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Stats Data And Models 4th Edition Richard D. De Veaux, Paul D. Velleman, David E. Bock - Solutions
In 2000, the Journal of the American Medical Association (JAMA) published a study that examined pregnancies that resulted in the birth of twins. Births were classified as preterm with intervention (induced labor or cesarean), preterm without procedures, or term/post-term. Researchers also
A company held a blood pressure screening clinic for its employees. The results are summarized in the table below by age group and blood pressure level:a) Find the marginal distribution of blood pressure level.b) Find the conditional distribution of blood pressure level within each age group.c)
The Centers for Disease Control and Prevention (CDC) has estimated that 19.8% of Americans over 15 years old are obese. The CDC conducts a survey on obesity and various behaviors. Here is a table on self-reported exercise classified by body mass index (BMI):a) Are these percentages column
Hearing anecdotal reports that some patients undergoing treatment for the eating disorder anorexia seemed to be responding positively to the antidepressant Prozac, medical researchers conducted an experiment to investigate. They found 93 women being treated for anorexia who volunteered to
Changing attitudes about marriage and families prompted Pew Research to ask how people felt about particular recent trends (pewresearch.org/pubs/1802/decline-marriage-rise-new-families). For each trend, participants were asked whether the trend "is a good thing," "is a bad thing," or "makes no
For a period of five years, physicians at McGill University Health Center followed more than 5000 adults over the age of 50. The researchers were investigating whether people taking a certain class of antidepressants (SSRIs) might be at greater risk of bone fractures. Their observations are
The table given below shows the number of licensed U.S. drivers (in millions) by age and by sex (www.dot.gov).a) What percent of total drivers are under 20? b) What percent of total drivers are male? c) Write a few sentences comparing the number of male and female licensed drivers in each age
A study by the University of Texas Southwestern Medical Center examined 626 people to see if an increased risk of contracting hepatitis C was associated with having a tattoo. If the subject had a tattoo, researchers asked whether it had been done in a commercial tattoo parlor or elsewhere. Write a
Most patients who undergo surgery make routine recoveries and are discharged as planned. Others suffer excessive bleeding, infection, or other postsurgical complications and have their discharges from the hospital delayed. Suppose your city has a large hospital and a small hospital, each performing
A company must decide which of two delivery services it will contract with. During a recent trial period, the company shipped numerous packages with each service and kept track of how often deliveries did not arrive on time. Here are the data:a) Compare the two services' overall percentage of late
A 1975 article in the magazine Science examined the graduate admissions process at Berkeley for evidence of sex discrimination. The table below shows the number of applicants accepted to each of four graduate programs:a) What percent of total applicants were admitted?b) Overall, was a higher
Two companies are vying for a city's "Best Local Employer" award, to be given to the company most committed to hiring local residents. Although both employers hired 300 new people in the past year, Company A brags that it deserves the award because 70% of its new jobs went to local residents,
The following table summarizes 348 films from 2010 that have been classified into a genre and have a MPAA rating.a) What percentage of these films were rated R? b) What percentage of these films were R-rated comedies? c) What percentage of R-rated films were comedies? d) What percentage of comedies
The following table shows the labor force status of people 16 years of age and older in the United States. Counts are in thousands of people.a) What percentage of the population were unemployed?b) What percentage of the population were unemployed and aged 25 to 54 years?c) What percentage of 20 to
Here are histograms for four manufactured sets of numbers. The histograms look rather different, but all four sets have the same 5-number summary, so the boxplots for all four sets are identical to the one shown. Using these plots as examples, explain some limitations in using boxplots to describe
Would you expect distributions of these variables to be uniform, unimodal, or bimodal? Symmetric or skewed? Explain why. a) The number of speeding tickets each student in the senior class of a college has ever had. b) Players' scores (number of strokes) at the U.S. Open golf tournament in a given
Would you expect distributions of these variables to be uniform, unimodal, or bimodal? Symmetric or skewed? Explain why. a) Ages of people at a Little League game. b) Number of siblings of people in your class. c) Pulse rates of college-age males. d) Number of times each face of a die shows in 100
The histogram displays the sugar content (as a percent of weight) of 49 brands of breakfast cereals.a) Describe this distribution. b) What do you think might account for this shape?
The display shows the heights of some of the singers in a chorus, collected so that the singers could be positioned on stage with shorter ones in front and taller ones in back.a) Describe the distribution. b) Can you account for the features you see here?
The histogram shows the sizes (in acres) of 36 vineyards in the Finger Lakes region of New York.a) Approximately what percentage of these vineyards are under 60 acres? b) Write a brief description of this distribution (shape, center, spread, unusual features).
