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intro stats
Stats Data And Models (Subscription) 3rd Edition Richard D De Veaux, Paul D Velleman, David E Bock - Solutions
Another wrong conclusion. After simulating the spread of a disease, a researcher wrote, “24% of the people contracted the disease.” What should the correct conclusion be?
Wrong conclusion. A Statistics student properly simulated the length of checkout lines in a grocery store and then reported, “The average length of the line will be 3.2 people.” What’s wrong with this conclusion?
More bad simulations. Explain why each of the following simulations fails to model the real situation:a) Use random numbers 2 through 12 to represent the sum of the faces when two dice are rolled.b) Use a random integer from 0 through 5 to represent the number of boys in a family of 5 children.c)
Bad simulations. Explain why each of the following simulations fails to model the real situation properly:a) Use a random integer from 0 through 9 to represent the number of heads when 9 coins are tossed.b) A basketball player takes a foul shot. Look at a random digit, using an odd digit to
Play it again, Sam. In Exercise 8 you imagined playing the lottery by using random digits to decide what numbers to play. Is this a particularly good or bad strategy?Explain.
Play the lottery. Some people play state-run lotteries by always playing the same favorite “lucky” number.Assuming that the lottery is truly random, is this strategy better, worse, or the same as choosing different numbers for each play? Explain.
Get rich. Your state’s BigBucks Lottery prize has reached$100,000,000, and you decide to play. You have to pick five numbers between 1 and 60, and you’ll win if your numbers match those drawn by the state. You decide to pick your“lucky” numbers using a random number table. Which numbers do
Geography. An elementary school teacher with 25 students plans to have each of them make a poster about two different states. The teacher first numbers the states(in alphabetical order, from 1-Alabama to 50-Wyoming), then uses a random number table to decide which states each student gets. Here are
Colorblind. By some estimates, about 10% of all males have some color perception defect, most commonly red–green colorblindness. How would you assign random numbers to conduct a simulation based on this statistic?
Birth defects. The American College of Obstetricians and Gynecologists says that out of every 100 babies born in the United States, 3 have some kind of major birth defect. How would you assign random numbers to conduct a simulation based on this statistic?
Games. Many kinds of games people play rely on randomness. Cite three different methods commonly used in the attempt to achieve this randomness, and discuss the effectiveness of each.
The lottery. Many states run lotteries, giving away millions of dollars if you match a certain set of winning numbers. How are those numbers determined? Do you think this method guarantees randomness? Explain.
Casino. A casino claims that its electronic “video roulette” machine is truly random. What should that claim mean?
Coin toss. Is a coin flip random? Why or why not?
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 - 0.1Speed and created this residual plot: a) Interpret the
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 this
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
Reading. To measure progress in reading ability, students at an elementary school take a reading comprehension test every year. Scores are measured in “gradelevel”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 school
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.
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 cause-and-effect relationships that might be present.
Match each of the green points (a–e) with the slope of the line after that one point is added: 1) -0.45 2) -0.30 3) 0.00 4) 0.05 5) 0.85
The extra point, revisited. The original five points in Exercise 13 produce a regression line with slope
is 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 the list given. a e
The extra point. The scatterplot shows five blue data points at the left. Not surprisingly, the correlation for these points r =
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
Unusual points. Each of the four scatterplots that follow 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
Tracking hurricanes 2007. In a previous chapter, we saw data on the errors (in nautical miles) made by the National Hurricane Center in predicting the path of hurricanes.The scatterplot shows the trend in the 24-hour tracking errors since 1970 (www.nhc.noaa.gov).a) Interpret the slope and intercept
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, June of 1997 is 7.5—halfway through the 7th year after
Smoking 2006, women and men. In Exercise 2 we examined the percentage of men aged 18–24 who smoked from 1965 to 2006 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 ways are
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 the
Bad model? A student who has created a linear model is disappointed to find that her 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.
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.
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 cell phone subscribers per 1000 people is positively associated with economic
Human Development Index. 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. In 2006, the HDI was as high as 0.965 for Norway and as low as 0.331 for Niger. The
Smoking 2006. The Centers for Disease Control and Prevention track cigarette smoking in the United States.How has the percentage of people who smoke changed since the danger became clear during the last half of the 20th century? The scatterplot shows percentages of smokers among men 18–24 years
Marriage age 2007. Is there evidence that the age at which women get married has changed over the past 100 years? The scatterplot shows the trend in age at first marriage for American women (www.census.gov).a) Is there a clear pattern? Describe the trend.b) Is the association strong?c) Is the
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.
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.
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 captured
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
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 variability in long jumps can be accounted for by high-jump performances?c) Do good high jumpers tend
Heptathlon 2004 again. We saw the data for the women’s 2004 Olympic heptathlon in Exercise
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 the 800-meter
Heptathlon 2004. We discussed the women’s 2004 Olympic heptathlon in Chapter
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 57, create and analyze that model.
