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Stats Data And Models 4th Edition Richard D. De Veaux, Paul D. Velleman, David E. Bock - Solutions

The table lists the amount of rainfall (in acre-feet) from the 26 clouds seeded with silver iodide discussed in Exercise 40:a) Why is acre-feet a good way to measure the amount of precipitation produced by cloud seeding? b) Plot these data, and describe the distribution. c) Create a re-expression
Stereograms appear to be composed entirely of random dots. However, they contain separate images that a viewer can "fuse" into a three-dimensional (3D) image by staring at the dots while defocusing the eyes. An experiment was performed to determine whether knowledge of the 20 embedded image
Here's a boxplot of all of the domestic load factors. It shows a single outlier. The boxplots of Exercise 4 show the same data, but have no outliers. Why do you think this is?
Here is a timeplot of each monthly load factor for domestic flights for 2000 to 2013 along with a lowess smooth.a) Describe the patterns you see in this plot. b) Do you expect the overall pattern to continue for another decade? Why or why not?
Here is a timeplot of the same domestic load factors as in Exercise 7 but this time with a different smoother (called a median smoother) applied.a) What patterns do you see in this plot? b) Do you expect the patterns you see here to continue for the next decade? Why or why not?
The mean score on the Stats exam was 75 points with a standard deviation of 5 points, and Gregor's z-score was —2. How many points did he score?
Based on the Normal model N(100, 16) describing IQ scores, what percent of people's IQs would you expect to be a) Over 80? b) Under 90? c) Between 112 and 132?
Corey has 4929 songs in his computer's music library. The lengths of the songs have a mean of 242.4 seconds and standard deviation of 114.51 seconds. A Normal probability plot of the song lengths looks like this:a) Do you think the distribution is Normal? Explain. b) If it isn't Normal, how does it
The histogram shows the distribution of mean ACT mathematics scores for all Wisconsin public schools in 2011. The vertical lines show the mean and one standard deviation above and below the mean. 78.8% of the data points are between the two outer lines.a) Give two reasons that a Normal model is not
Here are the summary statistics for the weekly payroll of a small company: lowest salary = $300, mean salary = $700, median = $500, range = $1200, IQR = $600, first quartile = $350, standard deviation = $400. a) Do you think the distribution of salaries is symmetric, skewed to the left, or skewed
A specialty foods company sells "gourmet hams" by mail order. The hams vary in size from 4.15 to 7.45 pounds, with a mean weight of 6 pounds and standard deviation of 0.65 pounds. The quartiles and median weights are 5.6, 6.2, and 6.55 pounds. a) Find the range and the IQR of the weights. b) Do you
Each year thousands of high school students take either the SAT or the ACT, standardized tests used in the college admissions process. Combined SAT Math and Verbal scores go as high as 1600, while the maximum ACT composite score is 36. Since the two exams use very different scales, comparisons of
A high school senior uses the Internet to get information on February temperatures in the town where he'll be going to college. He finds a website with some statistics, but they are given in degrees Celsius. The conversion formula is °F = 9/5°C + 32. Determine the Fahrenheit equivalents for the
Corey has 4929 songs in his computer's music library. The songs have a mean duration of 242.4 seconds with a standard deviation of 114.51 seconds. On the Nickel, by Tom Waits, is 380 seconds long. What is its z-score?
People with z-scores above 2.5 on an IQ test are sometimes classified as geniuses. If IQ scores have a mean of 100 and a standard deviation of 16 points, what IQ score do you need to be considered a genius?
