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intro stats

Intro Stats 4th International Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions

2. Load factors, Spring/Summer and Fall/Winter We can also compare domestic load factors for September through March versus those for April through August:Compare and contrast what these histograms show. 25 20 15 10 25 20 15 10 5 5 19 54 229 62 70 78 86 Fall/Winter 54 62 70 78 Spring/Summer 86
1. Load factors, domestic and international The Research and Innovative Technology Administration of the Bureau of Transportation Statistics (www.TranStats.bts.gov/Data_Elements.aspx?Data=2) reports load factors(passenger-miles as a percentage of available seat-miles)for commercial airlines for
60. Prisons 2006 A report from the U.S. Department of Justice (www.ojp.usdoj.gov/bjs/) reported the percent changes in federal prison populations in 21 northeastern and midwestern states during 2006. Using appropriate graphical displays and summary statistics, write a report on the changes in
59. Population growth The following data show the percentage change in population for the 50 states and the District of Columbia from 2000 to 2009. Using appropriate graphical displays and summary statistics, write a report on the percentage change in population by state. Alabama 5.9 Alaska 11.4
58. Boomtowns 2011 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
57. Math scores 2009 The National Center for Education Statistics (nces.ed.govationsreportcard/) reported 2005 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
56. ZIP codes revisited 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:What can these statistics tell you about the company’s sales? Count 500 Mean 64,970.0 StdDev 23,523.0 Median
55. ZIP codes 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
54. Final grades revisited 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. # of Students
53. Final grades A professor (of something other than Statistics!) distributed the following histogram to show the distribution of grades on his 200-point final exam.Comment on the display. # of Students 50 40 30 $20 10 50 100 150 200 Final Grade
Marijuana 2007 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 percentages of 16-year-olds who had used marijuana. Shown here are the results for 34 European
Acid rain 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:4.57 5.62 4.12 5.29 4.64 4.31 4.30
One student submitted the following display:a) Comment on this graph.b) Create your own histogram of the data. 250 200 150 100 50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Site
Return of the birds 2010 Students were given the assignment to make a histogram of the data on bird counts reported in Exercise
A-Rod again 2010 Students were asked to make a histogram of the number of home runs hit by Alex Rodriguez from 1994 to 2010 (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
Horsepower Create a stem-and-leaf display for these horsepowers of autos reviewed by Consumer Reports one year, and describe the distribution:T 155 103 130 80 65 142 125 129 71 69 125 115 138 68 78 150 133 135 90 97 68 105 88 115 110 95 85 109 115 71 97 110 65 90 75 120 80 70
Hurricanes 2010 The following data give the number of hurricanes classified as major hurricanes in the Atlantic Ocean each year from 1944 through 2010, as reported by NOAA (www.nhc.noaa.gov):3, 3, 1, 2, 4, 3, 8, 5, 3, 4, 2, 6, 2, 2, 5, 2, 2, 7, 1, 2, 6, 1, 3, 1, 0, 5, 2, 1, 0, 1, 2, 3, 2, 1, 2, 2,
Bird species 2010 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 some of the counts reported from sites in Texas during the 2010
A-Rod 2010 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 1994–2010 seasons. (www. baseballreference.com/players/r/rodrial01.shtml.) Describe the distribution, mentioning
Wayne Gretzky 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
States 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
The Great One 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
Gasoline 2011 In October 2011, 16 gas stations in eastern Wisconsin posted these prices for a gallon of regular gasoline:3.43 3.46 3.43 3.59 3.65 3.63 3.62 3.65 3.66 3.31 3.35 3.42 3.41 3.46 3.47 3.48a) Make a stem-and-leaf display of these gas prices.Use split stems; for example, use two 3.3
Singers 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. 2282 283 28 Height Count 60 Height Count 2 69 5 61 6 70
Payroll 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
Cold weather 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 36F, but he inadvertently recorded the Celsius value of 2. Assuming
Movie earnings The histogram shows total gross earnings(in millions of dollars) of major release movies in 2011.An industry publication reports that the average movie makes 41.7 million, but a watchdog group concerned with rising ticket prices says that the average earnings are 66.9 million. What
Golf drives II 2011 Exercise 34 looked at distances PGA golfers can hit the ball. The standard deviation of these average drive distances is 8.4 yards, and the quartiles are Q1 = 285.2 yards and Q3 = 297.5 yards.a) Write a sentence or two describing the spread in distances based on i) the
Movie lengths II 2010 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
Golf drives 2011 The display shows the average drive distance (in yards) for 186 professional golfers on the men’s PGA tour in 2011.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
Movie lengths 2010 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 12
Neck sizes again 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.
Pizza prices again 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.
