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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
22. Car speeds again For the car speed data in Exercise 20, 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
21. More cattle Recall that the beef cattle described in Exercise 19 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
20. Car speeds John Beale of Stanford, CA, recorded the speeds of cars driving past his house, where the speed limit is 20 mph (miles per hour). The mean of 100 readings was 23.84 mph, with a standard deviation of 3.56 mph. (He actually recorded every car for a twomonth period. These are 100
19. Cattle 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.a) How many standard deviations from the mean would a steer weighing
18. MP3s 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
17. Final exams Anna, a language major, took final exams in both French and Spanish and scored 83 on both. 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
16. Placement exams 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
15. Temperatures A town’s January high temperatures average 2°C with a standard deviation of 6°, while in July the mean high temperature is 24° and the standard deviation is 5°. In which month is it more unusual to have a day with a high temperature of 13°? Explain.
14. Cold U? A high school senior in the U.S. uses the Internet to get information on December temperatures in the Canadian 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
13. SAT or ACT? Each year thousands of high-school students in the U.S. 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
12. Hams 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)
11. Payroll 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,
10. Wisconsin ACT math 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 why
9. Music library 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
8. IQs revisited Based on the Normal model N(100, 16) describing IQ scores, what percent of people’s IQs would you expect to bea) over 80?b) under 90?c) between 112 and 132?
7. Normal cattle 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 weigha) over 1250 pounds?b) under 1200
6. IQ 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
5. Guzzlers? 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,
How many points did he score?
Stats test The mean score on the Stats exam was 75 points with a standard deviation of 5 points, and Gregor’s z-score was -
First Nations 2010 by province Let’s compare sizes of First Nations bands in Ontario and Saskatchewan.a) Using the boxplots, what is the approximate size of the largest band in Ontario? Do band sizes tend to be bigger in one province than in the other? From the plot, what can you say about the
Stereograms revisited Because of the skewness of the distributions of fusion times, we might consider a re-expression. Here are the boxplots of the log of fusion times. Is it better to analyze the original fusion times or the log fusion times? Explain. Log Fusion Time 1.6 1.2 0.8 0.4 0.0 NV VV
Stereograms 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 embedded
Rainmakers The table below lists the amount of rainfall (in acre-feet) from the 26 clouds seeded with silver iodide discussed in Exercise 32: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
Assets again Here are the same data you saw in Exercise 48 after re-expressions as the square root of assets and the logarithm of assets.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
Assets Here is a histogram of the assets (in millions of dollars) of 79 companies chosen from the Forbes list of top corporations.a) What aspect of this distribution makes it difficult to summarize or discuss centre and spread?b) What would you suggest doing with these data if we want to understand
Tsunamis 2013 Look again at the magnitudes of tsunami generating earthquakes (updated in the Tsunamis_2013 data file to early 2013). Delete all data from 1950 and earlier, so that only relatively recent data, from 1951 to 2013, will be examined. Use computer software to answer the following
World Series champs again What type of plot was the graph of Joe Carter’s home runs shown in Exercise 43 in Chapter 3? Summarize what you see.
Hurricanes 2015 again Here are the number of Atlantic hurricanes classified as major for the years 1944 to 2015: 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, 1, 2, 2, 2, 3, 1, 1, 1, 3, 0, 1, 3, 2, 1, 2, 1, 1, 0, 5, 6, 1, 3, 5, 3, 4, 2, 3, 6, 7,
Drunk Driving 2014 Accidents involving drunk drivers account for about 40% of all deaths on the nation’s highways. The following table tracks the number of alcoholrelated fatalities for 33 years. a) Create and a stem-and-leaf display or a histogram of these data.b) Create a timeplot.c) Using
He shoots, he scores the hat-trick Look once more at the data on total points scored each season by Wayne Gretzky, seen in Exercise 36 Chapter 3.a) Find the 5-number summary.b) Construct a boxplot.c) Explain why the season when Gretzky scored only 48 points would not be deemed a suspect outlier in
Eye and hair colour 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 colour. In the survey, the following codes were used:The Statistics students analyzing the data were asked
Homicides 2011 Examine the displayed data on homicides from Statistics Canada. The rate shown is the average homicide rate per 100 000 population over the 11 years from 2001 to 2011. Cities were classified into three size categories. We also classified them by geographic region below.a) Use graphs