One of the authors collected the times (in minutes) it took him to run 4 miles on various courses during a 10-year period. Here is a histogram of the times.Describe the distribution and summarize the important features. What is it about running that might account for the shape you see?
The histogram shows the lengths of hospital stays (in days) for all the female patients admitted to hospitals in New York during one year with a primary diagnosis of acute myocardial infarction (heart attack).a) From the histogram, would you expect the mean or median to be larger? Explain. b) Write
In a way, boxplots are the opposite of histograms. A histogram divides the number line into equal intervals and displays the number of data values in each interval. A boxplot divides the data into equal parts and displays the portion of the number line each part covers. These two plots display the
A university teacher saved every e-mail received from students in a large Introductory Statistics class during an entire term. He then counted, for each student who I had sent him at least one e-mail, how many e-mails each student had sent.a) From the histogram, would you expect the mean or the
How many points do football teams score in the Super Bowl? Here are the total numbers of points scored by both teams in each of the first 48 Super Bowl games: 45, 47, 23, 30, 29, 27, 21, 31, 22, 38, 46, 37, 66, 50, 37, 47, 44, 47, 54, 56, 59, 52, 36, 65, 39, 61, 69, 43, 75, 44, 56, 55, 53, 39, 41,
In the Super Bowl, by how many points does the winning team outscore the losers? Here are the winning margins for the first 48 Super Bowl games: 25, 19, 9, 16, 3, 21, 7, 17, 10, 4, 18, 17, 4, 12, 17, 5, 10, 29, 22, 36, 19, 32, 4, 45, 1, 13, 35, 17, 23, 10, 14, 7, 15, 7, 27, 3, 27, 3, 3, 11, 12, 3,
Here are costs of nine compact refrigerators rated very good or excellent by Consumer Reports on their website www.consumerreports.org. $150 150 160 180 150 140 120 130 120 Find these statistics: a) Mean b) Median and quartiles c) Range and IQR
Here are the annual numbers of deaths from tornadoes in the United States from 1998 through 2013: 130 94 40 40 555 54 35 38 67 81 125 21 45 553 70 54 Find these statistics: a) Mean b) Median and quartiles c) Range and IQR
A clerk entering salary data into a company spreadsheet accidentally put an extra "0" in the boss's salary, listing it as $2,000,000 instead of $200,000. Explain how this error will affect these summary statistics for the company payroll: a) Measures of center: median and mean. b) Measures of
During contract negotiations, a company seeks to change the number of sick days employees may take, saying that the annual "average" is 7 days of absence per employee. The union negotiators counter that the "average" employee misses only 3 days of work each year. Explain how both sides might be
For each lettered part, a through c, examine the two given sets of numbers. Without doing any calculations, decide which set has the larger standard deviation and explain why. Then check by finding the standard deviations.
For each lettered part, a through c, examine the two given sets of numbers. Without doing any calculations, decide which set has the larger standard deviation and explain why. Then check by finding the standard deviations.
The 5-number summary for the run times in minutes of the 150 highest grossing movies of 2010 looks like this:Are there any outliers in these data? How can you tell?
Look again at the histogram of the pizza prices in Exercise 29.a) Is the mean closer to $2.40, $2.60, or $2.80? Why? b) Is the standard deviation closer to $0.15, $0.50, or $1.00? Explain.
Look again at the histogram of men's neck sizes in Exercise 30.a) Is the mean closer to 14, 15, or 16 inches? Why? b) Is the standard deviation closer to 1 inch, 3 inches, or 5 inches? Explain.
The histogram shows the running times in minutes of the 150 top-grossing feature films released in 2010.a) You plan to see a movie this weekend. Based on these movies, how long do you expect a typical movie to run? b) Would you be surprised to find that your movie ran for 2 1/2 hours (150
The display shows the average drive distance (in yards) for 155 professional golfers during a week on the men's PGA tour in 2013.a) Describe this distribution. b) Approximately what proportion of professional male golfers drive, on average, 280 yards or less? c) Estimate the mean by examining the
Exercise 33 looked at the running times of movies released in 2010. The standard deviation of these running times is 16.6 minutes, and the quartiles are Q1 = 98 minutes and Q3 = 116 minutes.a) Write a sentence or two describing the spread in running times based on i) The quartiles. ii) The standard
Exercise 34 looked at distances PG golfers can hit the ball. The standard deviation of these average drive distances is 11.2 yards, and the quartiles are Q1 = 282.5 yards and Q3 = 295.6 yards.a) Write a sentence or two describing the spread in distances based on i) The quartiles. ii) The standard
A meteorologist preparing a talk about global warming compiled a list of weekly low temperatures (in degrees Fahrenheit) he observed at his southern Florida home last year. The coldest temperature for any week was 36°F, but he inadvertently recorded the Celsius value of 2°. Assuming that he
A small warehouse employs a supervisor at $ 1200 a week, an inventory manager at $700 a week, six stock boys at $400 a week, and four drivers at $500 a week. a) Find the mean and median wage. b) How many employees earn more than the mean wage? c) Which measure of center best describes a typical
The following table shows the mean and median ages in years of children adopted in different states in 2010. In all 50 states, the mean age is higher than the median. What might that imply about the shape of the distribution of ages of adopted children in each state?
