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intro stats

Stats Data And Models 3rd Canadian Edition Richard De Veaux, Paul Velleman, David Bock, Augustin Vukov, Augustine Wong - Solutions

Return of the birds 2013 Students were given the assignment to make a histogram of the data on bird counts reported in Exercise
World Series Champs again Students were asked to make a histogram of the number of home runs hit by Joe Carter from 1983 to 1998 (see Exercise 39). One student submitted the following display (he noted that Carter had hit no home runs in 1983 while playing in only 23 games):a) Comment on this
Horsepower Create a stem-and-leaf display for these horsepowers of autos reviewed by Consumer Reports one year, and describe the distribution: 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 2015 The following data give the number of hurricanes classified as major hurricanes in the Atlantic Ocean each year from 1944 through 2015, as reported by NOAA (Source: www.nhc.noaa.gov): 3, 3, 1, 2, 4, 3, 8, 5, 3, 4, 2, 6, 2, 2, 4, 2, 2, 7, 1, 2, 6, 1, 3, 1, 0, 5, 2, 1, 0, 1, 2, 3, 2,
Bird species 2013 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
World Series champs On Oct 23, 1993, Joe Carter hit the 9th inning game-winning home run (with the Jays trailing 6–5) to make the Toronto Blue Jays World Series champions for a second straight year. Here is a stemand-leaf display of the number of home runs hit by Joe Carter during the 1983–98
He shoots, he scores again In Exercise 36, you examined the total number of points scored 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 centre of this distribution? Why?b) Find the median.c) Without actually finding the
How tall? Students in a large class were asked to estimate the teacher’s height in centimetres. Here’s a histogram of their estimates:You want a good guess of the teacher’s true height (or at least a good guess of how tall the students think the teacher is). How would you summarize these
He shoots, he scores During his 20 seasons in the NHL, the “Great One”, 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 total
Alberta casinos 2013 Below are the numbers of gaming machines in each of Alberta’s 24 casinos: Height Count Height Count 60 2 69 5 61 6 70 11 62 9 71 8 63 7 72 9 64 5 73 4 65 20 74 2 66 18 75 4 67 7 76 1 68 12a) Find the 5-number summary and IQR.b) Find the mean and standard deviation.c) Display
Singers The frequency table shows the heights (in inches) of 130 members of a choir.
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 each, and four drivers at $500 a week each.a) Find the mean and median wage.b) How many employees earn more than the mean wage?c) Which measure of centre best describes
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 Set 2a) 4, 7, 7, 7, 10 4, 6, 7, 8,
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 Set 2a) 3, 5, 6, 7, 9 2, 4, 6, 8, 10b)
Sick days During contract negotiations, a company seeks to change the number of sick days employees may take, saying that the annual “average” is seven days of absence per employee. The union negotiators counter that the “average” employee misses only three days of work each year. Explain
Explain how this error will affect these summary statistics for the company payroll:a) Measures of centre: median and meanb) Measures of spread: range, IQR, and standard deviation
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
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 10 electric smoothtop ranges rated very good or excellent by Consumer Reports on their website www.consumerreports.org. $850, 900, 1400, 1200, 1050, 1000, 750, 1250, 1050, 565 Find these statistics by hand (no calculator!):a) Meanb) Median and quartilesc) Range and IQR
Emails A university professor saved every email 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 email, how many emails each student had sent.a) From the histogram, would you expect the mean or the
Election 2011 Below is a histogram of percentages of rejected ballots for each of the 308 federal electoral districts in the 2011 Canadian federal election. a) From the histogram, would you expect the mean or median to be larger? Explain. What can you say about the actual numerical value of the
Run times One of the authors collected the times (in minutes) it took him to run four 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?