Election 2006 Open up the Election 2006 data set available online at www.pearsoncanada.ca/deveaux, a small part of which is displayed below.a) Use boxplots to compare the percentage of voter turnout among the regions (ignore the territories), and point out the differences among regions. Be sure to
Election 2011 Open the 2011 Election data set available online at www.pearsoncanada.ca/deveaux, a small part of which is shown below.a) Use boxplots to compare the percentage of voter turnout by province, and point out the more (voting) motivated provinces and the less motivated provinces.b) Do you
Crime comparisons Below are crime rates per 100 000 residents for 18 of the biggest Canadian and U.S. cities. Rates are shown for six classes of criminal activity.a) For each type of crime, graphically compare Cana- dian cities with U.S. cities. Point out crimes where rates tend to be higher in the
Election 2000 and spoiled ballots Open the Election 2000 data set available online at www.pearsoncanada.ca/ deveaux, a small part of which is shown below. District & Elected Member Abitibi-Baie-James-Nunavik [Guy St-Julien (Lib.)] Province % Rejected Ballots Quebec 2.28 Acadie Bathurst [Yvon Godin
Women researchers 2009 Examine the display of data from Eurostat showing the percentage of female researchers in each of several employment categories for 35 countries, mostly EU members, but not exclusively (e.g., Japan is included).a) Graph the data with four side-by-side boxplots (one for each
Industrial experiment 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
Cholesterol 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 five years and then stopped. Create appropriate graphical displays for both groups and write a brief
PISA Math by gender 2009 At the PISA Website, www.pisa.oecd.org, there are summary statistics for math scores of 15-year-old males and females separately. For each OECD country below, we show the mean math scores for males, the mean math scores for females, and also the difference of the two means,
Cloud seeding 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).a) Which of the summary statistics are most appropriate for describing
Reading scores A class of Grade 4 students took a diagnostic reading test and the scores were 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 greatest range?c) Which group had the greatest
Framingham 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.) Create an approximate boxplot for these data and write a few
Derby speeds 2014 (Data in Kentucky Derby 2014) 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. Note that few have won running less than 33 miles per hour, but
Reading An educator believes that new reading activities for elementary schoolchildren will improve reading comprehension scores. She randomly assigns Grade 3 students to an eight-week program in which some will use these activities and others will experience traditional teaching methods. At the
Population growth 2010 Following is a “back-to-back” stem-and-leaf display that shows two data sets at once— one 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
PISA math scores 2009 Below are some summary statistics available at www.pisa.oecd.org showing mean, standard deviation, 5th, 10th, 25th, 75th, 90th, and 95th percentiles for 2009 PISA math scores of 15-year-old students in various Organisation for Economic Co-operation and Development (OECD)
Caffeine A student study of the effects of caffeine asked volunteers to take a memory test two 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
Cereals 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
Wines The boxplots display case prices (in dollars) of varieties of wines produced by vineyards along three of the Finger Lakes in New York State.a) Which lake region produces the most expensive wine?b) Which lake region produces the cheapest wine?c) In which region are the wines generally more
Women’s basketball Here are boxplots of the points scored during the first 10 games of the season for both Alexandra and Scyrine.a) Summarize the similarities and differences in their performance so far.b) The coach can take only one player to the provincial championship. Which one should she
Deaths 2011 A National Vital Statistics Report (www.cdc.govchs/) 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
Hospital stays The U.S. National Center for Health Statistics compiles data on the length of stay by patients in short-term hospitals and publishes its finding 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
Dots to boxes again For the blood pressure measurements: 102 115 124 128 129 130 132 133 135 137 142 160, create a dotplot (by hand or by computer). Take the dotplot and superimpose upon it a boxplot, following the steps below: i. Divide the data into two halves, spot the median, and draw a bar
Dots to boxes For the blood pressure measurements: 110 113 116 118 120 122 124 126 132 134 144 164, create a dotplot (by hand or by computer). Take the dotplot and superimpose upon it a boxplot, following the steps below: i. Divide the data into two halves, spot the median, and draw a bar there.
Graduation? A survey of major universities asked what percentage of incoming freshmen usually graduate “on time” in four years. Use the summary statistics given to answer these questions.a) Would you describe this distribution as symmetric or skewed? Explain.b) Are there any outliers?
