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intro stats

Intro Stats 4th International Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions

3. Components Playing a board game, you are stuck in jail until you roll “doubles” (same numbers) on a pair of dice. You will simulate using random digits to estimate how many turns you expect to remain in jail. Identify the component if you were to run a simulation.
2. More random outcomes For each of the following scenarios, decide if the outcome is random.a) You enter a contest in which the winning ticket is selected from a large drum of entries. Was the winner of the contest random?b) When playing a board game, the number of spaces you move is decided by
1. Random outcomes For each of the following scenarios, decide if the outcome is random.a) Flip a coin to decide who takes out the trash. Is who takes out the trash random?b) A friend asks you to quickly name a professional sports team. Is the sports team named random?c) Names are selected out of a
42. Chips A start-up company has developed an improved electronic chip for use in laboratory equipment. The company needs to project the manufacturing cost, so it develops a spreadsheet model that takes into account the purchase of production equipment, overhead, raw materials, depreciation,
41. Down the drain Most water tanks have a drain plug so that the tank may be emptied when it’s to be moved or repaired. How long it takes a certain size of tank to drain depends on the size of the plug, as shown in the table.Create a model. Plug Dia (in.) Drain Time (min.) 3 m100 12 1 2 31 12
40. Profit How are a company’s profits related to its sales?Let’s examine data from 71 large U.S. corporations.All amounts are in millions of dollars.a) Histograms of Profits and Sales and histograms of the logarithms of Profits and Sales are seen below. Why are the re-expressed data better for
39. Vehicle weights The Minnesota Department of Transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed “weigh-in-motion”scale. After installation of the scale, a study was conducted to find out whether the
38. Williams vs. Texas Here are the average weights of the football team for the University of Texas for various years in the 20th century.a) Fit a straight line to the relationship of Weight by Year for Texas football players.b) According to these models, in what year will the predicted weight of
37. Models Find the predicted value of y, using each model for x = 10.a) yn = 2 + 0.8 ln xb) log yn = 5 - 0.23x c)1 2yn = 17.1 - 1.66x
36. Football weights The Sears Cup was established in 1993 to honor institutions that maintain a broad-based athletic program, achieving success in many sports, both men’s and women’s. Since its Division III inception in 1995, the cup has been won by Williams College 15 of 17 years.Their
35. Tobacco and alcohol Are people who use tobacco products more likely to consume alcohol? Here are data on household spending (in pounds) taken by the British government on 11 regions in Great Britain. Do tobacco and alcohol spending appear to be related? What questions do you have about these
34. Gasoline Since clean-air regulations have dictated the use of unleaded gasoline, the supply of leaded gas in New York state has diminished. The following table was given on the August 2001 New York State Math B exam, a statewide achievement test for high school students.a) Create a linear model
33. Lunchtime Does how long toddlers sit at the lunch table help predict how much they eat? The table and graph show the number of minutes the kids stayed at the table and the number of calories they consumed. Create and interpret a model for these data. Calories Time Calories Time 472 21.4 450
32. Twins Twins are often born at less than 9 months gestation. The graph from the Journal of the American Medical Association (JAMA) shows the rate of preterm twin births in the United States over the past 20 years.In this study, JAMA categorized mothers by the level of prenatal medical care they
31. French Consider the association between a student’s score on a French vocabulary test and the weight of the student. What direction and strength of correlation would you expect in each of the following situations? Explain.a) The students are all in third grade.b) The students are in third
30. Modeling jumps 2008 Here are the summary statistics for the Olympic long jumps and high jumps displayed in the previous exercise.a) Write the equation of the line of regression for estimating High Jump from Long Jump.b) Interpret the slope of the line.c) In a year when the long jump is 8.9 m,
29. Jumps 2008 How are Olympic performances in various events related? The plot shows winning long-jump and high-jump distances, in meters, for the Summer Olympics from 1912 through 2008.a) Describe the association.b) Do long-jump performances somehow influence the high-jumpers? How do you account