Neck size The histogram shows the neck sizes (in inches)of 250 men recruited for a health study in Utah.Which summary statistics would you choose to summarize the center and spread in these data? Why? No. of Men 60 50 40 30 20 10 0 220 12 13 14 15 16 17 Neck Size (inches)
Pizza prices The histogram shows the distribution of the prices of plain pizza slices (in $) for 156 weeks in Dallas, TX.Which summary statistics would you choose to summarize the center and spread in these data? Why? Frequency 20 20 10 30 T 0 2.2 2.4 2.6 2.8 3.0 Price
Standard deviation II 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 by hand. Set 1 a) 4, 7, 7, 7, 10 b) 100, 140, 150, 160,
Standard deviation I 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 by hand. Set 1 a) 3, 5, 6, 7, 9 b) 10, 14, 15, 16, 20 c)
Sick days 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
Mistake 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 $200,000.Explain how this error will affect these summary statistics for the company payroll:a) measures of center: median and mean.b)
Tornadoes 2011 Here are the annual numbers of deaths from tornadoes in the United States from 1998 through 2011 (Source: NOAA):130 94 40 40 555 54 35 38 67 81 125 21 45 544 Find these statistics by hand (no calculator!):a) meanb) median and quartilesc) range and IQR
Summaries Here are costs of nine compact refrigerators rated very good or excellent by Consumer Reports on their website www.consumerreports.org.$ 150 150 160 180 150 140 120 130 120 Find these statistics by hand (no calculator!):a) meanb) median and quartilesc) range and IQR
Super Bowl wins 2010 In the Super Bowl, by how many points does the winning team outscore the losers? Here are the winning margins for the first 45 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,
Super Bowl points 2010 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 45 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,
E-mails 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 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
Heart attack stays 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
Run times 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? 50
Vineyards 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). 0 # of Vineyards 10 15 120
Singers 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? 20 20 5 # of Singers 10 60 68
Sugar in cereals 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? # of Cereals 4 CO 2 0 8 16 24 32 40 48 Sugar (%) 56
More shapes 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
Thinking about shape 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
In the news II Find an article in a newspaper, a magazine, or the Internet that discusses a measure of spread.a) Does the article discuss the W’s for the data?b) What are the units of the variable?c) Does the article use the range, IQR, or standard deviation?d) Is the choice of measure of spread
In the news Find an article in a newspaper, a magazine, or the Internet that discusses an “average.”a) Does the article discuss the W’s for the data?b) What are the units of the variable?c) Is the average used the median or the mean? How can you tell?d) Is the choice of median or mean
Not a histogram Find a graph other than a histogram that shows the distribution of a quantitative variable in a newspaper, a magazine, or the Internet.a) Does the article identify the W’s?b) Discuss whether the display is appropriate for the data.c) Discuss what the display reveals about the
Fuel economy The boxplot shows the fuel economy ratings for 67 model year 2012 subcompact cars. Some summary statistics are also provided. The extreme outlier is the Mitsubishi i-MiEV, an electric car whose electricity usage is equivalent to 112 miles per gallon.If that electric car is removed from
Test score spreads The professor in question 6 had also calculated the IQR and standard deviation of the test scores before realizing her mistake. (She had entered the top score as 46 but it was actually 56.) What effect will correcting the error have on the IQR and the standard deviation?
When she corrects this score, how will the mean and median be affected?
Test score centers After entering the test scores from her Statistics class of 25 students, the instructor calculated the mean and the median of the scores. Upon checking, she discovered that she had entered the top score as 46, but it should have been
Adoptions II Here is a histogram showing the total number of adoptions in each of the 50 states and the District of Columbia.Would you expect the mean number of adoptions or the median number of adoptions to be higher? Why? 20 20 15 Number of States 10 10 5- 0 0 1000 2000 3000 4000 5000 6000 Number
Adoptions 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? State Mean Age Median
Outliers 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? Min QI Med Q3 Max 43 98 104.5 116 160
Opposites 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
Details 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
Be a Simpson Can you design a Simpson’s paradox?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
Graduate admissions 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,
Delivery service 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
Hospitals 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
Tattoos 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.
Drivers’ licenses 2011 The table on the next page 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
The researchers were investigating whether people taking a certain class of antidepressants (SSRIs) might be at greater risk of bone fractures. Their observations are summarized in the table:Do these results suggest there’s an association between taking SSRI antidepressants and experiencing bone
Antidepressants and bone fractures For a period of five years, physicians at McGill University Health Center followed more than 5000 adults over the age of
Anorexia 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
Obesity and exercise 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
Blood pressure 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
Twin births 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
Weather forecasts Just how accurate are the weather forecasts we hear every day? The following table compares the daily forecast with a city’s actual weather for a year:a) On what percent of days did it actually rain?b) On what percent of days was rain predicted?c) What percent of the time was
Parking lots A survey of autos parked in student and staff lots at a large university classified the brands by country of origin, as seen in the table.a) What percent of all the cars surveyed were foreign?b) What percent of the American cars were owned by students?c) What percent of the students
Does it appear that the admissions decisions are made independent of the applicant’s ethnicity? Explain.