Population in Canada by age The table below gives the age distribution of the Canadian population in 2015 according to the data published by Statistics Canada.Make an appropriate display to compare the groups and interpret what you find. Age (in years) Male (in 1000) Female (in 1000) Under 5 990.9
Population in Ontario The table below gives the percentage of the Ontario population aged 65 years and older according to the Canadian Census from 1956 to 2011.Make an appropriate display and discuss what it shows. Year Percentage of Ontario population aged 65 years and older 1956 8.4 1961 8.1 1966
In the news again Find an article in a newspaper or a magazine or online that shows a timeplot.a) Does the article discuss the W’s?b) Is the timeplot appropriate for the data? Explain.c) Discuss what the timeplot reveals about the variable.d) Does the article accurately describe and interpret the
In the news Find an article in a newspaper or a magazine or online that compares two or more groups of quantitative data.a) Does the article discuss the W’s?b) Is the choice of graphics appropriate for the situation? Explain.c) Discuss what the display reveals about the groups.d) Does the
Exoplanets re-expressed 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? 25 20 15
Exoplanets Discoveries of planets beyond our solar system have grown rapidly. Here is a histogram showing the distance (in light-years) from earth to stars having known planets (as of 2014).Explain why it might be beneficial to re-express these distances. 40 30 20 10 22 0 1000 3000 Distance (ly)
Load factors 2013 over time, a second look 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
Load factors 2013 over time 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? Domestic Load Factor (%) 85
Extraordinary months again 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? 85 80 75 70 65 60 60 Domestic Load Factor (%) 55
The three outliers in September, October, and November are all from the year 2001 and reflect the terrorist attacks of 9/11. Do you think the data for these months should be set aside in any overall analysis of load factor patterns by month? Explain.
Extraordinary months Look at the boxplots by month in Exercise
Load factors 2013 by year Here is a display of the domestic load factors by year.Discuss the patterns you see in this display. Domestic Load Factor (%) 70 H 60 2000 '01 '02 '03 '04 '05 '06 '07 '08 '09 '10 '11 '12 '13 Year
Load factors 2013 by month Here is a display of the international load factors by month for the period from 2000 to 2013.Discuss the patterns you see in this display. HOH HOH HIH HOH 60 1 2 3 4 5 6 7 8 9 10 11 12 Month 85 80 75 70 65 22 18 Intemational Load Factor (%)
Load factors, 2013 by season We can also compare domestic load factors for September through March versus those for April through August:Compare and contrast what these histograms show. # of Months 15 225050 10 #5 60 65 70 75 80 85 90 Domestic Load Factor (%) Fall/Winter # of Months 50 270 15 10 60
Load factors, 2013 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 every month from January
Slalom times 2010 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)
Rock concert accidents Crowd Management Strategies (www.crowdsafe.com) 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’
Unequal bin widths II We emphasize using equal widths for the bins in a histogram. What’s the problem with using unequal bin widths?a) Draw a histogram for data containing five measurements between 10 and 11 cm, four measurements between 11 and 12 cm, three measurements between 12 and 13 cm, two
Unequal bin widths Look back at the histogram of times in Exercise 24.a) Construct by hand another histogram, for these data (estimate counts as best you can), where the bins are 28.5–29.0, 29.0–29.5, 29.5–30.0, 30.0–30.5, 30.5– 31.0, 31.0–31.5, 31.5–32.0, 32.0–32.5,
Grouped data II Look back at the points scored per season by Wayne Gretzky in Exercise 36.a) Compute his mean points per season.b) Group the data into bins: 40–60, 60–80, etc., and find the counts for each bin. Multiply each bin midpoint (50, 70, . . .) by its respective bin count. Add all of
Grouped data Suppose that the data on heights provided in Exercise 34 had been organized into only six bins, as follows:a) If you no longer had the actual data, but just this grouped data, could you still calculate the mean and standard deviation? Try the following: Pretend that each value in a bin
Test scores continued For the data provided in Exercise 23, explain how you would expect the mean, median, standard deviation, range, and IQR to change (with brief explanation), if you were to:a) Delete all the test scores between 0 and 5.b) Change all the test scores above 50 to scores of exactly
Run times continued For the times provided in Exercise 24, explain how you would expect the mean, median, standard deviation, range, and IQR to change if we were to:a) Change all times above 32.0 to 32.0.b) Add 50 new run times, all between 30.0 and 31.0.c) Add 30 new run times around 32.7 and
Family income 2011 According to Statistics Canada, Income Statistics Division, the mean after-tax family income in 2011 was $63 000, while the median was $50 700.In constant 2011 dollars, the mean and median in 1980 were $54 000 and $49 500 respectively.a) Why did you expect to find a higher mean