28. Depression The September 1998 issue of the American Psychologist published an article by Kraut et al. that reported on an experiment examining “the social and psychological impact of the Internet on 169 people in 73 households during their first 1 to 2 years online.”In the experiment, 73
27. Winter in the city Summary statistics for the data relating the latitude and average January temperature for 55 large U.S. cities are given below.Variable Mean StdDev Latitude 39.02 5.42 JanTemp 26.44 13.49 Correlation = -0.848a) What percent of the variation in January Temperature can be
26. Correlations The study of U.S. cities in Exercise 25 found the mean January Temperature (degrees Fahrenheit), Altitude (feet above sea level), and Latitude(degrees north of the equator) for 55 cities. Here’s the correlation matrix:Jan. Temp Latitude Altitude Jan. Temp 1.000 Latitude -0.848
25. U.S. cities Data from 50 large U.S. cities show the mean January Temperature and the Latitude. Describe what you see in the scatterplot. Avg. Jan. Temp (F) 09 45 30 + 15- 30 35 40 45 Latitude (N)
24. Tips It’s commonly believed that people use tips to reward good service. A researcher for the hospitality industry examined tips and ratings of service quality from 2645 dining parties at 21 different restaurants. The correlation between ratings of service and tip percentages was 0.11.
23. No smoking? The downward trend in smoking you saw in the last exercise is good news for the health of babies, but will it ever stop?a) Explain why you can’t use the linear model you created in Exercise 22 to see when smoking during pregnancy will cease altogether.b) Create a model that could
19. How old is that tree? One can determine how old a tree is by counting its rings, but that requires either cutting the tree down or extracting a sample from the tree’s core.Can we estimate the tree’s age simply from its diameter?A forester measured 27 trees of the same species that had been
18. Crocodile lengths The ranges inhabited by the Indian gharial crocodile and the Australian saltwater crocodile overlap in Bangladesh. Suppose a very large crocodile skeleton is found there, and we wish to determine the species of the animal. Wildlife scientists have measured the lengths of the
17. Old Faithful There is evidence that eruptions of Old Faithful can best be predicted by knowing the duration of the previous eruption.a) Describe what you see in the scatterplot of Intervals between eruptions vs. Duration of the previous eruption.b) Write the equation of the line of best fit.
16. Colorblind Although some women are colorblind, this condition is found primarily in men. Why is it wrong to say there’s a strong correlation between Sex and Colorblindness?
14. Autos, revisited Look again at the correlation table for cars in the previous exercise.a) Which two variables in the table exhibit the strongest association?b) Is that strong association necessarily cause-and-effect?Offer at least two explanations why that association might be so strong.c)
13. Car correlations What factor most explains differences in Fuel Efficiency among cars? Below is a correlation matrix exploring that relationship for the car’s Weight, Horsepower, engine size (Displacement), and number of Cylinders.a) Which factor seems most strongly associated with Fuel
12. Cramming One Thursday, researchers gave students enrolled in a section of basic Spanish a set of 50 new vocabulary words to memorize. On Friday, the students took a vocabulary test. When they returned to class the following Monday, they were retested—without advance warning. Here are the test
11. Traffic Highway planners investigated the relationship between traffic Density (number of automobiles per mile)and the average Speed of the traffic on a moderately large city thoroughfare. The data were collected at the same location at 10 different times over a span of 3 months.They found a
10. Grades A Statistics instructor created a linear regression equation to predict students’ final exam scores from their midterm exam scores. The regression equation was Fin = 10 + 0.9 Mid.a) If Susan scored a 70 on the midterm, what did the instructor predict for her score on the final?b) Susan
9. A manatee model 2010 Continue your analysis of the manatee situation from the previous exercise.a) Create a linear model of the association between Manatee Deaths and Powerboat Registrations.b) Interpret the slope of your model.c) Interpret the y-intercept of your model.d) How accurately did
8. Manatees 2010 Marine biologists warn that the growing number of powerboats registered in Florida threatens the existence of manatees. The data below come from the Florida Fish and Wildlife Conservation Commission(myfwc.com/research/manatee/) and the National Marine Manufacturers Association
7. Acid rain Biologists studying the effects of acid rain on wildlife collected data from 163 streams in the Adirondack Mountains. They recorded the pH (acidity) of the water and the BCI, a measure of biological diversity, and they calculated R2 = 27%. Here’s a scatterplot of BCI against pH:a)