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.a) Create a model to predict %Body Fat
Birthrates 2005. 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,
Climate change. The climate on earth is getting warmer.The most common theory relates an increase in atmospheric levels of carbon dioxide (CO2), a greenhouse gas, to increases in temperature. Here is a scatterplot showing the mean annual CO2 concentration in the atmosphere, measured in parts per
Candy 2006. The table shows the increase in Halloween candy sales over a 7-year period as reported by the National Confectioners Association (www.ecandy.com).Using these data, estimate the amount of candy sold in 2006. Discuss the appropriateness of your model and your faith in the estimate. Then
New York bridges. We saw in this chapter that in Tompkins County, NY, 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 Condition
Cost of living 2008. TheWorldwide 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 New
A second helping of burgers. In Exercise 49 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
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 in
Burgers. In the last chapter, you examined 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 in this context.c) Write the equation of the line of regression.d) Use the residuals
Veggie burgers. Recently Burger King introduced a meat-free burger. 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 the
More used cars 2007. Use the advertised prices for Toyota Corollas given in Exercise 45 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
Drug abuse. In the exercises of the last chapter you examined results of a survey conducted in the United States and 10 countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. Below is the scatterplot. Summary statistics showed that the mean
Used cars 2007. Classified ads in the Ithaca Journal offered several used Toyota Corollas for sale. Listed below 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 Corolla.c) Do you think a linear model
Wildfire size 2008. We saw in Exercise 43 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, together with some supporting plots:a) Is the regression model appropriate for these
Wildfires 2008. The National Interagency Fire Center(www.nifc.gov) reports statistics about wildfires. Here’s an analysis of the number of wildfires between 1985 and 2007.a) Is a linear model appropriate for these data? Explain.b) Interpret the slope in this context.c) Can we interpret the
Based on the statistics for college freshmen given in Exercise 40, what SAT score might be expected among freshmen who attained a first-semester GPA of 3.0?
Success, part
Predict her verbal score.e) Using that predicted verbal score and the equation you created in Exercise 39, predict her math score.f) Why doesn’t the result in part e come out to 500?
Suppose we wanted to use SAT math scores to estimate verbal scores based on the information in Exercise 39.a) What is the correlation?b) Write the equation of the line of regression predicting verbal scores from math scores.c) In general, what would a positive residual mean in this context?d) A
SAT, take
In the first semester these students attained a mean GPA of 2.66, with a standard deviation of 0.56. A scatterplot showed the association to be reasonably linear, and the correlation between SAT score and GPA was 0.47.a) Write the equation of the regression line.b) Explain what the y-intercept of
Success in college. Colleges use SAT scores in the admissions process because they believe these scores provide some insight into how a high school student will perform at the college level. Suppose the entering freshmen at a certain college have mean combined SAT Scores of 1222, with a standard
SAT scores. The SAT is a test often used as part of an application to college. SAT scores are between 200 and 800, but have no units. Tests are given in both Math and Verbal areas. Doing the SAT-Math problems also involves the ability to read and understand the questions, but can a person’s
Online clothes II. For the online clothing retailer discussed in the previous problem, the scatterplot of Total Yearly Purchases by Income looks like this:The correlation between Total Yearly Purchases and Income is 0.722. Summary statistics for the two variables are:a) What is the linear
Online clothes. An online clothing retailer keeps track of its customers’ purchases. For those customers who signed up for the company’s credit card, the company also has information on the customer’s Age and Income.A random sample of 500 of these customers shows the following scatterplot of
Interest rates and mortgages again. In Chapter 7, Exercise 32, we saw a plot of total mortgages in the United States (in millions of 2005 dollars) versus the interest rate at various times over the past 26 years. The correlation is The mean mortgage amount is$151.9 million and the mean interest
Income and housing revisited. In Chapter 7, Exercise 31, we learned that the Office of Federal Housing Enterprise Oversight (OFHEO) collects data on various aspects of housing costs around the United States. Here’s a scatterplot (by state) of the Housing Cost Index (HCI)versus the Median Family
Last inning 2006. Refer again to the regression analysis for average attendance and games won by American League baseball teams, seen in Exercise 30.a) Write the equation of the regression line.b) Estimate the Average Attendance for a team with 50 Wins.c) Interpret the meaning of the slope of the
Last cigarette. Take another look at the regression analysis of tar and nicotine content of the cigarettes in Exercise 29.a) Write the equation of the regression line.b) Estimate the Nicotine content of cigarettes with 4 milligrams of Tar.c) Interpret the meaning of the slope of the regression line
Second inning 2006. Consider again the regression of Average Attendance on Wins for the baseball teams examined in Exercise 30.a) What is the correlation between Wins and Average Attendance?b) What would you predict about the Average Attendance for a team that is 2 standard deviations above average
