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Stats Data And Models 3rd Canadian Edition Richard De Veaux, Paul Velleman, David Bock, Augustin Vukov, Augustine Wong - Solutions
23. Lunchtime Does how long children remain at the lunch table help predict how much they eat? The table gives data on 20 toddlers observed over several months at a nursery school. “Time” is the average number of minutes a child spent at the table when lunch was served. “Calories” is the
22. Antidepressants A study compared the effectiveness of several antidepressants by examining the experiments in which they had passed the FDA requirements. Each of those experiments compared the active drug to a placebo, an inert pill given to some of the subjects. In each experiment, some
21. Roller coasters 2014 Most roller coasters get their speed by dropping down a steep initial incline, so it makes sense that the height of that drop might be related to the speed of the coaster. Here’s a scatterplot of top Speed and largest Drop for 108 roller coasters around the world.a) Does
20. Matching II Here are several scatterplots. The calculated correlations are -0.977, -0.021, 0.736, and 0.951. Which is which? (a) (d)
18. Coffee sales Owners of a new coffee shop tracked sales for the first 20 days and displayed the data in a scatterplot (by day):a) Make a histogram of the daily sales since the shop has been in business.b) State one fact that is obvious from the scatterplot but not from the histogram.c) State one
17. Firing pottery A ceramics factory can fire eight large batches of pottery a day. Sometimes in the process a few of the pieces break. To better understand the problem, the factory records the number of broken pieces in each batch for three days and then creates the scatterplot shown.a) Make a
16. Kentucky Derby 2014 The fastest horse in Kentucky Derby history was Secretariat in 1973. The scatterplot shows speed (in miles per hour) of the winning horses each year. What do you see? In most sporting events, performances have improved and continue to improve, so surely we anticipate a
15. Performance IQ scores versus brain size A study examined brain size (measured as pixels counted in a digitized magnetic resonance image [MRI] of a crosssection of the brain) and IQ (four performance scales of the Weschler IQ test) for university students. The scatterplot shows the performance
14. Scatterplots II Which of the scatterplots below showa) little or no association?b) a negative association?c) a linear association?d) a moderately strong association?e) a very strong association? (1) (2) (4)
13. Scatterplots Which of the scatterplots below showa) little or no association?b) a negative association?c) a linear association?d) a moderately strong association?e) a very strong association? E (4)
12. Association IV Suppose you were to collect data for each pair of variables given below. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely
11. Association III Suppose you were to collect data for each pair of variables given below. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely
10. Dexterity scores Scores on a test of dexterity are recorded by timing a subject who is inverting pegs by picking them up with one hand, manipulating them to turn them over, and then placing them back in a frame. A typical 4-year-old needs about 2.5 seconds to invert a peg, but a 9-year-old
9. Salaries and logs For an analysis of the salaries of your company, you plot the salaries of all employees against the number of years they have worked for the company. You find that plotting the base-10 logarithm of salary makes the plot much straighter. A part-time shipping clerk, who has
8. Blizzards A study finds that during blizzards, online sales are highly associated with the number of snow plows on the road; the more plows, the more online purchases. The director of an association of online merchants suggests that the organization should encourage municipalities to send out
7. Bookstore sales again A larger firm is considering acquiring the bookstore of Exercise 3. An analyst for the firm, noting the relationship seen in Exercise 3, suggests that when they acquire the store they should hire more people because that will drive higher sales. Is his conclusion
6. Correlation facts II If we assume that the conditions for correlation are met, which of the following are true? If false, explain briefly.a) A correlation of 0.02 indicates a strong positive association.b) Standardizing the variables will make the correlation 0.c) Adding an outlier can
5. Correlation facts If we assume that the conditions for correlation are met, which of the following are true? If false, explain briefly.a) A correlation of - 0.98 indicates a strong, negative association.b) Multiplying every value of x by 2 will double the correlation.c) The units of the
