and high school GPA b. Number of children and mother’s religion c. Happiness (not too happy, pretty happy, very happy) and whether
Go to the GSS Web site sda.berkeley.edu/GSS, click on GSS, with No Weight as the default weight selection, type SEX for the row variable and HAPPY for the column variable, put a check in the row box only for percentaging in the table options, and click on Run the Table. a. Report the contingency
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 reported eating fish at least
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 by buffering us from
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 apply: (i) ŷ =
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 (y - ) double, and the standard deviation sy doubles. b. Using the formula for calculating the correlation, explain why
For the 100 cars on the lot of a used-car dealership, would you expect a positive association, negative association, or no association between each of the following pairs of variables? Explain why. a. The age of the car and the number of miles on the odometer b. The age of the car and the resale
Consider the formula b = r(sy/sx) 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 deviations are not usually
Consider the formula a = - b for the y -intercept.a. Show that = a + b. Explain why this means that the predicted value of the response variable is ŷ = when x = .b. Show that an alternative way of expressing the regression model is as (ŷ - ) = b(x - ). Interpret this formula.
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, show that (ŷ - ) = 0.70(x - ).b. Explain why
The Internet Use data file on the text CD contains data on the number of individuals with broadband access and Gross Domestic Product (GDP) for 33 nations. Let x represent GDP (in billions of U.S. dollars) and y = number of broadband users (in thousands).a. The MINITAB output shows a scatterplot.
The previous problem discusses GDP, which is a commonly used measure of the overall economic activity of a nation. For this group of nations, the GDP data have a mean of 1771 and a standard deviation of 2781 (in billions of U.S. dollars). a. The five-number summary of GDP is minimum = 245, Q1 =
For the FL Student Survey data file on the text CD, the correlation between y = political ideology (scored 1 = very liberal to 7 = very conservative) and x = number of times a week reading a newspaper is -0.07. a. Would you call this association strong or weak? Explain. b. The correlation between
For the 33 nations in the Internet Use data file on the text CD, consider the following correlations:a. Which pair of variables exhibits the strongest linear relationship? b. Which pair of variables exhibits the weakest linear relationship? c. In Example 7, we found the correlation between Internet
Match the scatterplots below with the correlation values.1. r = -0.92. r = -0.53. r = 04. r = 0.6a.b. c. d.
Consider the data:a. Sketch a scatterplot. b. If one pair of (x, y) values is removed, the correlation for the remaining four pairs equals 1. Which pair is it? c. If one y value is changed, the correlation for the five pairs equals 1. Identify the y value and how it must be changed for this to
Use the points from the previous exercise with x = 3, 5, 6, 7.a. Find the z -scores on x and on y for each point. Comment on how zx and zy relate to each other for each point.b. Compute r using the z -scores from part a for the four observations. Is this the value you expected to get for r? Why?
Sketch a scatterplot for which r > 0, but r = 0 after one of the points is deleted.
Each month, the owner of Fay’s Tanning Salon records in a data files the monthly total sales receipts and the amount spent that month on advertising. a. Identify the two variables. b. For each variable, indicate whether it is quantitative or categorical. c. Identify the response variable and the
Describe a situation in which it is inappropriate to use the correlation to measure the association between two quantitative variables.
Is there a relationship between the weight of a mountain bike and its price? A lighter bike is often preferred, but do lighter bikes tend to be more expensive? The following table, from the Mountain Bike data file on the text CD, gives data on price, weight, and type of suspension (FU = full, FE =
Is there a relationship between the protein content and the cost of Subway sandwiches? Use software to analyze the data in the following table:a. Construct a scatterplot to show how protein depends on cost. Is the association positive or negative? Do you notice any unusual observations? b. What
Refer to Example 6 and the Buchanan and the Butterfly Ballot data file on the text CD. Let y = Buchanan vote and x = Gore vote. a. Construct a box plot for each variable. Summarize what you learn. b. Construct a scatterplot. Identify any unusual points. What can you learn from a scatterplot that
Identify the values of the y -intercept a and the slope b, and sketch the following regression lines, for values of x between 0 and 10. a. ŷ = 7 + 0.5x b. ŷ = 7 + x c. ŷ = 7 - x d. ŷ = 7
Is there a relationship between how many sit-ups you can do and how fast you can run 40 yards? The EXCEL output shows the relationship between these variables for a study of female athletes to be discussed in Chapter 12.a. The regression equation is 6.71Å· - 0.024x. Find the predicted
The House Selling Prices FL data file on the text CD lists selling prices of homes in Gainesville, Florida, in 2003 and some predictors for the selling price. For the response variable y = selling price in thousands of dollars and the explanatory variable x = size of house in thousands of square
Zagat restaurant guides publish ratings of restaurants for many large cities around the world (see www.zagat.com). The review for each restaurant gives a verbal summary as well as a 0- to 30-point rating of the quality of food, décor, service, and the cost of a dinner with one drink and tip. For
For the 33 nations in Example 7, we found a correlation of 0.682 between Internet use and Facebook use (both as percentages of population). The regression equation is predicted Facebook use = 3.09 + 0.460 Internet use a. Based on the correlation value, the slope had to be positive. Why? b.