In the last chapter, we looked at three outliers arising from a plot of Average Wind Speed by Month in the Hopkins Forest. Each was associated with an unusually strong storm, but which was the most remarkable for its month?Here are the summary statistics for each of those three months:The outliers
The first Stat exam had a mean of 80 and a standard deviation of 4 points; the second had a mean of 70 and a standard deviation of 15 points. Reginald scored an 80 on the first test and an 85 on the second. Sara scored an 88 on the first but only a 65 on the second. Although Reginald's total score
Anna, a language major, took final exams in both French and Spanish and scored 83 on each. Her roommate Megan, also taking both courses, scored 77 on the French exam and 95 on the Spanish exam. Overall, student scores on the French exam had a mean of 81 and a standard deviation of 5, and the
Two companies market new batteries targeted at owners of personal music players. DuraTunes claims a mean battery life of 11 hours, while RockReady advertises 12 hours. a) Explain why you would also like to know the standard deviations of the battery lifespans before deciding which brand to buy. b)
Using N(1152, 84), the Normal model for weights of Angus steers in Exercise 9, a) How many standard deviations from the mean would a steer weighing 1000 pounds be? b) Which would be more unusual, a steer weighing 1000 pounds or one weighing 1250 pounds?
John Beale of Stanford, California, recorded the speeds of cars driving past his house, where the speed limit read 20 mph. The mean of 100 readings was 23.84 mph, with a standard deviation of 3.56 mph. (He actually recorded every car for a two-month period. These are 100 representative
Recall that the beef cattle described in Exercise 25 had a mean weight of 1152 pounds, with a standard deviation of 84 pounds. a) Cattle buyers hope that yearling Angus steers will weigh at least 1000 pounds. To see how much over (or under) that goal the cattle are, we could subtract 1000 pounds
For the car speed data in Exercise 26, recall that the mean speed recorded was 23.84 mph, with a standard deviation of 3.56 mph. To see how many cars are speeding, John subtracts 20 mph from all speeds. a) What is the mean speed now? What is the new standard deviation? b) His friend in Berlin wants
Suppose the auctioneer in Exercise 27 sold a herd of cattle whose minimum weight was 980 pounds, median was 1140 pounds, standard deviation 84 pounds, and IQR 102 pounds. They sold for 40 cents a pound, and the auctioneer took a $20 commission on each animal. Then, for example, a steer weighing
A town's January high temperatures average 36°F with a standard deviation of 10°, while in July the mean high temperature is 74° and the standard deviation is 8°. In which month is it more unusual to have a day with a high temperature of 55°? Explain.
Suppose police set up radar surveillance on the Stanford street described in Exercise 26. They handed out a large number of tickets to speeders going a mean of 28 mph, with a standard deviation of 2.4 mph, a maximum of 33 mph, and an IQR of 3.2 mph. Local law prescribes fines of $100, plus $10 per
A friend tells you about a recent study dealing with the number of years of teaching experience among current college professors. He remembers the mean but can't recall whether the standard deviation was 6 months, 6 years, or 16 years. Tell him which one it must have been, and why.
A popular band on tour played a series of concerts in large venues. They always drew a large crowd, averaging 21,359 fans. While the band did not announce (and probably never calculated) the standard deviation, which of these values do you think is most likely to be correct: 20, 200, 2000, or
In Exercise 25, we suggested the model N(1152, 84) for weights in pounds of yearling Angus steers. What weight would you consider to be unusually low for such an animal? Explain.
Exercise 8, proposes modeling IQ scores with N(100, 16). What IQ would you consider to be unusually high? Explain.