Test scores Below is a histogram of 110 students’ test scores on a one-hour test in STA220 at the University of Toronto during summer 2007. The test was out of 50, not 100. a) Approximately what percentage of students got A grades? An A was 40 or higher, since the test was out of 50 (some scored
Chorus heights 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 15 15 # of Singers 10
More shapes Would you expect distributions of these variables to be uniform, unimodal, or bimodal? Symmetric or skewed? Explain.a) Ages of people at a pee-wee hockey game.b) Number of siblings of people in your class.c) Pulse rates of college- or university-age males.d) Number of times each face of
Thinking about shape Would you expect distributions of these variables to be uniform, unimodal, or bimodal? Symmetric or skewed? Explain.a) The number of speeding tickets each student in their final year of university has ever had.b) Players’ scores (number of strokes) at the RBC Canadian Open
In the news II Find an article in a newspaper, a magazine, or on the Internet that discusses a measure of spread.a) Does the article discuss the W’s for the data?b) What are the units for the variable?c) Does the article use the range, IQR, or standard deviation?d) Is the choice of measure of
In the news Find an article in a newspaper, a magazine, or on the Internet that discusses an “average.”a) Does the article discuss the W’s for the data?b) What are the units for 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 on 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
Histogram Find a histogram that shows the distribution of a variable in a newspaper, a magazine, or on 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 variable and its distribution.d) Does
Fuel economy The boxplot shows the fuel economy (miles per gallon) 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 mpg.If that electric car is
Test score spreads The professor in Exercise 12 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 centres 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? 220 15 10 10 Number of States 53 0 0 1000 2000 3000 4000 5000 6000 Number
Bicycle Deaths The total number of bicyclists killed in crashes in the U.S. from 1994 to 2013 are:Obtain the 5-number summary and the boxplot for this data set. 796 828 761 811 757 750 689 729 663 626 722 784 769 699 716 628 616 680 730 747
Temperature The day time high temperatures (in Celsius) for Toronto in June 2016 are: Obtain the 5-number summary and the boxplot for this data set. 20 30 25 26 25 25 20 14 20 23 30 21 19 21 24 26 29 31 33 34 26 26 23 27 28 33 33 22 26 27
Compute the IQR.
Divorce Rate The divorce rates (per 100,000 residents per year) in Canada from 1989 to 2008 are recorded in question
Compute the IQR.
Blue Jays The numbers of wins that the Toronto Blue Jays have since they won World Series are recorded in question
Divorce Rate The divorce rates (per 100 000 residents per year) in Canada from 1989 to 2008 areWhat is the median divorce rate (per 100 000 residents per year) in Canada from 1989 to 2008? 296.9 283.4 274.7 278.6| 272.7 272.0 264.9 |241.6|225.4|229.1 233.2 231.8 229.2 223.8 223.9 218.0 221.0 229.3
Blue Jays The numbers of season wins that the Toronto Blue Jays have since they won the World Series in 1993 areWhat is the median number of wins by the Blue Jays since they last won the World Series? 55 56 74 76 88 84 83 80 78 86 67 80 87 83 86 75 85 81 73 74 83 93
Incarcerated This histogram displays the number of incarcerated prisoners in each U.S. state as of 2012. 10 # of States 07 2 4 50,000 100,000 Number of Prisoners per State 150,000
Incomes in Canada What do you expect the distribution of individual incomes in Canada to look like? Will it be uniform, unimodal, or bimodal? Will it be symmetric or skewed? Explain why.
Stem-and-leaf Consider the following data set: 18 28 28 28 37 31 24 29 8 27 24 12 21 32 27 24 23 33 31 29a) Display the stem-and-leaf plot without splitting the “stems”.b) Redo part (a) but put the leaves 0-4 on one line and 5-9 on another.c) Which stem-and-leaf plot do you prefer? Explain.