4. Disk drives 2014 Disk drives have been getting larger. Their capacity is now often given in terabytes (TB) where 1 TB = 1000 gigabytes, or about a trillion bytes. A search of prices for external disk drives on Amazon.com in early 2014 found the following data:a) Prepare a scatterplot of Price
3. Bookstore sales Consider the following data from a small bookstore. a) Prepare a scatterplot of Sales against Number of Sales People Working.b) What can you say about the direction of the association?c) What can you say about the form of the relationship?d) What can you say about the strength
2. Association II Suppose you were to collect data for each pair of variables given below. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely
1. Association Suppose you were to collect data for each pair of variables given below. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction,
38. Profits The following stem-and-leaf display shows profits as a percent of sales for 29 of the Forbes 500 largest U.S. corporations. The stems are split; each stem represents a span of 5%, from a loss of 9% to a profit of 25%.a) Find the 5-number summary.b) Draw a boxplot for these data.c) Find
37. Some assembly required (Challenging) A company that markets build-it-yourself furniture sells a computer desk that is advertised with the claim “less than an hour to assemble.” However, through post-purchase surveys the company has learned that only 25% of its customers succeeded in
36. Men with brooms 2013 Canadian men will do the sweeping, as long as it is on ice. Canada excels not only in hockey, but also in the sport of curling. Below is a portion of the complete data set (available online at http://www.pearsoncanada.ca/deveaux) showing scores in games between Canada and
35. Toronto teams Below are salaries for the 2008 season for two popular Toronto sports teams.a) Using appropriate methods, compare the two distributions with graphs and numbers.b) Which team would you rather play for if you are a true superstar? A new guy starting out? An average player? (Just
34. Pay According to the U.S. Bureau of Labor Statistics, the mean hourly wage for chief executives in 2009 was $80.43 and the median hourly wage was $77.27. By contrast, for general and operations managers, the mean hourly wage was $53.15 and the median was $44.55. Are these wage distributions
33. Toronto students Below is information about region of birth of Toronto public school students (2005). Make a pie chart with two categories: Canada and Outside of Canada. Next, make both a pie chart and a bar chart showing the breakdown for those born outside of Canada. In the pie chart, do some
32. Engines, again Horsepower is another measure commonly used to describe auto engines. Below are the summary statistics and histogram displaying horsepowers of the same group of 38 cars.a) Describe the shape, centre, and spread of this distribution.b) What is the interquartile range?c) Are any of
31. Engines One measure of the size of an automobile engine is its “displacement,” the total volume (in litres or cubic inches) of its cylinders. Summary statistics for several models of new cars are shown below. These displacements were measured in cubic inches.a) How many cars were
30. Birth order revisited Consider again the data on birth order and university programs of study in Exercise 28.a) What is the marginal distribution of field?b) What is the conditional distribution of field for the oldest children?c) What is the conditional distribution of field for the children
29. Herbal medicine Researchers for the Herbal Medicine Council collected information on people’s experiences with a new herbal remedy for colds. They went to a store that sold natural health products. There they asked 100 customers whether they had taken the cold remedy and, if so, to rate its
28. Birth order Is your birth order related to your choice of program of study? A Statistics professor at a large university polled his students to find out what their specialist programs were and what position they held in the family birth order. The results are summarized in the table.a) What
27. Mail Here are the number of pieces of mail received at a school office for 36 days: 123 70 90 80 78 72 52 103 138 112 92 93 118 118 106 95 131 59 151 115 97 100 128 130 66 135 76 143 100 88 110 75 60 115 105 85a) Plot these data.b) Find appropriate summary statistics.c) Write a brief
26. Music and memory Is it a good idea to listen to music when studying for a big test? In a study conducted by some Statistics students, 62 people were randomly assigned to listen to rap music, Mozart, or no music while attempting to memorize objects pictured on a page. They were then asked to
