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Stats Data And Models (Subscription) 3rd Edition Richard D De Veaux, Paul D Velleman, David E Bock - Solutions
Cereal, again. The correlation between a cereal’s fiber and potassium contents is r = 0.903. What fraction of the variability in potassium is accounted for by the variation in the amount of fiber that servings contain?
More horsepower. In Exercise 2, the regression model mpg = 46.87 - 0.084HP relates cars’ horsepower to their fuel economy (in mpg). Explain what the slope means.
Another bowl. In Exercise 1, the regression model Potassium = 38 + 27Fiber 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 33 we examined the relationship between the fuel economy (mpg) and horsepower for 15 models of cars. Further analysis produces the regression model mpg = 46.87 - 0.084HP. If the car you are thinking of buying has a 200-horsepower engine, what does this model
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 part a is not a
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
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
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 pitchers, often weak hitters, 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
Burgers II. 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:a) Analyze the association between fat content and calories using correlation and scatterplots.*b) Repeat
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.a) Analyze the association between fat content and sodium using correlation and scatterplots.*b) Find
Drug abuse. A survey was conducted in the United States and 10 countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. The results are summarized in the table.a) Create a scatterplot.b) What is the correlation between the percent of teens who
Fuel economy 2007. Here are advertised horsepower ratings and expected gas mileage for several 2007 vehicles. (http://www.kbb.com)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 per gallon.d) Write a
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.a)
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 1none = 1, little = 2, some = 3, much = 4, extreme = 52 and presence of Heart Disease They found a correlation of 0.089 between the two variables.Comment
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
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
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
Prediction units. The errors in predicting hurricane tracks (examined in this chapter) were given in nautical miles. A statutory mile is 0.86898 nautical mile. Most people living on the Gulf Coast of the United States would prefer to know the prediction errors in statutory miles rather than
Discouraged, he didn’t bother making a scatterplot. Explain to him how the scatterplot could still reveal the strong association he anticipated.
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
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:a) Is it appropriate to summarize the strength of association with a correlation? Explain.*b) Would Spearman’s correlation be a better
Streams and 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):a) Is it appropriate to summarize the strength of association with a correlation? Explain.*b) Would Kendall’s tau be an
Antidepressants. Astudy 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.a) Does the
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.
Matching. Here are several scatterplots. The calculated correlations are , 0.736, and 0.951. Which is which? (a) (b) (c) + + +(d)
Matching. Here are several scatterplots. The calculated correlations are and 0.777. Which is which? (c) (a) I (a) H
Coffee sales. Owners of a new coffee shop tracked sales for the first 20 days and displayed the data in a scatterplot (by day).a) Make a histogram of the daily sales since the shop has been in business.b) State one fact that is obvious from the scatterplot, but not from the histogram.c) State one
Firing pottery. A ceramics factory can fire eight large batches of pottery a day. Sometimes a few of the pieces break in the process. In order to understand the problem better, the factory records the number of broken pieces in each batch for 3 days and then creates the scatterplot shown.a) Make a
Kentucky Derby 2007. The fastest horse in Kentucky Derby history was Secretariat in 1973. The scatterplot shows speed (in miles per hour) of the winning horses each year.What do you see? In most sporting events, performances have improved and continue to improve, so surely we anticipate a positive
Performance IQ scores vs. brain size. A study examined brain size (measured as pixels counted in a digitized magnetic resonance image [MRI] of a cross section of the brain) and IQ (4 Performance scales of the Weschler IQ test) for college students. The scatterplot shows the Performance IQ scores
Scatterplots. Which of these scatterplots showa) little or no association?b) a negative association?c) a linear association?d) a moderately strong association?e) a very strong association?