Another cigarette. Consider again the regression of Nicotine content on Tar (both in milligrams) for the cigarettes examined in Exercise 29.a) What is the correlation between Tar and Nicotine?b) What would you predict about the average Nicotine content of cigarettes that are 2 standard deviations
Attendance 2006. In the previous chapter you looked at the relationship between the number of wins by American League baseball teams and the average attendance at their home games for the 2006 season. Here are the scatterplot, the residuals plot, and part of the regression analysis:a) Do you think
Cigarettes. Is the nicotine content of a cigarette related to the “tars”? A collection of data (in milligrams) on 29 cigarettes produced the scatterplot, residuals plot, and regression analysis shown:a) Do you think a linear model is appropriate here?Explain.b) Explain the meaning of in this
Last ride. Consider the roller coasters described in Exercise 16 again. The regression analysis gives the model Duration = 91.033 + 0.242 Drop.a) Explain what the slope of the line says about how long a roller coaster ride may last and the height of the coaster.b) A new roller coaster advertises an
More real estate. Consider the Albuquerque home sales from Exercise 15 again. The regression analysis gives the model Price = 47.82 + 0.061 Size.a) Explain what the slope of the line says about housing prices and house size.b) What price would you predict for a 3000-square-foot house in this
SI jinx. Players in any sport who are having great seasons, turning in performances that are much better than anyone might have anticipated, often are pictured on the cover of Sports Illustrated. Frequently, their performances then falter somewhat, leading some athletes to believe in a “Sports
ESP. People who claim to “have ESP” participate in a screening test in which they have to guess which of several images someone is thinking of. You and a friend both took the test. You scored 2 standard deviations above the mean, and your friend scored 1 standard deviation below the mean. The
Another ride. The regression of Duration of a roller coaster ride on the height of its initial Drop, described in Exercise 16, had R2 = 12.4%.a) What is the correlation between Drop and Duration?b) What would you predict about the Duration of the ride on a coaster whose initial Drop was 1 standard
Real estate redux. The regression of Price on Size of homes in Albuquerque had R2 = 71.4%, as described in Exercise 15.a) What is the correlation between Size and Price?b) What would you predict about the Price of a home 1 SD above average in Size?c) What would you predict about the Price of a home
More misinterpretations. A Sociology student investigated the association between a country’s Literacy Rate and Life Expectancy, then drew the conclusions listed below. Explain why each statement is incorrect. (Assume that all the calculations were done properly.)a) The of 64 means that the
Misinterpretations. A Biology student who created a regression model to use a bird’s Height when perched for predicting its Wingspan made these two statements.Assuming the calculations were done correctly, explain what is wrong with each interpretation.a) My of 93% shows that this linear model is
Coasters, again. Exercise 16 examined the association between the Duration of a roller coaster ride and the height of its initial Drop, reporting that R2 = 12.4%.Write a sentence (in context, of course) summarizing what the R2 says about this regression.
Write a sentence (in context, of course)summarizing what the says about this regression.
Real estate, again. The regression of Price on Size of homes in Albuquerque had R2 = 71.4%, as described in Exercise
What slope? If you create a regression model for estimating the Height of a pine tree (in feet) based on the Circumference of its trunk (in inches), is the slope most likely to be 0.1, 1, 10, or 100? Explain.
What slope? If you create a regression model for predicting the Weight of a car (in pounds) from its Length (in feet), is the slope most likely to be 3, 30, 300, or 3000?Explain.
Roller coaster. People who responded to a July 2004 Discovery Channel poll named the 10 best roller coasters in the United States. A table in the previous chapter’s exercises shows the length of the initial drop (in feet) and the duration of the ride (in seconds). A regression to predict Duration
Real estate. A random sample of records of sales of homes from Feb. 15 to Apr. 30, 1993, from the files maintained by the Albuquerque Board of Realtors gives the Price and Size (in square feet) of 117 homes. A regression to predict Price (in thousands of dollars) from Size has an of 71.4%. The
Residuals. Tell what each of the residual plots below indicates about the appropriateness of the linear model that was fit to the data. a)
Residuals. Tell what each of the residual plots below indicates about the appropriateness of the linear model that was fit to the data.
More regression equations. Fill in the missing information in the following table. X Sx V Sy + = b + bx a) 30 4 18 6 -0.2 b) 100 18 60 10 0.9 c) 0.8 50 15 = -10 + 15x d) 18 4 -0.6 =30-2x
Regression equations. Fill in the missing information in the following table. X ST y Sy = bo + bix a) b) c) 12 10 2 20 3 0.5 2 0.06 7.2 1.2 -0.4 16 -0.8 200 - 4x d) 2.5 1.2 100 = -100 + 50x
Last tank! For Exercise 2’s regression model predicting fuel economy (in mpg) from the car’s horsepower, se = 3.287. Explain in this context what that means.
Last bowl! For Exercise 1’s regression model predicting potassium content (in milligrams) from the amount of fiber (in grams) in breakfast cereals, se = 30.77. Explain in this context what that means.
Another car. The correlation between a car’s horsepower and its fuel economy (in mpg) is r = -0.869. What fraction of the variability in fuel economy is accounted for by the horsepower?
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