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inferential statistics
Stats Modeling The World AP Edition Grades 9-12 3rd Edition David E. Bock, Paul F. Velleman, Richard D. De Veaux - Solutions
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) collects data in the developing world to help countries solve global and national development challenges. In the UNDP annual
Smoking 2004. 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 of
Marriage age 2003. 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) Do you think there is a clear pattern? Describe the trend.b) Is the association strong?c)
Least squares. Consider the four points (200,1950),(400,1650), (600,1800), and (800,1600). The least squares line is 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 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
Heptathlon 2004 again. We saw the data for the women s 2004 Olympic heptathlon in Exercise 59. 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
Heptathlon 2004. We discussed the women s 2004 Olympic heptathlon in Chapter 6. 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):
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.
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.gov/nchs/)
El Niño. Concern over the weather associated with El Niño has increased interest in the possibility that 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
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
Cell phones. Most people prefer digital cell phone service to analog because it is clearer and more private.Nonetheless, many calls are switched to analog channels because digital lines are busy, or because the calls are between people with different carriers. These analog calls require more power,
Cost of living 2006. 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 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:
Burgers. In the last chapter, you examined the association between the amounts of Fat and Calories in fast-food hamburgers. Here are the data:
Veggie burgers. Recently Burger King introduced a meat-free burger. The nutrition label is shown here:
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
Fire damage. We saw in Exercise 43 that even though the number of fires was falling, the amount of damage due to wildfires has been increasing. Could it be that individual fires are getting bigger? Here s a regression that examines the trend in Acres per Fire, together with some supporting plots:
Wildfire damage. In an example earlier in the chapter, we saw that the number of wildfires in the United States has been declining. But has the damage done by wildfires also been declining? Here s a scatterplot of the amount of land lost to wildfires (in millions of acres) during the same period,
Success, part 2. 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?
SAT, take 2. Suppose we wanted to use SAT math scores to estimate verbal scores based on the information in Exercise 39.
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 1833, 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 verbal
Online clothes II. For the online clothing retailer discussed in the previous problem, the scatterplot of Total Yearly Purchases by Income shows
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 Total
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:
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, hada) 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 deviation
Real estate redux. The regression of Price on Size of homes in Albuquerque had 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 one standard deviation above average in Size?c) What would you predict about the Price of
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 Literacy Rate determines 64%
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 R2 of 93% shows that this linear model
Coasters again. Exercise 16 examined the association between the Duration of a roller coaster ride and the height of its initial Drop, reporting that Write a sentence (in context, of course) summarizing what the R2 says about this regression.
Real estate again. The regression of Price on Size of homes in Albuquerque had as described in Exercise 15. Write a sentence (in context, of course) summarizing what the R2 says about this regression.
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 last 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 from
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 R-squared of
Residuals. Tell what each of the residual plots below indicates about the appropriateness of the linear model that was fit to the data.
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 table below.
Regression equations. Fill in the missing information in the table below.
Last tank! For Exercise 2 s regression model predicting fuel economy (in mpg) from the car s horsepower,. 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, . Explain in this context what that means.
Another car. The correlation between a car s horsepower and its fuel economy (in mpg) is What fraction of the variability in fuel economy is accounted for by the horsepower?
Cereal again. The correlation between a cereal s fiber and potassium contents is What fraction of the variability in potassium is accounted for by the amount of fiber that servings contain?
More horsepower. In Exercise 2, the regression model relates cars horsepower to their fuel economy (in mpg). Explain what the slope means.
Another bowl. In Exercise 1, the regression model relates fiber (in grams) and potassium content (in milligrams) in servings of breakfast cereals. Explain what the slope means.
Horsepower, again. Exercise 2 describes a regression model that uses a car s horsepower to estimate its fuel economy. In this context, what does it mean to say that a certain car has a positive residual?
More cereal. Exercise 1 describes a regression model that estimates a cereal s potassium content from the amount of fiber it contains. In this context, what does it mean to say that a cereal has a negative residual?
Horsepower. In Chapter 7 s Exercise 35 we examined the relationship between the fuel economy (mpg) and horsepower for 15 models of cars. Further analysis produces the regression model . If the car you are thinking of buying has a 200-horsepower engine, what does this model suggest your gas mileage
Cereals. For many people, breakfast cereal is an important source of fiber in their diets. Cereals also contain potassium, a mineral shown to be associated with maintaining a healthy blood pressure. An analysis of the amount of fiber (in grams) and the potassium content (in milligrams) in servings
Flights. The number of flights by U.S. Airlines has grown rapidly. Here are the number of flights flown in each year from 1995 to 2005.a) Find the correlation of Flights with Year.b) Make a scatterplot and describe the trend.c) Note two reasons that the correlation you found in(a) is not a suitable
Planets (more or less). On August 24, 2006, the International Astronomical Union voted that Pluto is not a planet. Some members of the public have been reluctant to accept that decision. Let s look at some of the data.(We ll see more in the next chapter.) Is there any pattern to the locations of
Oil production 2005. The following table shows the oil production of the United States from 1949 to 2005 (in thousands of barrels per year):
Thrills. People who responded to a July 2004 Discovery Channel poll named the 10 best roller coasters in the United States. The table below shows the length of the initial drop (in feet) and the duration of the ride(in seconds). What do these data indicate about the height of a roller coaster and
Second inning 2006. Perhaps fans are just more interested in teams that win. The displays below are based on American League teams for the 2006 season. (http://espn.go.com) Are the teams that win necessarily those which score the most runs?a) Do winning teams generally enjoy greater attendance at
Attendance 2006. American League baseball games are played under the designated hitter rule, meaning that weak-hitting pitchers do not come to bat. Baseball owners believe that the designated hitter rule means more runs scored, which in turn means higher attendance. Is there evidence that more fans
Burgers. In the previous exercise you analyzed the association between the amounts of fat and sodium in fast food hamburgers. What about fat and calories? Here are data for the same burgers
Burgers. Fast food is often considered unhealthy because much of it is high in both fat and sodium. But are the two related? Here are the fat and sodium contents of several brands of burgers. Analyze the association between fat content and sodium.