Scatterplots. Which of these scatterplots showa) little or no association?b) a negative association?c) a linear association?d) a moderately strong association?e) a very strong association? (1) (2) + (4)
Association. Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and
Association. Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and
Association. Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and
Association. Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and
Profits. Here is a stem-and-leaf display showing profits as a percent of sales for 29 of the Forbes 500 largest U.S. corporations. The stems are split; each stem represents a span of 5%, from a loss of 9% to a profit of 25%.a) Find the 5-number summary.b) Draw a boxplot for these data.c) Find the
Some assembly required. A company that markets build-it-yourself furniture sells a computer desk that is advertised with the claim “less than an hour to assemble.” However, through postpurchase surveys the company has learned that only 25% of its customers succeeded in building the desk in
Bike safety. The Bicycle Helmet Safety Institute website includes a report on the number of bicycle fatalities per year in the United States. The table below shows the counts for the years 1994–2003.a) What are the W’s for these data?b) Display the data in a stem-and-leaf display.c) Display the
Age and party II. Consider again the Pew Research Center results on age and political party in Exercise 33.a) What is the marginal distribution of party affiliation?b) Create segmented bar graphs displaying the conditional distribution of party affiliation for each age group.c) Summarize these poll
Pay. According to the 2006 National Occupational Employment and Wage Estimates for Management Occupations, the mean hourly wage for Chief Executives was $69.52 and the median hourly wage was “over $70.00.” By contrast, for General and Operations Managers, the mean hourly wage was $47.73 and the
Age and party 2007. The Pew Research Center conducts surveys regularly asking respondents which political party they identify with. Among their results is the following table relating preferred political party and age.(http://people-press.org/reports/)a) What percent of people surveyed were
Engines, again. Horsepower is another measure commonly used to describe auto engines. Here are the summary statistics and histogram displaying horsepowers of the same group of 38 cars discussed in Exercise 31.a) Describe the shape, center, and spread of this distribution.b) What is the
Engines. One measure of the size of an automobile engine is its “displacement,” the total volume (in liters or cubic inches) of its cylinders. Summary statistics for several models of new cars are shown. These displacements were measured in cubic inches.a) How many cars were measured?b) Why
Birth order revisited. Consider again the data on birth order and college majors in Exercise 28.a) What is the marginal distribution of majors?b) What is the conditional distribution of majors for the oldest children?c) What is the conditional distribution of majors for the children born second?d)
Herbal medicine. Researchers for the Herbal Medicine Council collected information on people’s experiences with a new herbal remedy for colds. They went to a store that sold natural health products. There they asked 100 customers whether they had taken the cold remedy and, if so, to rate its
Birth order. Is your birth order related to your choice of major? A Statistics professor at a large university polled his students to find out what their majors were and what position they held in the family birth order. The results are summarized in the table.a) What percent of these students are
Mail. Here are the number of pieces of mail received at a school office for 36 days.a) Plot these data.b) Find appropriate summary statistics.c) Write a brief description of the school’s mail deliveries.d) What percent of the days actually lie within one standard deviation of the mean? Comment.
Mail. Here are the number of pieces of mail received at a school office for 36 days.a) Describe the W’s for these data: Who, What, Where, Why, When, How.b) Name the variables and classify each as categorical or quantitative.c) Create parallel boxplots as best you can from these summary statistics
Music and memory. Is it a good idea to listen to music when studying for a big test? In a study conducted by some Statistics students, 62 people were randomly assigned to listen to rap music, Mozart, or no music while attempting to memorize objects pictured on a page.They were then asked to list
Be quick! Avoiding an accident when driving can depend on reaction time. That time, measured from the moment the driver first sees the danger until he or she steps on the brake pedal, is thought to follow a Normal model with a mean of 1.5 seconds and a standard deviation of 0.18 second.a) Use the
Sluggers. Babe Ruth was the first great “slugger” in baseball. His record of 60 home runs in one season held for 34 years until Roger Maris hit 61 in 1961. Mark McGwire(with the aid of steroids) set a new standard of 70 in 1998.Listed below are the home run totals for each season McGwire
Sample. A study in South Africa focusing on the impact of health insurance identified 1590 children at birth and then sought to conduct follow-up health studies 5 years later. Only 416 of the original group participated in the 5-year follow-up study. This made researchers concerned that the
Winter Olympics 2006 speed skating. The top 25 women’s 500-m speed skating times are listed in the table:a) The mean finishing time was 78.21 seconds, with a standard deviation of 1.03 seconds. If the Normal model is appropriate, what percent of the times should be within 0.5 second of 78.21?b)
Liberty’s nose. Is the Statue of Liberty’s nose too long?Her nose measures , but she is a large statue, after all. Her arm is 42 feet long. That means her arm is times as long as her nose. Is that a reasonable ratio? Shown in the table are arm and nose lengths of 18 girls in a Statistics class,
Teen drivers. In its Traffic Safety Facts 2005, the National Highway Traffic Safety Administration reported that 6.3% of licensed drivers were between the ages of 15 and 20, yet this age group was behind the wheel in 15.9% of all fatal crashes. Use these statistics to explain the concept of
Old Faithful? Does the duration of an eruption have an effect on the length of time that elapses before the next eruption?a) The histogram below shows the duration (in minutes)of those 222 eruptions. Describe this distribution.b) Explain why it is not appropriate to find summary statistics for this
Old Faithful. It is a common belief that Yellowstone’s most famous geyser erupts once an hour at very predictable intervals. The histogram below shows the time gaps (in minutes) between 222 successive eruptions.Describe this distribution. 40 30 30 #of Inter-eruption Intervals 20 20 10 40.0 65.0
Seasons. Average daily temperatures in January and July for 60 large U.S. cities are graphed in the histograms below.a) What aspect of these histograms makes it difficult to compare the distributions?b) What differences do you see between the distributions of January and July average
Hard water II. The data set from England and Wales also notes for each town whether it was south or north of Derby. Here are some summary statistics and a comparative boxplot for the two regions.a) What is the overall mean mortality rate for the two regions?b) Do you see evidence of a difference in
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
Accidents. In 2001, Progressive Insurance asked customers who had been involved in auto accidents how far they were from home when the accident happened.The data are summarized in the table.a) Create an appropriate graph of these data.b) Do these data indicate that driving near home is particularly
Let’s play cards. You pick a card from a deck (see description in Chapter 11) and record its denomination(7, say) and its suit (maybe spades).a) Is the variable suit categorical or quantitative?b) Name a game you might be playing for which you would consider the variable denomination to be
Computers and Internet. A U.S. Census Bureau report(August 2000, Current Population Survey) found that 51.0%of homes had a personal computer and 41.5% had access to the Internet. A newspaper concluded that 92.5% of homes had either a computer or access to the Internet. Do you agree? Explain.