25. Be quick! Avoiding an accident when driving can depend on reaction time. That time, measured from the moment the driver first sees the danger until he or she gets a foot on the brake pedal, is thought to follow a Normal model with a mean of 1.5 seconds and a standard deviation of 0.18
24. Sluggers Babe Ruth was the first great “slugger” in baseball. His record of 60 home runs in one season held for 34 years until Roger Maris hit 61 in 1961. Mark McGwire, with the aid of steroids, shocked the baseball world with 70 home runs in 1998. Listed below are the home run totals for
23. Simpson’s paradox A study in South Africa focusing on the impact of health insurance identified 1590 children at birth and then sought to conduct follow-up health studies five years later. Only 416 of the original group participated in the five-year follow-up study. This made researchers
22. Winter Olympics 2010 speed skating The top 34 women’s 500-m speed skating times are listed in the following table.studies five years later. Only 416 of the original group participated in the five-year follow-up study. This made researchers concerned that the follow-up group might not
21. Liberty’s nose Is the Statue of Liberty’s nose too long? Her nose measures 4’6” (4.5 feet), but she is a large statue, after all. Her arm is 42 feet long. That means her arm is 42/4.5 = 9.3 times as long as her nose. Is that a reasonable ratio? Shown in the table are arm and nose
20. Very, very rich According to the World Wealth Report 20085 , we have the following distributions of High Net Worth Individuals (HNWIs; $1 million or more in assets) and Ultra High Net Worth Individuals (Ultra-HNWIs; $30 million or more in assets):a) What is this type of display called? To make
19. Old Faithful? Does the duration of an eruption have an effect on the length of time that elapses before the next eruption?a) The histogram below shows the duration (in minutes) of those 222 eruptions. Describe this distribution.b) Which summary statistics would you choose to describe this
18. Old Faithful It is a common belief that Yellowstone’s most famous geyser erupts once an hour at very predictable intervals. The histogram below shows the time gaps (in minutes) between 222 successive eruptions. Describe this distribution. 30 30 20 20 # of Inter-Eruption Intervals 10 T T 40.0
17. Seasons The histograms below show the average daily temperatures in January and in July for 60 large U.S. cities.a) What aspect of these histograms makes it difficult to compare the distributions?b) What differences do you see between the distributions of January and July average
16. Hard water II The data set from England and Wales also notes for each town whether it was south or north of Derby. Here are some summary statistics and a comparative boxplot for the two regionsa) What is the overall mean mortality rate for the two regions?b) Do you see evidence of a difference
15. Hard water In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100 000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per million, ppm) in the
14. Accidents Progressive Insurance asked customers who had been involved in auto accidents how far they were from home when the accident happened. The data are summarized in the table.a) Create an appropriate graph of these data.b) Do these data indicate that driving near home is particularly
13. Off or on reserve 2011 Below is a table with information about age and residence status of the registered First Nations population of Canada as of December 31, 20104 :a) Compare the two conditional age distributions, using pie charts. Describe the difference.b) The total living on-reserve was
12. Band sizes 2011 Below is a chart of First Nations registry groups (similar to bands) in Canada by size, on December 31, 20103 :a) Which types of graphs are appropriate for displaying these data? Name them all.b) Present the data in an appropriate graph.c) The size of a band is actually what
11. Cramming One Thursday, researchers gave students enrolled in a section of basic French a set of 50 new vocabulary words to memorize. On Friday, the students took a vocabulary test. When they returned to class the following Monday, they were retested—without advance warning. Both test scores
10. Streams As part of the course work, a class at a northern BC college collects data on streams each year. Students record a number of biological, chemical, and physical variables, including the stream name, the substrate of the stream (limestone, shale, or mixed), the pH, the temperature (°C),
9. Fraud detection A credit card bank is investigating the incidence of fraudulent card use. The bank suspects that the type of product bought may provide clues to the fraud. To examine this situation, the bank looks at the Standard Industrial Code (SIC) of the business related to the transaction.