The frequency table shows the heights (in inches) of 130 members of a choir.a) Find the median and IQR. b) Find the mean and standard deviation. c) Display these data with a histogram. d) Write a few sentences describing the distribution.
In January 2014, 16 gas stations in eastern Wisconsin posted these prices for a gallon of regular gasoline:a) Make a stem-and-leaf display of these gas prices. Use split stems; for example, use two 3.2 stemsone for prices between $3.20 and $3.24 and the other for prices from $3.25 to
During his 20 seasons in the NHL, Wayne Gretzky scored 50% more points than anyone who ever played professional hockey. He accomplished this amazing feat while playing in 280 fewer games than Gordie Howe, the previous record holder. Here are the number of games Gretzky played during each
The stem-and-leaf display shows populations of the 50 states, in millions of people, according to the 2010 census.a) What measures of center and spread are most appropriate? b) Without doing any calculations, which must be larger: the median or the mean? Explain how you know. c) From the
In Exercise 42, you examined the number of games played by hockey great Wayne Gretzky during his 20-year career in the NHL. a) Would you use the median or the mean to describe the center of this distribution? Why? b) Find the median. c) Without actually finding the mean, would you expect it to be
Alex Rodriguez (known to fans as A-Rod) was the youngest player ever to hit 500 home runs. Here is a stem-and-leaf display of the number of home runs hit by A-Rod during the 1994-2013 seasons, (www.baseball-reference.com/players/r/rodrialOl.shtml.) Describe the distribution, mentioning its shape
The Cornell Lab of Ornithology holds an annual Christmas Bird Count (www.birdsource.org), in which bird watchers at various locations around the country see how many different species of birds they can spot. Here are the number of species counted from the 20 sites with the most species in 2013:a)
Create a stem-and-leaf display for these horsepowers of autos reviewed by Consumer Reports, and describe the distribution:
Students were asked to make a histogram of the number of home runs hit by Alex Rodriguez from 1994 to 2013 (see Exercise 45). One student submitted the following display (he noted that A Rod had hit no home runs in 1994):a) Comment on this graph. b) Create your own histogram of the data.
Students were given the assignment to make a histogram of the data on bird counts reported in Exercise 46. One student submitted the following display:a) Comment on this graph. b) Create your own histogram of the data.
Two researchers measured the pH (a scale on which a value of 7 is neutral and values below 7 are acidic) of water collected from rain and snow over a 6-month period in Allegheny County, Pennsylvania. Describe their data with a graph and a few sentences:
In 2007 the Council of Europe published a report entitled The European School Survey Project on Alcohol and Other Drugs (www.espad.org). Among other issues, the survey investigated the percent ages of 16-year-olds who had used marijuana. Shown here are the results for 34 European countries. Create
After receiving many complaints about his final-grade histogram from students currently taking a Statistics course, the professor from Exercise 53 distributed the following revised histogram:a) Comment on this display. b) Describe the distribution of grades.
Holes-R-Us, an Internet company that sells piercing jewelry keeps transaction records on its sales. At a recent sales meeting, one of the staff presented a histogram of the ZIP codes of the last 500 customers, so that the staff might understand where sales are coming from. Comment on the usefulness
Here are some summary statistics to go with the histogram of the ZIP codes of 500 customers from the Holes-R-Us Internet Jewelry Salon that we saw in Exercise 55: Count …………… 500 Mean ……………. 64,970.0 StdDev ………….. 23,523.0 Median …………. 64,871 IQR
The National Center for Education Statistics (nces.ed.gov/nations report card/) reports average mathematics achievement scores for eighth graders in all 50 states:a) Find the median, the IQR, the mean, and the standard deviation of these state averages. b) Which summary statistics would you report
In 2011, the website NewGeography .com listed its ranking of the best cities for job growth in the United States. Here is the magazine's top 20 larger cites, along with their weighted job rating index.a) Make a suitable display of the weighted growth indices. b) Summarize the typical growth index
The following data show the percentage change in population for the 50 states and the District of Columbia from the 2000 census to the 2010 census. Using appropriate graphical displays and summary statistics, write a report on the percentage change in population by state.