6. Dow Jones 2012 The Dow Jones stock index measures the performance of the stocks of America’s largest companies (finance.yahoo.com). A regression of the Dow prices on years 1972–2012 looks like this:Dependent variable is Dow Index R-squared = 83.9% s = 1659 Variable Coefficient Intercept
5. More twins 2009? As the table shows, the number of twins born in the United States has been increasing.(www.cdc.govchs/births.htm)a) Find the equation of the regression line for predicting the number of twin births.b) Explain in this context what the slope means.c) Predict the number of twin
4. Vineyards again Instead of Age, perhaps the Size of the vineyard (in acres) is associated with the price of the wines. Look at the scatterplota) Do you see any evidence of an association?b) What concern do you have about this scatterplot?c) If the red “+” data point is removed, would the
3. Vineyards Here are the scatterplot and regression analysis for Case Prices of 36 wines from vineyards in the Finger Lakes region of New York State and the Ages of the vineyards..Dependent variable is Case Price R-squared = 2.7%Variable Coefficient Constant 92.7650 Age 0.567284a) Does it appear
2. Togetherness Are good grades in high school associated with family togetherness? A random sample of 142 high school students was asked how many meals per week their families ate together. Their responses produced a mean of 3.78 meals per week, with a standard deviation of 2.2.Researchers then
1. College Every year, US News and World Report publishes a special issue on many U.S. colleges and universities. The scatterplots below have Student/Faculty Ratio (number of students per faculty member) for the colleges and universities on the y-axes plotted against 4 other variables. The correct
48. This question has been intentionally omitted from this text.
47. Inflation 2011 The Consumer Price Index (CPI) tracks the prices of consumer goods in the United States, as shown in the following table. The CPI is reported monthly, but we can look at selected values. The table shows the January CPI at five-year intervals. It indicates, for example, that the
46. This question has been intentionally omitted from this text.
45. Life expectancy 2010 Data for 26 Western Hemisphere countries can be used to examine the association between life expectancy and the birth rate (number of births per 1000 population).a) Create a scatterplot relating these two variables and describe the association.b) Find the equation of the
44. Bridges covered Tompkins County is the home of the oldest covered bridge in daily use in New York State.Built in 1853, it was recently judged to have a condition of 4.523.Dependent variable is Condition R@squared = 51.8% s = 0.7192 Variable Coefficient Intercept -44.9905 Year 0.025601a) If we
43. Marriage age 2010 revisited Suppose you wanted to predict the trend in marriage age for American women into the early part of this century.a) How could you use the data graphed in Exercise 15 to get a good prediction? Marriage ages in selected years starting in 1900 are listed below. Use all or
42. Another swim 2010 In Exercise 40, we saw that Vicki Keith’s round-trip swim of Lake Ontario was an obvious outlier among the other one-way times. Here is the new regression after this unusual point is removed:Dependent variable is Time R@Squared = 6.0% s = 326.1 Variable Coefficient Intercept
41. Elephants and hippos We removed humans from the scatterplot in Exercise 39 because our species was an outlier in life expectancy. The resulting scatterplot (below)shows two points that now may be of concern. The point in the upper right corner of this scatterplot is for elephants, and the other
40. Swim the lake 2010 People swam across Lake Ontario 48 times between 1974 and 2010 (www.soloswims.com).We might be interested in whether they are getting any faster or slower. Here are the regression of the crossing Times (minutes) against the Year of the crossing and the residuals plot:a) What
39. Gestation For humans, pregnancy lasts about 280 days.In other species of animals, the length of time from conception to birth varies. Is there any evidence that the gestation period is related to the animal’s life span? The first scatterplot shows Gestation Period (in days) vs. Life
38. Ages of couples again Has the trend of decreasing difference in age at first marriage seen in Exercise 36 gotten stronger recently? The scatterplot and residual plot for the data from 1980 through 2010, along with a regression for just those years, are below.Dependent variable is Men - Women
37. Interest rates revisited In Exercise 35, you investigated the federal rate on 3-month Treasury bills between 1950 and 1980. The scatterplot below shows that the trend changed dramatically after 1980, so we computed a new regression model for the years 1980 to 2005.Here’s the model for the