8. Acid rain Based on long-term investigation, researchers have suggested that the acidity (pH) of rainfall in Shenandoah Mountains storms can be described by the Normal model N(4.9, 0.6).a) Draw and carefully label the model.b) What percent of storms produce rainfall with pH over 6?c) What percent
7. University survey Public relations staff at a Canadian university phoned 850 local residents. After identifying themselves, the callers asked the survey participants their ages, whether they had attended college or university, and whether they had a favourable opinion of the university. The
6. Bread Tobermory Bakery is trying to predict how many loaves to bake. In the past 100 days, they have sold between 95 and 140 loaves per day. Here is a histogram of the number of loaves they sold for the past 100 days.a) Describe the distribution.b) Which should be larger, the mean number of
5. Beanstalks Beanstalk Clubs are social clubs for very tall people. To join, a man must be over 6’2” tall, and a woman over 5’10”. Heights of adults are approximately Normally distributed, with mean heights of 69.1” for men and 64.0” for women. The respective standard deviations are
4. Dialysis In a study of dialysis, researchers found that “of the three patients who were currently on dialysis, 67% had developed blindness and 33% had their toes amputated.” What kind of display might be appropriate for these data? Explain.
3. Singers The boxplots shown display the heights (in inches) of 130 members of a choir.a) It appears that the median height for sopranos is missing, but actually the median and the upper quartile are equal. How could that happen?b) Write a few sentences describing what you see. 76 72 2 18 64
2. Prenatal care Results of a 1996 American Medical Association report about the infant mortality rate for twins carried for the full term of a normal pregnancy are shown below, broken down by the level of prenatal care the mother had received. Full-Term Pregnancies, Level of Prenatal Care Infant
1. Homicide across Canada 2011 Below are annual homicide rates (per 100 000 population) in Canadian cities bigger than 100 000 in population, averaged over the period 2001–11.a) Display the data with an appropriate graph, and describe the distribution as best you can. Include any appropriate
62. And more simulations Use your statistical software to draw a random sample of 100 observations from a uniform distribution extending from 0 to 1 (look for menu items like Random and Uniform and plug in 0 and 1 for the parameters). Plot the data in a histogram and in a Normal probability
61. Some more simulations Use your statistical software to draw a random sample of 100 observations from a standard Normal distribution (look for menu items like Random and Normal and plug in 0 and 1 for the parameters). Plot the data in a histogram and in a Normal probability plot.a) Is the NPP
60. More simulations Use your statistical software to draw a random sample of 30 observations from a uniform distribution extending from 0 to 1 (look for menu items like Random and Uniform and plug in 0 and 1 for the parameters). Plot the data in a histogram and in a Normal probability plot.a)
59. Simulations Use your statistical software to draw a random sample of 30 observations from a standard Normal distribution (look for menu items like Random and Normal and plug in 0 and 1 for the parameters). Plot the data in a histogram and in a Normal probability plot.a) Compare the two plots.
58. First Nations bands 2010 again Plot the data on sizes of the 138 First Nations registry groups in Ontario from Exercise 59 in Chapter 3 in a histogram, boxplot, and NPP. Does the distribution appear roughly Normal? If not, how does it appear to depart from Normality, and how do you see possible
57. Tsunamis 2013 again We discussed tsumani-causing earthquakes in the previous chapter. Plot the magnitudes of these earthquakes (updated to early 2013 in our data file) in a histogram, boxplot, and NPP. Does the distribution appear roughly Normal? If not, how does it appear to depart from
56. Ages of Oscar Winners The histogram below shows the distribution of ages of actors and actresses at the time that they won Oscars for the categories of Best Actor and Best Actress. The vertical lines show the mean and one standard deviation above and below the mean. 66.46% of the data points
55. Flight Departure Delays The flights delay time (in minutes) data from Vancouver to Toronto are collected with a mean of 11.22 minutes and a standard deviation of 31.25 minutes. The Normal probability plot shows the following: a) Do you think the distribution of delay times is Normal?