A report from the U.S. Department of Justice (www.ojp.usdoj.gov/bjs/) reported the percent changes in federal prison populations in 20 northeastern and midwestern states from 2000 to 2012. Using appropriate graphical displays and summary statistics, write a report on the changes in prison
The Research and Innovative Technology Administration of the Bureau of Transportation Statistics reports load factors (passenger-miles as a percentage of available seat-miles) for commercial airlines for every month from 2000 through September 2013. Here are histograms comparing the domestic and
Here are the exoplanet distances of Exercise 9, re-expressed to the log scale.a) Is this a better scale to understand these distances? b) The low outlier is "sol"- that is, it is the distance of the sun from the earth. Do you think it belongs with these data?
A company that sells frozen pizza to stores in four markets in the United States (Denver, Baltimore, Dallas, and Chicago) wants to examine the prices that the stores charge for pizza slices. Here are boxplots comparing data from a sample of stores in each market:a) Do prices appear to be the same
To help travelers know what to expect, researchers collected the prices of commodities in 16 cities throughout the world. Here are boxplots comparing the prices of a ride on public transportation, a newspaper, and a cup of coffee in the 16 cities (prices are all in US$).a) On average, which
Crowd Management Strategies monitors accidents at rock concerts. In their database, they list the names and other variables of victims whose deaths were attributed to "crowd crush" at rock concerts. Here are the histogram and boxplot of the victims' ages for data from a recent one-year period.a)
The Men's Giant Slalom skiing event consists of two runs whose times are added together for a final score. Two displays of the giant slalom times in the 2010 Winter Olympics are shown below.a) What features of the distribution can you see in both the histogram and the boxplot? b) What summary
Sugar is a major ingredient in many breakfast cereals. The histogram displays the sugar content as a percentage of weight for 49 brands of cereal. The boxplots compare sugar content for adult and children's cereals.a) What is the range of the sugar contents of these cereals? b) Describe the shape
We can also compare domestic load factors for September through March versus those for April through August:Compare and contrast what these histograms show.
People with spinal cord injuries may lose function in some, but not all, of their muscles. The ability to push oneself up is particularly important for shifting position when seated and for transferring into and out of wheelchairs. Surgeons compared two operations to restore the ability to push up
Below is a "back-to-back" stem-and-leaf display that shows two data sets at onceone going to the left, one to the right The display compares the percent change in population for two regions of the United States (based on census figures for 2000 and 2010). The fastest growing state was
Shown below are the histogram and summary statistics for the number of camp sites at public parks in Vermont.a) Which statistics would you use to identify the center and spread of this distribution? Why? b) How many parks would you classify as outliers? Explain. c) Create a boxplot for these
The U.S. National Center for Health Statistics compiles data on the length of stay by patients in short-term hospitals and publishes its findings in Vital and Health Statistics. Data from a sample of 39 male patients and 35 female patients on length of stay (in days) are displayed in the following
A National Vital Statistics Report (www.cdc.gov/nchs/) indicated that nearly 290,000 black Americans died in 2011, compared with just over 2 million white Americans. Below are histograms displaying the distributions of their ages at death.a) Describe the overall shapes of these distributions. b)
Here are boxplots of the points scored during the first 10 games of the season for both Scyrine and Alexandra:a) Summarize the similarities and differences in their performance so far. b) The coach can take only one player to the state championship. Which one should she take? Why?
Here are boxplots of weekly gas prices for regular gas in the United States as reported by the U.S. Energy Information Administration for 2009 through 2013.a) Compare the distribution of prices over the five years. b) Compare the stability of prices over the five years.
In 1975, did men and women marry at the same age? Here are boxplots of the age at first marriage for a sample of U.S. citizens then. Write a brief report discussing what these data show.
Describe what these boxplots tell you about the relationship between the number of cylinders a car's engine has and the car's fuel economy (mpg).
The Environmental Protection Agency provides fuel economy and pollution information on over 2000 car models. Here is a boxplot of Combined Fuel Economy (using an average of driving conditions) in miles per gallon by vehicle Type (midsize car, standard pickup truck, or SUV) for 2012 model vehicles.