36. Marriage Age 2010 The graph shows the ages of both men and women at first marriage (www.census.gov).Clearly, the patterns for men and women are similar.But are the two lines getting closer together?Here’s a timeplot showing the difference in average age (men’s age - women’s age) at first
35. Interest rates Here’s a plot showing the federal rate on 3-month Treasury bills from 1950 to 1980, and a regression model fit to the relationship between the Rate (in %) and Years Since 1950 (www.gpoaccess.gov/eop/).a) What is the correlation between Rate and Year?b) Interpret the slope and
34. Speed How does the speed at which you drive affect your fuel economy? To find out, researchers drove a compact car for 200 miles at speeds ranging from 35 to 75 miles per hour. From their data, they created the model Fuel Efficiency = 32 - 0.1 Speed and created this residual plot:a) Interpret
33. Heating After keeping track of his heating expenses for several winters, a homeowner believes he can estimate the monthly cost from the average daily Fahrenheit temperature by using the model Cost = 133 - 2.13 Temp.Here is the residuals plot for his data:a) Interpret the slope of the line in
32. Grades A college admissions officer, defending the college’s use of SAT scores in the admissions process, produced the following graph. It shows the mean GPAs for last year’s freshmen, grouped by SAT scores. How strong is the evidence that SAT Score is a good predictor of GPA? What concerns
31. Reading To measure progress in reading ability, students at an elementary school take a reading comprehension test every year. Scores are measured in “grade-level” units;that is, a score of 4.2 means that a student is reading at slightly above the expected level for a fourth grader. The
30. What’s the effect? A researcher studying violent behavior in elementary school children asks the children’s parents how much time each child spends playing computer games and has their teachers rate each child on the level of aggressiveness they display while playing with other children.
29. What’s the cause? Suppose a researcher studying health issues measures blood pressure and the percentage of body fat for several adult males and finds a strong positive association. Describe three different possible causeand-effect relationships that might be present.
28. The extra point revisited The original five points in Exercise 27 produce a regression line with slope 0.Match each of the green points (a–e) with the slope of the line after that one point is added:1) -0.45 4) 0.05 2) -0.30 5) 0.85 3) 0.00
27. The extra point The scatterplot shows five blue data points at the left. Not surprisingly, the correlation for these points is r = 0. Suppose one additional data point is added at one of the five positions suggested below in green. Match each point (a–e) with the correct new correlation from
26. More unusual points Each of the following scatterplots shows a cluster of points and one “stray” point. For each, answer these questions:1) In what way is the point unusual? Does it have high leverage, a large residual, or both?2) Do you think that point is an influential point?3) If that
25. Unusual points Each of these four scatterplots shows a cluster of points and one “stray” point. For each, answer these questions:1) In what way is the point unusual? Does it have high leverage, a large residual, or both?2) Do you think that point is an influential point?3) If that point
24. Tracking hurricanes 2010 The scatterplot at the top of the next page shows the trend in the 24-hour tracking errors (in nautical miles) made by the National Hurricane Center in predicting the path of hurricanes since 1970(www.nhc.noaa.gov).Dependent variable is Error R@squared = 68.7% s = 16.44
23. Oakland passengers The scatterplot below shows the number of passengers departing from Oakland (CA) airport month by month since the start of 1997. Time is shown as years since 1990, with fractional years used to represent each month. (Thus, July of 1997 is 7.5—halfway through the 7th year
22. Smoking 2009, women and men In Exercise 16, we examined the percentage of men aged 18–24 who smoked from 1965 to 2009 according to the Centers for Disease Control and Prevention. How about women? Here’s a scatterplot showing the corresponding percentages for both men and women:a) In what
21. Movie dramas Here’s a scatterplot of the production budgets (in millions of dollars) vs. the running time (in minutes) for major release movies in 2005. Dramas are plotted as red x’s and all other genres are plotted as blue dots. (The re-make of King Kong is plotted as a black “-”.At
20. Bad model? A student who has created a linear model is disappointed to find that her R2 value is a very low 13%.a) Does this mean that a linear model is not appropriate?Explain.b) Does this model allow the student to make accurate predictions? Explain.