Every General Social Survey includes the question, €œTaken all together, would you say that you are very happy, pretty happy, or not too happy?€ The table uses the 2008 survey to cross-tabulate happiness with family income, measured as the response to the question, €œCompared with
The Internet Use data file on the text CD contains data on the number of individuals in a country with broadband access and the population size for each of 33 nations. When using population size as the explanatory variable, x, and broadband subscribers as the response variable, y, the regression
The SAT2010 data file on the text CD contains average reading and math SAT scores for each of the 50 states and Washington D.C. Let the explanatory variable x = reading and the response variable y = math. The regression equation is ŷ = 18.1 + 0.975x.a. California had an average reading score of
A study in 2000 by the National Highway Traffic Safety Administration estimated that failure to wear seat belts led to 9200 deaths in the previous year, and that the number of deaths would decrease by 270 for every 1 percentage point gain in seat belt usage. Let ŷ = predicted number of deaths in a
The figure shows the result of a MINITAB regression analysis of the explanatory variable x = sugar and the response variable y = sodium for the breakfast cereal data set discussed in Chapter 2 (the Cereal data file on the text CD).a. Suppose you had fit a line to the scatterplot by eyeballing. In
Each month, the owner of Fay’s Tanning Salon records in a data file y = monthly total sales receipts and x = amount spent that month on advertising, both in thousands of dollars. For the first three months of operation, the observations are as shown in the table.Advertising Sales0.........
For students who take Statistics 101 at Lake Wobegon College in Minnesota, both the midterm and final exams have mean = 75 and standard deviation = 10. The professor explores using the midterm exam score to predict the final exam score. The regression equation relating y = final exam score to x =
In an introductory statistics course, x = midterm exam score and y = final exam score. Both have mean = 80 and standard deviation = 10. The correlation between the exam scores is 0.70.a. Find the regression equation.b. Find the predicted final exam score for a student with midterm exam score = 80.
Example 9 related y = team scoring (per game) and x = team batting average for American League teams. For National League teams in 2010, ŷ = -6.25 + 41.5x. a. The team batting averages fell between 0.242 and 0.272. Explain how to interpret the slope in context. b. The standard deviations were
A graduate teaching assistant (Euijung Ryu) for Introduction to Statistics (STA 2023) at the University of Florida collected data from one of her classes in spring 2007 to investigate the relationship between using the explanatory variable x = study time per week (average number of hours) to
In a recent General Social Survey, respondents answered the question, €œIn the past month, about how many hours have you spent praying, meditating, reading religious books, listening to religious broadcasts, etc.?€ The responses on this variable were cross-tabulated with the
An article in the September 16, 2006, issue of The Economist showed a scatterplot for many nations relating the response variable y = annual oil consumption per person (in barrels) and the explanatory variable x = gross domestic product (GDP, per person, in thousands of dollars). The values shown
Is there a relationship between the weight and price of a mountain bike? This question was considered in Exercise 3.21. We will analyze the Mountain Bike data file on the text CD. (The data also were shown in Exercise 3.21.) a. Construct a scatterplot. Interpret. b. Find the regression equation.
Refer to the previous exercise. The data file contains price, weight, and type of suspension system (FU = full, FE = front-end in the scatterplot shown).a. Do you observe a linear relationship? Is the single regression line, which is Å· = 1896 - 40.45x, the best way to fit the data?