Ozone levels (in parts per billion, ppb) were recorded at sites in New Jersey monthly between 1926 and 1971. Here are boxplots of the data for each month (over the 46 years), lined up in order (January = 1):a) In what month was the highest ozone level ever recorded? b) Which month has the largest
Three Statistics classes all took the same test. Histograms and boxplots of the scores for each class are shown below. Match each class with the corresponding boxplot.
A survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools. Two of the questions concerned eye and hair color. In the survey, the following codes were used:The Statistics students analyzing the data were asked to study the
A survey of major universities asked what percentage of incoming freshmen usually graduate "on time" in 4 years. Use the summary statistics given to answer the questions that follow. % on Time Count ……………………. 48 Mean ……………………. 68.35 Median
Here are summary statistics for the sizes (in acres) of the Finger Lakes vineyards (of Exercise 3.17):Suppose you didn't have access to the data. Answer the following questions from the summary statistics alone: a) Would you describe this distribution as symmetric or skewed? Explain. b) Are there
A student study of the effects of caffeine asked volunteers to take a memory test 2 hours after drinking soda. Some drank caffeine-free cola, some drank regular cola (with caffeine), and others drank a mixture of the two (getting a half-dose of caffeine). Here are the 5-number summaries for each
Here are the summary statistics for Verbal SAT scores for a high school graduating class:a) Create side-by-side boxplots comparing the scores of boys and girls as best you can from the information given. b) Write a brief report on these results. Be sure to discuss the shape, center, and spread of
How fast do horses run? Kentucky Derby winners top 30 miles per hour, as shown in this graph. The graph shows the percentage of Derby winners that have run slower than each given speed. Few have won running less than 33 miles per hour, but about 86% of the winning horses have run less than 37 miles
The Framingham Heart Study recorded the cholesterol levels of more than 1400 men. Here is an ogive of the distribution of these cholesterol measures. (An ogive shows the percentage of cases at or below a certain value.) Construct a boxplot for these data, and write a few sentences describing the
A class of fourth graders takes a diagnostic reading test, and the scores are reported by reading grade level. The 5-number summaries for the 14 boys and 11 girls are shown:a) Which group had the highest score?b) Which group had the greater range?c) Which group had the greater interquartile
In an experiment to determine whether seeding clouds with silver iodide increases rainfall, 52 clouds were randomly assigned to be seeded or not. The amount of rain they generated was then measured (in acre-feet). Here are the summary statistics:a) Which of the summary statistics are most
Engineers at a computer production plant tested two methods for accuracy in drilling holes into a PC board. They tested how fast they could set the drilling machine by running 10 boards at each of two different speeds. To assess the results, they measured the distance (in inches) from the center of
A study examining the health risks of smoking measured the cholesterol levels of people who had smoked for at least 25 years and people of similar ages who had smoked for no more than 5 years and then stopped. Create appropriate graphical displays for both groups, and write a brief report comparing
A consumer organization wants to compare gas mileage figures for several models of cars made in the United States with autos manufactured in other countries. The data for a random sample of cars classified as "midsize" are shown in the table.a) Create graphical displays for these two groups.b)
American League baseball teams play their games with the designated hitter rule, meaning that pitchers do not bat. The League believes that replacing the pitcher, typically a weak hitter, with another player in the batting order produces more runs and generates more interest among fans. Following
Researchers tracked a population of 1,203,646 fruit flies, counting how many died each day for 171 days. Here are three timeplots offering different views of these data. One shows the number of flies alive on each day, one the number who died that day, and the third the mortality
Accidents involving drunk drivers account for about 40% of all deaths on the nation's highways. The table in the next column tracks the number of alcohol-related fatalities for 26 years.a) Create a stem-and-leaf display or a histogram of these data. b) Create a timeplot. c) Using features apparent
Here is a histogram of the assets (in millions of dollars) of 79 companies chosen from the Forbes list o the nation's top corporations:a) What aspect of this distribution makes it difficult to summarize, or to discuss, center and spread? b) What would you suggest doing with these data if we want to
Students were asked how many songs they had in their digital music libraries. Here's a display of the responses:a) What aspect of this distribution makes it difficult to summarize, or to discuss, center and spread? b) What would you suggest doing with these data if we want to understand them better?
Here are the same data you saw in Exercise 47 after re-expressions as the square root of assets (in $M) and the logarithm of assets (in $M):a) Which re-expression do you prefer? Why? b) In the square root re-expression, what does the value 50 actually indicate about the company's assets? c) In the
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