54. Tomatoes Agricultural scientists are working on developing an improved variety of Roma tomatoes. Marketing research indicates that customers are likely to bypass Romas that weigh less than 70 grams. The current variety of Roma plants produces fruit that average 74 grams, but 11% of the
53. Eggs Hens usually begin laying eggs when they are about six months old. Young hens tend to lay smaller eggs, often weighing less than the desired minimum weight of 54 grams.a) The average weight of the eggs produced by the young hens is 50.9 grams, and only 28% of their eggs exceed the desired
52. Blackjack If you play the card game of Blackjack using the well-known basic strategy, you can expect to lose an average 3 cents for every 10-dollar bet, in the long run (learn to count cards and you can do even better). Suppose that thousands of people played Blackjack using the basic
51. TOEFL scores again TOEFL test scores are commonly used to assess English language ability. The paper-based test scores are close to Normally distributed, though the top scores are slightly more tightly compressed than the bottom scores, perhaps due to bumping up against a maximum score of 677.
50. Newborns At-term newborns in Canada vary in weight according to, approximately, a Normal distribution, with a mean of 3500 grams and standard deviation of 500 grams.a) Heavy birth weight (HBW) babies are those weighing over 4500 grams. Approximately how many at-term newborns among the next 10
49. Helmet sizes Adult women’s head circumferences are approximately Normally distributed with a mean of 56.0 cm and standard deviation of 1.8 cm. You are manufacturing a new type of helmet for female recruits in the Canadian Armed Forces, and are planning on producing three sizes: small,
48. Big mouth! A Cornell University researcher measured the mouth volumes of 31 men and 30 women. She found a mean of 66 cc for men (SD = 17 cc) and a mean of 54 cc for women (SD = 14.5 cc). The man with the largest mouth had a mouth volume of 111.2 cc. The woman with the largest mouth had a mouth
47. Undercover? We learned in this chapter that the average Dutch man is 184 cm tall. The standard deviation of Caucasian adult male heights is about 7 cm. The average Greek 18-year-old in Athens is 167.8 cm tall. How easily could the average Dutch man hide in Athens? (Let’s assume he dyes his
46. Body temperatures Most people think that the “Normal” adult body temperature is 37.0°C. That figure, based on a nineteenth-century study, has recently been challenged. In a 1992 article in the Journal of the American Medical Association, researchers reported that a more accurate figure
45. Kindergarten Companies who design furniture for elementary school classrooms produce a variety of sizes for kids of different ages. Suppose the heights of kindergarten children can be described by a Normal model with a mean of 97.0 cm and standard deviation of 4.9 cm.a) What fraction of
44. Tires A tire manufacturer believes that the treadlife of its snow tires can be described by a Normal model with a mean of 52 000 km and standard deviation of 2500 km.a) If you buy a set of these tires, would it be reasonable for you to hope they’ll last 60 000 km? Explain.b) Approximately
43. Cholesterol Assume the cholesterol levels of adult women can be described by a Normal model with a mean of 188 mg/dL and a standard deviation of 24.a) Draw and label the Normal model.b) What percent of adult women do you expect to have cholesterol levels over 200 mg/dL?c) What percent of adult
42. TOEFL scores, Internet test The mean and standard deviation for all 2007 writers of the Internet-based TOEFL were 78 and 24, respectively.8 The test results are a bit left or negatively skewed.a) The maximum score possible is 120. How does this suggest that a Normal model might not be a very
41. Human Gestation, finis The length of pregnancy is assumed to be normally distributed with a mean of 266 days and a standard deviation of 16 days.a) What length of pregnancies represent the 40th percentile?b) What length of pregnancies represent the 99th percentile?c) What’s the IQR of the
40. More Human Gestation The length of pregnancy is assumed to be normally distributed with a mean of 266 days and a standard deviation of 16 days. What are the cutoff values fora) the longest 10% of the length of pregnancies?b) the shortest 20% of the length of pregnancies?c) the middle 40% of the
39. Human Gestation The length of pregnancy is assumed to be normally distributed with a mean of 266 days and a standard deviation of 16 days. What percentage of pregnancies lasta) over 285 days?b) under 275 days?c) between 237 and 256 days?