Election 2011 again Below are a graph and some calculations describing the distribution of voter turnout percentage for all federal ridings in the 2011 federal election in Canada.a) What does the relationship between the mean and median suggest?b) Give a brief report about percentage of voter
First Nations 2010 on reserves Open up the data file First Nations 2010 available online at http://www.pearsoncanada.ca/deveaux. For each band, you see both the band size as well as the number of individuals living on reserve. Let’s analyze the latter variable.a) Construct a histogram for band
Bi-lingual Ni-lingual 2011 Canada is officially bilingual, according equal treatment of English and French languages, but individual Canadians who are fluent in English and French are uncommon in many regions of the country. And how many Canadians speak neither English nor French? Below are data
Election 2011 Maritimes Below are results from the 2011 Canadian federal election for the Maritime provinces, showing the riding name, winning candidate, and percentage of rejected ballots:a) Make a suitable display of the percentages of rejected ballots.b) Find the mean and standard deviation.c)
First Nations 2010 Below are the first few entries from a data file you can find online at www.pearsoncanada.ca/ deveaux showing the sizes of First Nations registry groups in Ontario. Registry groups are usually the same as bands, except that occasionally a band may consist of more than one
Incarceration rates 2013 Below is a portion of the data set you can find online at http://www.pearsoncanada.ca/ deveaux showing incarceration rates (prisoners per 100 000 of the nation’s population) for 221 nations of the world, according to the World Prison Brief at the International Centre for
Math scores 2009 The Programme for International Student Assessment (PISA) reported 2009 average mathematics performance scores for 15-year-olds in 34 Organisation for Economic Co-operation and Development (OECD) nations. Korea led the group, with an average score of 546, while Mexico had the
Women’s Olympic alpine 2010 The women’s super combined alpine event consists of a downhill and a slalom. Here are the total times (adding the two race times) for the 2010 Vancouver Olympics.a) By hand, construct a boxplot directly below the histogram, using the same x-axis (assume data points
Golf courses One measure of the difficulty of a golf course is its length: the total distance (in yards) from tee to hole for all 18 holes. Here are the histogram and summary statistics for the lengths of all the golf courses in Vermont. a) By hand, construct a boxplot directly below the
Industry codes An investment analyst has been assigned to analyze the companies that make up the Fortune 800, a collection of the largest U.S. companies. He codes each company by the type of industry to which it belongs. Here is a table showing some of the industry types and the corresponding codes
Zip codes Holes-R-Us, an Internet company that sells piercing jewellery, keeps transaction records on its sales. At a recent sales meeting, one of the staff presented a histogram and summary statistics for the U.S. zip codes of the last 500 U.S. customers so that they might understand where sales
Final grades revisited After receiving many complaints about his final-grade histogram from students currently taking a Statistics course, the professor from Exercise 51 distributed the following revised histogram:a) Comment on this display.b) Describe the distribution of grades. # of Students 4321
Raptors 2011 Below are the lengths of all the Toronto Raptor loss streaks in the 2011–2012 season: 3, 2, 8, 1, 2, 3, 4, 1, 1, 1, 2, 1, 3, 2, 1, 4, 4a) Construct a stem-and-leaf plot for these data.b) Calculate the median, the 5% trimmed mean (see previous exercise), and the ordinary mean. Place
c) Explain the relative order of the three measures in each of the above data sets. Note that the ordinary mean is just a 0% trimmed mean and the median is essentially a 50% trimmed mean. A 5% or 10% trimmed mean can be a nice compromise between these two measures, more resistant than the mean,
Trimmed mean We can make the ordinary mean a more resistant measure by trimming off a certain percent of the biggest values and the smallest values. Let TrMean(x%) represent the mean of the data after placing the data in order from smallest to biggest and deleting x% at each end. So the 10% trimmed
Getting high 2011 The European School Survey Project on Alcohol and other Drugs issued in its 2011 report: Substance Use Among Students in 36 European Countries, (www.espad.org). Among other issues, the survey investigated the percentages of 15–16 year olds who had used alcohol together with
Housing price boom House prices were booming in some Canadian cities during 2015–16. Below are percentage increases in new home prices in major citiesa) Give a stem-and-leaf plot for these data after rounding (not truncating) the values to the nearest 1.0. Split your stems, writing each one
Sip size Researchers in Cornell University’s Food Sciences department study how people experience foods. One study considered how much liquid people typically take into their mouths in one “sip” (in millilitres). The researchers also recorded the height (metres) and weight (kilograms) of the
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 six-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
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