A forester measured 27 of the trees in a large woods that is up for sale. He found a mean diameter of 10.4 inches and a standard deviation of 4.7 inches. Suppose that these trees provide an accurate description of the whole forest and that a Normal model applies. a) Draw the Normal model for tree
A company that manufactures rivets believes the shear strength (in pounds) is modeled by N(800, 50). a) Draw and label the Normal model. b) Would it be safe to use these rivets in a situation requiring a shear strength of 750 pounds? Explain. c) About what percent of these rivets would you expect
Fifty-nine men completed the men's alpine downhill race in Vancouver. The gold medal winner finished in 114.3 seconds. Here are the times (in seconds) for all competitors (espn.go.com/olympics/winter/2010/results/_/sport/l/event/2):a) The mean time was 117.34 seconds, with a standard deviation of
An incoming freshman took her college's placement exams in French and mathematics. In French, she scored 82 and in math 86. The overall results on the French exam had a mean of 72 and a standard deviation of 8, while the mean math score was 68, with a standard deviation of 12. On which exam did she
The mean of the 100 car speeds in Exercise 26 was 23.84 mph, with a standard deviation of 3.56 mph.a) Using a Normal model, what values should border the middle 95% of all car speeds?b) Here are some summary statistics.From your answer in part a, how well does the model do in predicting those
NFL data from the 2013 football season reported the number of yards gained by each of the league's 181 wide receivers:The mean is 426.98 yards, with a standard deviation of 408.34 yards. a) According to the Normal model, what percent of receivers would you expect to gain more yards than 2 standard
A large philanthropic organization keeps records on the people who have contributed. In addition to keeping records of past giving, the organization buys demographic data on neighborhoods from the U.S. Census Bureau. Eighteen of these variables concern ethnicity. Here are a histogram and summary
Based on the model N(1152, 84) describing Angus steer weights from Exercise 25, what are the cutoff values for a) The highest 10% of the weights? b) The lowest 20% of the weights? c) The middle 40% of the weights?
In the Normal model N(100, 16) from Exercise 2, what cutoff value bounds a) The highest 5% of all IQs? b) The lowest 30% of the IQs? c) The middle 80% of the IQs?
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?
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?
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 adult
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 one of these tires, would it be reasonable for you to hope it will last 40,000 miles? Explain. b) Approximately what
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 kindergarten
A company selling clothing on the Internet reports that the packages it ships have a median weight of 68 ounces and an IQR of 40 ounces. a) The company plans to include a sales flyer weighing 4 ounces in each package. What will the new median and IQR be? b) If the company recorded the shipping
Most people think that the "normal" adult body temperature is 98.6°F. 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 98.2°F. Furthermore, the
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 minimum
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 are too
A company's customer service hotline handles many calls relating to orders, refunds, and other issues. The company's records indicate that the median length of calls to the hotline is 4.4 minutes with an IQR of 2.3 minutes. a) If the company were to describe the duration of these calls in seconds
Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested recently predicted a mean of 24.8 mpg and a standard deviation of 6.2 mpg for highway driving. Assume that a Normal model can be applied. a) Draw the model for auto fuel economy. Clearly label it, showing what
Some IQ tests are standardized to a Normal model, with a mean of 100 and a standard deviation of 16. a) Draw the model for these IQ scores. Clearly label it, showing what the 68-95-99.7 Rule predicts. b) In what interval would you expect the central 95% of IQ scores to be found? c) About what
The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds. Suppose that weights of all such animals can be described by a Normal model with a standard deviation of 84 pounds. What percent of steers weigh a) Over 1250 pounds? b) Under 1200 pounds? c)
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 strength.a) Apples:
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 strength.a) When
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 strength.a) Legal
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
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?
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 direction. But what
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 histogram
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 fact that is
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 strength.a)
A candidate for office claims that "there is a correlation between television watching and crime." Criticize this statement on statistical grounds.
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 type of car you
Most roller coasters get 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 107 roller coasters around the world.a) Does the scatterplot indicate
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 treated with the
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 Temperature to be?
Consider the following data from a small bookstore.a) Prepare a scatterplot of Sales against Number of sales people working. b) What can you say about the direction of the association? c) What can you say about the form of the relationship? d) What can you say about the strength of the
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 of your classmates
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?
A survey of the world's nations in 2014 shows a strong positive correlation between percentage of the country using smart phones and life expectancy in years at birth.a) Does this mean that smart phones are good for your health?b) What might explain the strong correlation?