Drug abuse. A survey was conducted in the United States and 10 countries of Western Europe to determinea) Create a scatterplot.b) What is the correlation between the percent of teens who have used marijuana and the percent who have used other drugs?c) Write a brief description of the association.d)
Fuel economy 2007. Here are advertised horsepower ratings and expected gas mileage for several 2007 vehicles.(http://www.kbb.com/KBB/ReviewsAndRatings)a) Make a scatterplot for these data.b) Describe the direction, form, and strength of the plot.c) Find the correlation between horsepower and miles
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 weight-in-motion scale. To see if the new device was accurate, they conducted a calibration test. They weighed
Lunchtime. Does how long children remain at the lunch table help predict how much they eat? The table gives data on 20 toddlers observed over several months at a nursery school. Time is the average number of minutes a child spent at the table when lunch wasa) Find the correlation for these data.b)
Interest rates and mortgages. Since 1980, average mortgage interest rates have fluctuated from a low of under 6% to a high of over 14%. Is there a relationship between the amount of money people borrow and the interest rate that s offered? Here is a scatterplot of Total Mortgages in the United
Income and housing. The Office of Federal Housing Enterprise Oversight (www.ofheo.gov) collects data on various aspects of housing costs around the United States.Here is a scatterplot of the Housing Cost Index versus the Median Family Income for each of the 50 states. The correlation is 0.65.
Sample survey. A polling organization is checking its database to see if the two data sources it used sampled the same zip codes. The variable if the data source is MetroMedia, 2 if the data source is DataQwest, and 3 if it s RollingPoll. The organization finds that the correlation between
Baldness and heart disease. Medical researchers followed 1435 middle-aged men for a period of 5 years, measuring the amount of Baldness present and presence of Heart Disease They found a correlation of 0.089 between the two variables.Comment on their conclusion that this shows that baldness is not
Correlation conclusions II. The correlation between Fuel Efficiency (as measured by miles per gallon) and Price of 150 cars at a large dealership is Explain whether or not each of these possible conclusions is justified:a) The more you pay, the lower the fuel efficiency of your car will be.b) The
Correlation conclusions I. The correlation between Age and Income as measured on 100 people is Explain whether or not each of these possible conclusions is justified:a) When Age increases, Income increases as well.b) The form of the relationship between Age and Income is straight.c) There are no
Cellular telephones and life expectancy. A survey of the world s nations in 2004 shows a strong positive correlation between percentage of the country using cell phones and life expectancy in years at birth.a) Does this mean that cell phones are good for your health?b) What might explain the strong
Height and reading. A researcher studies children in elementary school and finds a strong positive linear association between height and reading scores.a) Does this mean that taller children are generally better readers?b) What might explain the strong correlation?
More correlation errors. Students in the Economics class discussed in Exercise 23 also wrote these conclusions. Explain the mistakes they made.a) There was a very strong correlation of 1.22 between Life Expectancy and GDP.b) The correlation between Literacy Rate and GDP was 0.83. This shows that
Correlation errors. Your Economics instructor assigns your class to investigate factors associated with the gross domestic product (GDP) of nations. Each student examines a different factor (such as Life Expectancy, Literacy Rate, etc.) for a few countries and reports to the class. Apparently, some
More predictions. Hurricane Katrina s hurricane force winds extended 120 miles from its center. Katrina was a big storm, and that affects how we think about the prediction errors. Suppose we add 120 miles to each error to get an idea of how far from the predicted track we might still find damaging
Prediction units. The errors in predicting hurricane tracks (examined in this chapter) were given in nautical miles. An ordinary mile is 0.86898 nautical miles. Most people living on the Gulf Coast of the United States would prefer to know the prediction errors in miles rather than nautical miles.
Association. A researcher investigating the association between two variables collected some data and was surprised when he calculated the correlation. He had expected to find a fairly strong association, yet the correlation was near 0. Discouraged, he didn t bother making a scatterplot.Explain to
Cold nights. Is there an association between time of year and the nighttime temperature in North Dakota?A researcher assigned the numbers 1 365 to the days January 1 December 31 and recorded the temperature at 2:00 a.m. for each. What might you expect the correlation between DayNumber and
Traffic headaches. A study of traffic delays in 68 U.S.cities found the following relationship between total delays (in total hours lost) and mean highway speed:
Hard water. In a study of streams in the Adirondack Mountains, the following relationship was found between the water s pH and its hardness (measured in grains):Is it appropriate to summarize the strength of association with a correlation? Explain.
Antidepressants. A study compared the effectiveness of several antidepressants by examining the experiments in which they had passed the FDA requirements. Each of those experiments compared the active drug with a placebo, an inert pill given to some of the subjects. In each experiment some patients
Roller coasters. Roller coasters get all their speed by dropping down a steep initial incline, so it makes sense that the height of that drop might be related to the speed of the coaster. Here s a scatterplot of top Speed and largest Drop for 75 roller coasters around the world.
Car thefts. The National Insurance Crime Bureau reports that Honda Accords, Honda Civics, and Toyota Camrys are the cars most frequently reported stolen, while Ford Tauruses, Pontiac Vibes, and Buick LeSabres are stolen least often. Is it reasonable to say that there s a correlation between the
Politics. A candidate for office claims that there is a correlation between television watching and crime.Criticize this statement on statistical grounds.
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