19. Good model? In justifying his choice of a model, a student wrote, “I know this is the correct model because R2 = 99.4%.”a) Is this reasoning correct? Explain.b) Does this model allow the student to make accurate predictions? Explain.
18. HDI revisited The United Nations Development Programme (UNDP) uses the Human Development Index (HDI) in an attempt to summarize in one number the progress in health, education, and economics of a country. The number of phone subscribers per 100 people is positively associated with economic
8. Revenue and advanced sales The production company of Exercise 7 offers advanced sales to “Frequent Buyers”through its website. Here’s a relevant scatterplot:a) Explain why fitting a linear model to these data might be misleading.b) If you fit a linear model to the data, what do you think a
7. Revenue and large venues A regression of Total Revenue on Ticket Sales by the concert production company of Exercises 2 and 4 finds the model Revenue = -14,228 + 36.87 TicketSales.a) Management is considering adding a stadium-style venue that would seat 10,000. What does this model predict that
6. Stopping times Using data from 20 compact cars, a consumer group develops a model that predicts the stopping time for a vehicle by using its weight. You consider using this model to predict the stopping time for your large SUV. Explain why this is not advisable.
5. Cell phone costs Noting a recent study predicting the increase in cell phone costs, a friend remarks that by the time he’s a grandfather, no one will be able to afford a cell phone. Explain where his thinking went awry.
4. Revenue and ticket sales The concert production company of Exercise 2 made a second scatterplot, this time relating Total Revenue to Ticket Sales.a) Describe the relationship between Ticket Sales and Total Revenue.b) How are the results for the two venues similar?c) How are they different? Total
2. Revenue and talent cost A concert production company examined its records. The manager made the following scatterplot. The company places concerts in two venues, a smaller, more intimate theater (plotted with blue circles) and a larger auditorium-style venue(red x’s).a) Describe the
1. Credit card spending An analysis of spending by a sample of credit card bank cardholders shows that spending by cardholders in January (Jan) is related to their spending in December (Dec):The assumptions and conditions of the linear regression seemed to be satisfied and an analyst was about to
78. Least squares Consider the four points (200,1950),(400,1650), (600,1800), and (800,1600). The least squares line is yn = 1975 - 0.45x. Explain what “least squares” means, using these data as a specific example.
77. Least squares Consider the four points (10,10),(20,50), (40,20), and (50,80). The least squares line is yn = 7.0 + 1.1x. Explain what “least squares” means, using these data as a specific example.
76. Gators Wildlife researchers monitor many wildlife populations by taking aerial photographs. Can they estimate the weights of alligators accurately from the air? Here is a regression analysis of the Weight of alligators (in pounds) and their Length (in inches) based on data collected about
75. Hard water In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per million, ppm) in the
74. Heptathlon 2004 again We saw the data for the women’s 2004 Olympic heptathlon in Exercise 73. Are the two jumping events associated? Perform a regression of the long-jump results on the high-jump results.a) What is the regression equation? What does the slope mean?b) What percentage of the
73. Heptathlon 2004 Here are the results from the high jump, 800-meter run, and long jump for the 26 women who successfully completed all three events in the 2004 Olympics (www.espn.com):Let’s examine the association among these events.Perform a regression to predict high-jump performance from
72. Body fat again Would a model that uses the person’s Waist size be able to predict the %Body Fat more accurately than one that uses Weight? Using the data in Exercise 71, create and analyze that model.