The correlation between Age and Income as measured on 100 people is r = 0.75. 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 outliers in the
The correlation between Fuel Efficiency (as measured by miles per gallon) and Price of 150 cars at a large dealership is r = -0.34. 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 form of the
A polling organization is checking its database to see if the two data sources it used sampled the same ZIP codes. The variable Datasource = 1 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
The Office of Federal Housing Enterprise Oversight (www.fhfa.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) Describe the
Disk drives have been getting larger. Their capacity is now often given in terabytes (TB) where 1 TB = 1000 gigabytes, or about a trillion bytes. A search of prices for external disk drives on Amazon.com in early 2014 found the following data: Capacity (in TB) Price (in $) 0.50
Since 1985, average mortgage interest rates have fluctuated from a low of nearly 3% 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 Mortgage Loan Amount in the United States (in trillions of 2013
Here are advertised engine size (in liters) and gas mileage (estimated combined city and highway) for several 2014 vehicles.a) Make a scatterplot for these data. b) Describe the direction, form, and strength of the plot. c) Find the correlation between engine size and miles per gallon. d) Write a
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 following table.a) Create a scatterplot. b) What is the correlation between the percent of teens who have
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 Spearman's rho
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 your analysis
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 more fans attend
Perhaps fans are just more interested in teams that win. The displays below are based on American League teams for the 2013 season, (espn.go.com) (Use the data set Attendance_2013).a) Do winning teams generally enjoy greater attendance at their home games? Describe the association. b) Is attendance
Since 1994, the Best Roller Coaster Poll (www.ushsho.com/bestrollercoasterpoll.htm) has been ranking the world€™s best roller coasters. In 2011, Bizarro earned the top steel coaster rank for the sixth straight year. Here are data on the top 10 steel coasters from this poll:What do these
For the roller coaster data in Exercise 47:a) Examine the relationship between Initial Drop and Speed.b) Examine the relationship between Initial Drop and Height.c) What conclusions can you safely draw about the initial drop of a roller coaster? Is Initial Drop strongly correlated with other
For the roller coaster data in Exercise 47:a) Explain why in looking for a variable that explains rank, you will be hoping for a negative correlation.b) Do any of the provided variables provide a strong predictor for roller coaster rank?c) What other (unaccounted) for variables might help explain
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 several stopped
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. Is there any pattern to the locations of the planets? The table shows the average distance of each of
Here are the number of domestic flights flown in each year from 2000 to 2012. Year Flights 2000 ……… 7,905,617 2001 ……… 7,626,312 2002 ……… 8,085,083 2003 ……… 9,458,818 2004 ……… 9,968,047 2005 ……… 10,038,373 2006 ……… 9,712,750 2007
A larger firm is considering acquiring the bookstore of Exercise 3. An analyst for the firm, noting the relationship seen in Exercise 3, suggests that when they acquire the store they should hire more people because that will drive higher sales. Is his conclusion justified? What alternative
A study finds that during blizzards, online sales are highly associated with the number of snow plows on the road; the more plows, the more online purchases. The director of an association of online merchants suggests that the organization should encourage municipalities to send out more plows
For an analysis of the salaries of your company, you plot the salaries of all employees against the number of years they have worked for the company. You find that plotting the base-10 logarithm of salary makes the plot much straighter. A part-time shipping clerk, who has worked at the company for
If false, explain briefly. a) We choose the linear model that passes through the most data points on the scatterplot. b) The residuals are the observed y-values minus the y-values predicted by the linear model. c) Least squares means that the square of the largest residual is as small as it could
Here are the residuals for a regression of Price on Capacity for the hard drives of Exercise 6. (Based on the hand-computed coefficients.)a) Which residual contributes the most to the sum that is minimized by the Least Squares criterion? b) Five of the residuals are negative. What does that mean
Here are residual plots (residuals plotted against predicted values) for three linear regression models. Indicate which condition appears to be violated (linearity, outlier or equal spread) in each case.a)b) c)
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 of 77
In Chapter 6, Exercise 41 we examined the relationship between the fuel economy (mpg) and Engine Size for 35 models of cars (Data in Fuel Economy 2014). Further analysis produces the regression model mpg = 36.25 - 3.867 Engine size. If the car you are thinking of buying has a 4 liter engine, what
Fill in the missing information in the following table.
Fill in the missing information in the following table.
Tell what each of the residual plots below indicates about the appropriateness of the linear model that was fit to the data.
Tell what each of the residual plots below indicates about the appropriateness of the linear model that was fit to the data.

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