Explaina) Explain the differences between a bar chart and a histogram.b) Explain the differences between a histogram and a stem-and-leaf plot
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. While 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 following table shows the number of applicants accepted to each of four graduate programs.a) What percent of total applicants were admitted?b)
Delivery service A company must decide which of two delivery services they will contract with. During a recent trial period they 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
Dim sum 2011 When in China, one of the authors would sometimes mention a favourite Chinese treat, called dim sum—and some types of dim sum like har gow, cheong fun, and siu mei—to people in various parts of the country. But they didn’t understand! These expressions are in the Cantonese
Indigenous identity 2011 Following are 2011 estimated counts of the Indigenous identity population for Canada, provinces, and territories.a) Aside from the placement of marginal totals at the top and left rather than bottom and right, the table is not exactly the standard contingency table. Why
Self-reported BMI Self-reported measures are often unreliable. For example, people tend to understate their weight and overstate their height, resulting in understatement of one’s body mass index or BMI (weight divided by height squared). Analyses based on understated BMIs may overstate health
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
Twins In 2000, the Journal of the American Medical Association (JAMA) published a study that examined pregnancies that resulted in the birth of twins.10 Births were classified as preterm with intervention (induced labour or caesarean), preterm without procedures, or term/post-term. Researchers also
Cell phones A researcher wanted to determine the possible association between using a cell phone and car accidents. He surveyed 180 drivers and found that 78 regularly used a cell phone while driving, of which 20 had had crashes in the past year, whereas 102 drivers did not use cell phones while
Blood proteins Blood samples were obtained from a random sample of 100 individuals, and blood type (A or B) along with presence or absence of a certain blood protein were determined for each individual. The following counts were obtained:Examine the association between the presence of the protein
The researchers were investigating whether people taking a certain class of antidepressants (SSRIs = Selective Serotonin Reuptake Inhibitors) might be at greater risk of bone fractures. Their observations are summarized in the following table. Do these results suggest there’s an association
Antidepressants and bone fractures. For a period of five years, physicians at McGill University Health Centre followed more than 5000 adults over the age of
Pet ownership The U.S. Census Bureau reports on the number of households owning various types of pets. Specifically, they keep track of dogs, cats, birds, and horses.a) Do you think the income distributions of the households who own these different animals should be roughly the same? What is your
Smoking gene? In a study of Icelandic smokers, the association of smoking and a genetic variant is shown below.a) Find the marginal distribution of genotype for these individuals.b) Find the conditional distribution of genotype for each category of smoker.c) Plot the conditional distributions and
Neighbourhood density How do people distribute themselves in our cities? From the 2001 Canadian census, we know what types of neighbourhoods people live in, for example, whether the neighbourhoods are high, medium, or low density. Low density means that 66.6% or more of the housing stock is
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
Fat and Fatter Following are estimated population counts (in thousands), using data from the National Population Health Survey, on changes from one body mass index (BMI) category to another between 1995 and 2011 for the Canadian household population aged 18 to 56 (who reported their height and
Drivers’ licenses 2014 The following table shows the number of licensed Canadian drivers by age and by sex (https://www.tc.gc.ca/media/documents/roadsafety/ cmvtcs2014_eng.pdf).a) What percent of total drivers are under 20?b) What percent of total drivers are male?c) Write a few sentences
Attraction, repulsion In a certain geographical region, 200 one-metre-square quadrants were randomly selected. In each quadrant, it was noted whether there were any specimens of grass species Agropyron and whether there were any specimens of grass species Agrostis. We are often interested in
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
Tattoos A study by the University of Texas Southwestern Medical Center examined 626 people to see if there was an increased risk of contracting hepatitis C associated with having a tattoo. If the subject had a tattoo, researchers asked whether it had been done in a commercial tattoo parlour or
Canadian languages 2011 Statistics Canada provides, on its website, the following data on the Canadian population.a) What percent of Canadian citizens speak only English?b) What percent of Canadian citizens speak French?c) What percent of Quebec residents speak French?d) What percent of
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 part a).
More politics Look once more at the table summarizing the political views of Intro Stats students in Exercise
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 display that compares the two distributions.d) Do the variables Politics and Sex appear to be independent?
Politics revisited Look again at the table of political views for the Intro Stats students in Exercise
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
Spatial distribution We divided a tract of land into four equal quadrants, in the east–west direction. We randomly selected 100 longleaf pine trees from the tract of land and counted the number of trees in each quadrant, yielding the counts below:a) Is it possible that the longleaf pine trees are
Indigenous languages 2011 Many Indigenous languages in Canada are endangered, and extinction for some may be only a generation away. In the 2011 Census, a vast majority of Canadians of Indigenous identity reported English as their mother tongue. Following are Census counts for Indigenous people who
Complications The survey of athletic trainers reported in Exercise 18 summarizes the complications most commonly associated with cryotherapy (ice). The trainers were asked to report the most common side effects. Of those identifying cryotherapy, 86 respondents reported allergic reactions, 23
Modalities A survey of athletic trainers9 asked what modalities (treatment methods, such as ice, whirlpool, ultrasound, or exercise) they commonly use to treat injuries. Respondents were each asked to list three modalities. The article included the figure shown hera) What problems do you see with
Global warming The Pew Research Center for the People and the Press (http://people-press.org) asked a representative sample of U.S. adults about global warming, repeating the question over time. In October 2010, the responses reflected an increased belief that global warming is real and due to
Winter Olympics 2014 Twenty-six countries won medals in the 2014 Winter Olympics in Sochi. The table lists them along with the total number of medals each won.a) Try to make a display of these data. What problems did you encounter?b) Can you find a way to organize the data so that the graph is more
Oil spills 2013 Data from the International Tanker Owners Pollution Federation Limited give the cause of spillage for 459 oil tanker accidents resulting in spills of more than 700 tons of oil from 1970 to 2013 (www. itopf.com/information-services/data-and-statistics/ statistics). a) Write a brief
Bad countries According to the January 2008 Canada’s World Poll (conducted by Environics, principal sponsor The Simon Foundation8 ), when asked to name countries that stand out as a negative force in the world today, approximately half (52%) of Canadians pointed to their nearest neighbour, the
Teen smokers The organization Monitoring the Future (www.monitoringthefuture.org) asked 2048 U.S. Grade 8 students 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
Forest fires 2014 by region Of those forest fires discussed in Exercise 11, 292 were in Quebec, 303 in Ontario, 1470 in Alberta, and 1465 in British Columbia. Determine the relative frequency distribution of forest fire locations within Canada, and describe it in a sentence or two.