71. Body fat It is difficult to determine a person’s body fat percentage accurately without immersing him or her in water. Researchers hoping to find ways to make a good estimate immersed 20 male subjects, then measured their waists and recorded their weights shown in the table at the top of the
70. Birthrates 2009 The table shows the number of live births per 1000 women aged 15–44 years in the United States, starting in 1965. (National Center for Health Statistics, www.cdc.govchs/)a) Make a scatterplot and describe the general trend in Birthrates.(Enter Year as years since 1900: 65, 70,
69. Climate change 2011 The earth’s climate is getting warmer. The most common theory attributes the increase to an increase in atmospheric levels of carbon dioxide(CO2), a greenhouse gas. Here is a scatterplot showing the mean annual CO2 concentration in the atmosphere, measured in parts per
68. Candy The table shows the increase in Halloween candy sales over a 6-year period as reported by the National Confectioners Association (www.candyusa.com). Using these data, estimate the amount of candy sold in 2009. Discuss the appropriateness of your model and your faith in the estimate.Then
67. New York bridges We saw in this chapter that in Tompkins County, New York, older bridges were in worse condition than newer ones. Tompkins is a rural area. Is this relationship true in New York City as well? Here are data on the Condition (as measured by the state Department of Transportation
66. Cost of living 2008 The Worldwide Cost of Living Survey City Rankings determine the cost of living in the 25 most expensive cities in the world. (www.finfacts.com/costofliving.htm) These rankings scale New York City as 100, and express the cost of living in other cities as a percentage of the
65. A second helping of burgers In Exercise 63, you created a model that can estimate the number of Calories in a burger when the Fat content is known.a) Explain why you cannot use that model to estimate the fat content of a burger with 600 calories.b) Using an appropriate model, estimate the fat
64. Chicken Chicken sandwiches are often advertised as a healthier alternative to beef because many are lower in fat. Tests on 11 brands of fast-food chicken sandwiches produced the following summary statistics and scatterplot from a graphing calculator:a) Do you think a linear model is appropriate
63. Burgers Examine the association between the amounts of Fat and Calories in fast-food hamburgers. Here are the data:a) Create a scatterplot of Calories vs. Fat.b) Interpret the value of R2 in this context.c) Write the equation of the line of regression.d) Use the residuals plot to explain
62. Veggie burgers Burger King introduced a meat-free burger in 2002. The nutrition label is shown here:a) Use the regression model created in this chapter, Fat = 6.8 + 0.97 Protein, to predict the fat content of this burger from its protein content.b) What is its residual? How would you explain
61. More used cars 2011 Use the advertised prices for Toyota Corollas given in Exercise 59 to create a linear model for the relationship between a car’s Age and its Price.a) Find the equation of the regression line.b) Explain the meaning of the slope of the line.c) Explain the meaning of the
60. Drug abuse A survey conducted in the United States and 10 countries of Western Europe determined the percentage of teenagers who had used marijuana and other drugs. Below is the scatterplot. Summary statistics showed that the mean percent that had used marijuana was 23.9%, with a standard
59. Used cars 2011 Carmax.com lists numerous Toyota Corollas for sale within a 250 mile radius of Redlands, CA. Listed at the top of the next column are the ages of the cars and the advertised prices.a) Make a scatterplot for these data.b) Describe the association between Age and Price of a used
58. Wildfires 2010—sizes We saw in Exercise 57 that the number of fires was nearly constant. But has the damage they cause remained constant as well? Here’s a regression that examines the trend in Acres per Fire, (in hundreds of thousands of acres) together with some supporting plots:a) Is the

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