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. Both sets of test
Streams. As part of the course work, a class at an upstate NY college collects data on streams each year. Students record a number of biological, chemical, and physical variables, including the stream name, the substrate of the stream (limestone, shale, or mixed), the pH, the temperature(°C), and
Fraud detection. A credit card bank is investigating the incidence of fraudulent card use. The bank suspects that the type of product bought may provide clues to the fraud. To examine this situation, the bank looks at the Standard Industrial Code (SIC) of the business related to the transaction.
Acid rain. Based on long-term investigation, researchers have suggested that the acidity (pH) of rainfall in the Shenandoah Mountains can be described by the Normal model N(4.9, 0.6).a) Draw and carefully label the model.b) What percent of storms produce rainfall with pH over 6?c) What percent of
State University. Public relations staff at State U. phoned 850 local residents. After identifying themselves, the callers asked the survey participants their ages, whether they had attended college, and whether they had a favorable opinion of the university. The official report to the
Bread. Clarksburg Bakery is trying to predict how many loaves to bake. In the last 100 days, they have sold between 95 and 140 loaves per day. Here is a histogram of the number of loaves they sold for the last 100 days.a) Describe the distribution.b) Which should be larger, the mean number of sales
Beanstalks. Beanstalk Clubs are social clubs for very tall people. To join, a man must be over tall, and a woman over The National Health Survey suggests that heights of adults may be Normally distributed, with mean heights of for men and for women. The respective standard deviations are anda) You
Dialysis. In a study of dialysis, researchers found that “of the three patients who were currently on dialysis, 67%had developed blindness and 33% had their toes amputated.”What kind of display might be appropriate for these data? Explain.
Singers. The boxplots shown display the heights (in inches) of 130 members of a choir.a) It appears that the median height for sopranos is missing, but actually the median and the upper quartile are equal. How could that happen?b) Write a few sentences describing what you see. 76 72 72 Height (in.)
Prenatal care. Results of a 1996 American Medical Association report about the infant mortality rate for twins carried for the full term of a normal pregnancy are shown on the next page, broken down by the level of prenatal care the mother had received.a) Is the overall rate the average of the
Bananas. Here are the prices (in cents per pound) of bananas reported from 15 markets surveyed by the U.S.Department of Agriculture.a) Display these data with an appropriate graph.b) Report appropriate summary statistics.c) Write a few sentences about this distribution. 51 52 45 48 53 52 48 50 49
Tomatoes. Agricultural scientists are working on developing an improved variety of Roma tomatoes. Marketing research indicates that customers are likely to bypass Romas that weigh less than 70 grams. The current variety of Roma plants produces fruit that averages 74 grams, but 11% of the tomatoes
Eggs. Hens usually begin laying eggs when they are about 6 months old. Young hens tend to lay smaller eggs, often weighing less than the desired minimum weight of 54 grams.a) The average weight of the eggs produced by the young hens is 50.9 grams, and only 28% of their eggs exceed the desired
Body temperatures. Most people think that the“normal” adult body temperature is That figure, based on a 19th-century study, has recently been challenged. In a 1992 article in the Journal of the American Medical Association, researchers reported that a more accurate figure may be Furthermore,
Kindergarten. Companies that design furniture for elementary school classrooms produce a variety of sizes for kids of different ages. Suppose the heights of kindergarten children can be described by a Normal model with a mean of 38.2 inches and standard deviation of 1.8 inches.a) What fraction of
Tires. A tire manufacturer believes that the treadlife of its snow tires can be described by a Normal model with a mean of 32,000 miles and standard deviation of 2500 miles.a) If you buy a set of these tires, would it be reasonable for you to hope they’ll last 40,000 miles? Explain.b)
Cholesterol. Assume the cholesterol levels of adult American women can be described by a Normal model with a mean of 188 mg/dL and a standard deviation of 24.a) Draw and label the Normal model.b) What percent of adult women do you expect to have cholesterol levels over 200 mg/dL?c) What percent of
IQ, finis. Consider the IQ model N(100, 16) one last time.a) What IQ represents the 15th percentile?b) What IQ represents the 98th percentile?c) What’s the IQR of the IQs?
Cattle, finis. Consider the Angus weights model N(1152, 84) one last time.a) What weight represents the 40th percentile?b) What weight represents the 99th percentile?c) What’s the IQR of the weights of these Angus steers?
More IQs. In the Normal model N(100, 16), what cutoff value boundsa) the highest 5% of all IQs?b) the lowest 30% of the IQs?c) the middle 80% of the IQs?
More cattle. Based on the model N(1152, 84) describing Angus steer weights, what are the cutoff values fora) the highest 10% of the weights?b) the lowest 20% of the weights?c) the middle 40% of the weights?
IQs revisited. Based on the Normal model N(100, 16)describing IQ scores, what percent of people’s IQs would you expect to bea) over 80?b) under 90?c) between 112 and 132?
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