Forest fires 2014 Every year, thousands of forest fires burn throughout Canada. According to the National Forestry Database7 , in 2014, a fewer-than-average 5152 forest fires were started, affecting 4 563 327 hectares of land. Of these, 2375 fires were caused by lightning,affecting 4 522 257
Tables in the news II Find a contingency table of categorical data from a newspaper, a magazine, or the Internet.a) Is it clearly labelled?b) Does it display percentages or counts?c) Does the accompanying article tell the W’s of the variable?d) Do you think the article correctly interprets the
Tables in the news I Find a frequency table of categorical data from a newspaper, a magazine, or the Internet.a) Is it clearly labelled?b) Does it display percentages or counts?c) Does the accompanying article tell the W’s of the variable?d) Do you think the article correctly interprets the
Graphs in the news II Find a pie chart of categorical data from a newspaper, a magazine, or the Internet.a) Is the graph clearly labelled?b) Does it violate the area principle?c) Does the accompanying article tell the W’s of the variable?d) Do you think the article correctly interprets the data?
Graphs in the news I Find a bar chart of categorical data from a newspaper, a magazine, or the Internet.a) Is the graph clearly labelled?b) Does it violate the area principle?c) Does the accompanying article tell the W’s of the variable?d) Do you think the article correctly interprets the data?
Labour force The following table shows the labour force status of individuals 15 years of age and older in Canada in June 2016. Counts are in hundreds 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
Movies again 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
Marriage in decline Changing attitudes about marriage and families prompted Pew Research to ask how people felt about 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,”
Movie genres The Motion Picture Association of America (MPAA) rates each film to designate the appropriate audience. The ratings are G, PG, PG-13, and R. The ratings of the 20 top-grossing movies in the years 1996, 2006, 2008, and 2012 are shown in the following bar charts. The pie charts show the
Nonoccupant fatalities The frequencies of traffic fatalities of nonoccupants of vehicles are shown in the following bar chart. Change this to a bar chart of relative frequencies. Frequency Nonoccupant Fatalities 5000 4432 4000 3000 2000 1000 0 637 198 Pedestrian Pedalcyclist Other Type of Fatality
Automobile fatalities The following table gives the numbers of passenger car occupants killed in accidents in 2011 by car type. Convert this table to a relative frequency table. Subcompact and Mini 1351 Compact 3789 Intermediate 4050 Full 2627 Unknown 164 Source: Bureau of Transportation
Stanley Cup 2015 Lord Stanley’s Cup is the oldest professional sports trophy in North America and has been awarded to the championship-winning hockey team every year since 1893. It was awarded to amateur champions in the early years, before the professional leagues had been formed. Below are
Kentucky Derby 2015 The Kentucky Derby is a horse race that has been run every year since 1875 at Churchill Downs, Louisville, Kentucky. The race started as a 1.5- mile race, but in 1896, it was shortened to 1.25 miles because experts felt that 3-year-old horses shouldn’t run such a long race
Walking in circles People who get lost in the desert, mountains, or woods often seem to wander in circles rather than walk in straight lines. To see whether people naturally walk in circles in the absence of visual clues, researcher Andrea Axtell tested 32 people on a football field. One at a time,
Refrigerators A Consumer Reports article evaluating refrigerators listed 41 models, giving the brand, cost, size (cu. ft.), type (such as top freezer), estimated annual energy cost, overall rating (good, excellent, etc.), and the repair history for that brand (percentage requiring repairs over the

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