Back to school Examine the table about ethnicity and acceptance for the Houston Independent School District’s magnet schools program, shown in Exercise
More politics Look once more at the table summarizing the political views of Intro Stats students in Exercise 28.a) Produce a graphical display comparing the conditional distributions of males and females among the three categories of politics.b) Comment briefly on what you see from the display in
Magnet schools revisited The Chance magazine article described in Exercise 15 further examined the impact of an applicant’s ethnicity on the likelihood of admission to the Houston Independent School District’s magnet schools programs. Those data are summarized in the table below.a) What percent
Politics revisited Look again at the table of political views for the Intro Stats students in Exercise 28.a) Find the conditional distributions (percentages)of political views for the females.b) Find the conditional distributions (percentages) of political views for the males.c) Make a graphical
More about seniors Look again at the table of postgraduation plans for the senior class in Exercise 27.a) Find the conditional distributions (percentages) of plans for the white students.b) Find the conditional distributions (percentages) of plans for the minority students.c) Create a graph
Politics Students in an Intro Stats course were asked to describe their politics as “Liberal,” “Moderate,” or“Conservative.” Here are the results:a) What percent of the class is male?b) What percent of the class considers themselves to be “Conservative”?c) What percent of the males
Seniors Prior to graduation, a high school class was surveyed about its plans. The following table displays the results for white and minority students (the “Minority”group included African-American, Asian, Hispanic, and Native American students):a) What percent of the seniors are white?b) What
The last picture show Here’s another table showing information on 348 movies released in 2010. This table gives percentages of the overall total:a) How can you tell that this table holds overall percentages (rather than row or column percentages)?b) What was the most common genre/rating
Movies by genre and rating Here’s a table that classifies movies released in 2010 by genre and MPAA rating:a) The table gives column percents. How could you tell that from the table itself?b) What percentage of these movies were comedies?c) What percentage of the PG-rated movies were comedies?d)
Handguns In an effort to reduce the number of gunrelated homicides, some cities have run buyback programs in which the police offer cash (often $50) to anyone who turns in an operating handgun. Chance magazine looked at results from a four-year period in Milwaukee. The table below shows what types
Teen smokers The organization Monitoring the Future(www.monitoringthefuture.org) asked 2048 eighth graders who said they smoked cigarettes what brands they preferred. The table below shows brand preferences for two regions of the country. Write a few sentences describing the similarities and
Modalities A survey of athletic trainers (Source: Scott F. Nadler, Michael Prybicien, Gerard A. Malanga, and Dan Sicher, “Complications from Therapeutic Modalities:Results of a National Survey of Athletic Trainers.”Archives of Physical Medical Rehabilitation 84 [June 2003]) asked what
Global warming The Pew Research Center for the People and the Press (people-press.org) has asked a representative sample of U.S. adults about global warming, repeating the question over time. In October 2010, the responses reflected a decreased belief that global warming is real and due to human
Winter Olympics 2010 Twenty-six countries won medals in the 2010 Winter Olympics. The table lists them, along with the total number of medals each won:a) Try to make a display of these data. What problems do you encounter?b) Organize the data so that the graph is more successful. Country Medals
Oil spills as of 2010 Data from the International Tanker Owners Pollution Federation Limited give the cause of spillage for 460 oil tanker accidents resulting in spills of more than 700 tons of oil from 1970–2010 (www.itopf.com/information-services/data-and-statistics/statistics). On the next
Plane crashes An investigation compiled information about recent nonmilitary plane crashes. The causes, to the extent that they could be determined, are summarized in the table.a) Is it reasonable to conclude that the weather or mechanical failures caused only about 37% of recent plane crashes?b)
Causes of death 2007 The Centers for Disease Control and Prevention lists causes of death in the United States during 2007:a) Is it reasonable to conclude that heart or respiratory diseases were the cause of approximately 30.7% of U.S. deaths in 2007?b) What percent of deaths were from causes not
Magnet schools again The Chance article about the Houston magnet schools program described in Exercise 15 also indicated that 517 applicants were black or Hispanic, 292 Asian, and 946 white. Summarize the relative frequency distribution of ethnicity with a sentence or two (in the proper context, of
Magnet schools An article in the Winter 2003 issue of Chance magazine reported on the Houston Independent School District’s magnet schools programs.Of the 1755 qualified applicants, 931 were accepted, 298 were wait-listed, and 526 were turned away for lack of space. Find the relative frequency
Ratings again Here is a bar chart of the 2005 movie ratings seen in the pie chart in Exercise 12.a) Which was the least common rating?b) An editorial claimed that there’s been a growth in PG-13 rated films that, according to the writer, “have too much sex and violence,” at the expense of
Genres again Here is a bar chart summarizing the 2012 movie genres from the suburban multiplex theatre, as seen in the pie chart in Exercise 11.a) Were Action/Adventure or SciFi/Fantasy films more common?b) Is it easier to see that in a pie chart or the bar chart?Explain. T 70 60 50 40 288 T 98 30
Movie ratings The pie chart shows the ratings assigned to the 20 top-grossing movies for each year from 2005 to 2008.a) Is this an appropriate display for these data? Explain.b) Which was the most common rating? Film Ratings Ple Chart PG-13 PG G R

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