The SAT2010 data file on the text CD contains combined average SAT scores for each of the 50 states and Washington D.C., and also the corresponding participation rate of each state. Let’s consider using the explanatory variable x = participation rate (in %) to predict the response variable y =
The SPSS figure shows the data and regression line for the 50 states in Table 3.6 relating x = percentage of single-parent families to y = annual murder rate (number of murders per 100,000 people in the population). a. The lowest x value was for Utah and the highest was for Mississippi. Using the
The Olympic winning men€™s long jump distances (in meters) from 1896 to 2008 and the fitted regression line for predicting them using x = year are displayed in the MINITAB output below.a. Identify an observation that may influence the fit of the regression line. Why did you identify this
Use the U.S. Temperatures data file on the text CD. a. Fit a trend line, and interpret the slope. b. Predict the annual mean U.S. temperature for the year (i) 2010 and (ii) 3000. c. In which prediction in part b do you have more faith? Why?
Example 13 found the regression line ŷ = -3.1 + 0.33x for all 51 observations on y = murder rate and x = percent with a college education. a. Show that the predicted murder rates increase from 1.85 to 10.1 as percent with a college education increases from x = 15, to x = 40, roughly the range of
For Table 3.6, the regression equation for the 50 states and D.C. relating y = murder rate and x = percent of people who live below the poverty level is ŷ = -4.1 + 0.81x . For D.C., x = 17.4 and y = 41.8. a. When the observation for D.C. is removed from the data set, ŷ = 0.4 + 0.36x. Does D.C.
The figure shows recent data on x = the number of televisions per 100 people and y = the birth rate (number of births per 1000 people) for six African and Asian nations. The regression line, Å· = 29.8 - 0.024x applies to the data for these six countries. For illustration, another point
The Harvard School of Public Health, in its College Alcohol Study Survey, surveyed college students in about 200 colleges in 1993, 1997, 1999, and 2001. The survey asked students questions about their drinking habits. Binge drinking was defined as five drinks in a row for males and four drinks in a
Using software, analyze the relationship between x = college education and y = percentage single-parent families, for the data in Table 3.6, which are in the U.S. Statewide Crime data file on the text CD. a. Construct a scatterplot. Based on your plot, identify two observations that seem quite
Let x = sodium and y = sugar for the breakfast cereal data in the Cereal data file on the text CD and in Table 2.3 in Chapter 2. a. Construct a scatterplot. Do any points satisfy the two criteria for a point to be potentially influential on the regression? Explain. b. Find the regression line and
An article (by M. Dupagne and D. Waterman, Journal of Broadcasting and Electronic Media, vol. 42, 1998 pp. 208–220 ), studied variables relating to the percentage of TV programs in 17 Western European countries that consisted of fiction programs imported from the United States. One explanatory
Do tall students tend to have better vocabulary skills than short students? We might think so looking at a sample of students from grades 1, 6, and 12 of Lake Wobegon school district. The correlation was 0.81 between their height and their vocabulary test score: Taller students tended to have
Data are available for all fires in Chicago last year on x = number of firefighters at the fire and y = cost of damages due to the fire. a. If the correlation is positive, does this mean that having more firefighters at a fire causes the damage to be worse? Explain. b. Identify a third variable
An Associated Press story (June 13, 2002) reported, “A survey of teens conducted for the Partnership for a Drug Free America found kids who see or hear antidrug ads at least once a day are less likely to do drugs than youngsters who don’t see or hear ads frequently. When asked about marijuana,
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 Olympic distance of about 26
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 for education, crime
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.Originally published in Florida Law Review. Michael Radelet and Glenn L.
Eighth-grade math scores on the National Assessment of Educational Progress had a mean of 277 in Nebraska compared to a mean of 271 in New Jersey (H. Wainer and L. Brown, American Statistician, vol. 58, 2004, p. 119). a. Identify the response variable and the explanatory variable. b. For white
A survey of 1000 adult Americans ( Rasmussen Reports , April 15, 2004) asked each whether the best way to fight terrorism is to let the terrorists know we will fight back aggressively or to work with other nations to find an international solution. The first option was picked by 53% of the men but
A study observes that the subjects in the study who say they exercise regularly reported only half as many serious illnesses per year, on the average, as those who say they do not exercise regularly. One paragraph in the results section of an article about the study starts out, “We next analyzed
For the following pairs of variables, identify the response variable and the explanatory variable. a. Number of square feet in a house and assessed value of the house. b. Political party preference (Democrat, Independent, Republican) and gender. c. Annual income and number of years of education. d.