38. Yet another Normal model In a standard Normal model, what value(s) of z cut(s) off the region described? Remember to draw a picture first.a) the lowest 12%b) the highest 30%c) the highest 7%d) the middle 50%
37. More Normal models In a standard Normal model, what value(s) of z cut(s) off the region described? Don’t forget to draw a picture.a) the highest 20%b) the highest 75%c) the lowest 3%d) the middle 90%
36. Normal models, again What percent of a standard Normal model is found in each region? Draw a picture first.a) z 7 -2.05b) z 6 -0.33c) 1.2 6 z 6 1.8d) z 6 1.28
35. Normal models What percent of a standard Normal model is found in each region? Be sure to draw a picture first.a) z 7 1.5b) z 6 2.25c) -1 6 z 6 1.15d) z 6 0.5
34. Receivers 2013 NFL data from the 2013 football season reported the number of yards gained by each of the league’s 181 wide receivers:The mean is 426.98 yards, with a standard deviation of 408.34 yards.a) According to the Normal model, what percent of receivers would you expect to gain more
33. TV watching A survey of 200 university students showed the following distribution of the number of hours of television watched per week.The mean is 3.66 hours, with a standard deviation of 4.93 hours.a) According to the Normal model, what percent of students will watch fewer than one standard
32. Check the model Recall that the mean of the 100 car speeds in Exercises 20 and 30 was 23.84 mph, with a standard deviation of 3.56 mph.a) Using a Normal model, what values should border the middle 95% of all car speeds?b) Here are some summary statistics. From your answer in part a), how well
31. Winter Olympics 2010 downhill Fifty-nine men completed the men’s alpine downhill race in Vancouver. The gold medal winner finished in 114.3 seconds. Here are the times (in seconds) for all competitors (Source: Data from 2010 Winter Olympics Results - Alpine Skiing from
30. Car speeds, the picture Here is the histogram, boxplot, and Normal probability plot of the 100 readings for the car speed data from Exercise 20. Do you think it is appropriate to apply a Normal model here? Explain. 20+ 15- 10 5 # of cars 15.0 22.5 30.0 Speed (mph) 32 28 24 20 Speed (mph) -1.25
29. Trees, part II Later on, the forester in Exercise 27 shows you a histogram of the tree diameters he used in analyzing the wooded area that was for sale. Do you think he was justified in using a Normal model? Explain, citing some specific concerns. # of Trees 3 2 1 8. 0.0 11.5 23.0 Diameter (cm)
28. Rivets A company that manufactures rivets believes the shear strength (in kg) is modelled by N(400, 25).a) Draw and label the Normal model.b) Would it be safe to use these rivets in a situation requiring a shear strength of 375 kg? Explain.c) About what percent of these rivets would you expect
27. Trees A forester measured 27 of the trees in a large wooded area that is up for sale. He found a mean diameter of 26 cm and a standard deviation of 12 cm. Suppose these trees provide an accurate description of the whole forest and that a Normal model applies.a) Draw the Normal model for tree
26. Rock concerts A popular band on tour played a series of concerts in large venues. They always drew a large crowd, averaging 21 359 fans. While the band did not announce (and probably never calculated) the standard deviation, which of these values do you think is most likely to be correct: 20,
25. Professors A friend tells you about a recent study dealing with the number of years of teaching experience among current college professors. He remembers the mean but can’t recall whether the standard deviation was 6 months, 6 years, or 16 years. Tell him which one it must have been, and why.
24. Caught speeding Suppose police set up radar surveillance on the Stanford street described in Exercise 20. They handed out a large number of tickets to drivers going a mean of 28 mph, with a standard deviation of 2.4 mph, a maximum of 33 mph, and an IQR of 3.2 mph. Local law prescribes fines of
23. Cattle, part III Suppose the auctioneer in Exercise 21 sold a herd of cattle whose minimum weight was 980 pounds, median was 1140 pounds, standard deviation was 84 pounds, and IQR was 102 pounds. They sold for 40 cents a pound, and the auctioneer took a $20 commission on each animal. Then, for
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