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.
In a recent General Social Survey, respondents answered the question, €œDo you believe in a life after death?€ The table shows the responses cross-tabulated with gender. Opinion about Life after Death by Gendera. Construct a table of conditional proportions.b. Summarize results. Is there
Go to the GSS Web site sda.berkeley.edu/GSS, click on GSS, with No Weight as the default weight selection, type GOD for the row variable and HAPPY for the column variable, and click on Run the Table.a. Report the contingency table of counts.b. Treating reported happiness as the response variable,
The mean annual salaries earned in 2005 by year-round workers with various educational degrees are given in the table: Degree Mean Salary No diploma....... $19,964 High school diploma... $29,448 Bachelor’s degree.... $54,689 Master’s degree..... $67,898 Doctoral
Consider the Whooping Cough data file on the text CD. a. Identify the response variable and the explanatory variable. b. Construct a graph using bars to display the incidence rate of whooping cough contingent on year. Interpret.
The following side by-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 first two bars in this graph.
The Web site 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 nearly 7000
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 shows UN data from 2007 on the
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 scatter plots were given
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 ŷ = 24.5 + 0.56x. a. Using the slope, find the difference in predicted crime rates between counties that are 100% urban
A recent analysis of data for the 50 U.S. states on y = violent crime rate (measured as number of violent crimes per 100,000 people in the state) and x = poverty rate (percent of people in the state living at or below the poverty level) yielded the regression equation, ŷ = 209.9 + 25.5x. a.
The headline of an article in the Gainesville Sun (October 17, 2003) stated, “Height can yield a taller paycheck.” It described an analysis of four large studies in the United States and Britain by a University of Florida professor on subjects’ height and salaries. The article reported that
An admissions officer claims that at his college the regression equation ŷ = 0.5 + 7x approximates the relationship between y = college GPA and x = high school GPA, both measured on a four point scale. a. Sketch this equation between x = 0 and 4, labeling the x - and y -axes. Is this equation
Refer to the previous exercise. Suppose the regression equation is ŷ = x. Identify the y -intercept and slope. Interpret the line in context.
In 2002, a Census Bureau survey reported that the mean total earnings that a full-time worker in the United States can expect to earn between ages 25 and 64 is $1.2 million for those with only a high-school education and $2.1 million for those with a college degree but no advanced degree. a.
The table shows a short excerpt from the Car Weight and Mileage data file on the text CD. 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 = 47.32 - 0.0052x.a. Interpret the
We now use data from the Human Development data file on cell phones use and Internet use for 39 countries.a. The MINITAB output below shows a scatter plot. Describe it in terms of (i) identifying the response variable and the explanatory variable, (ii) indicating whether it shows a positive or a
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 with at least a high school
The last time the questions in the previous exercise were asked in the GSS, 955 subjects answered “yes” to both questions, 188 answered “no” to both, 162 answered “yes” to heaven but “no” to hell, and 9 answered “no” to heaven but “yes” to hell. a. Display the data as a
Refer to the Human Development data file on the text CD. Use x = GDP and y = fertility (mean number of children per adult woman). a. Construct a scatter plot, and indicate whether regression seems appropriate. b. Find the correlation and the regression equation. c. With x = percent using
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 ŷ = 36.3 - 0.30x and a correlation of -0.55. a. Describe the
The regression equation for a sample of 100 people relating x = years of education and y = annual income (in dollars) is ŷ = -20,000 + 4000x, and the correlation equals 0.50. The standard deviations were 2.0 for education and 16,000 for annual income. a. Show how to find the slope in the
Refer to the previous exercise. Results in the regression equation ŷ = -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. (What does 20,000 dollars equal in euros?) b. Find
Refer to the Cereal data file on the text CD, with x = sugar (g) and y = sodium (mg), for which ŷ = 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 which remain the same? Clearly interpret

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