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intro stats
Intro Stats 4th International Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions
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 justified?
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
b) Multiplying every value of x by 2 will double the correlation.c) The units of the correlation are the same as the units of y.
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.
4. Disk drives 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 survey of prices for external disk drives found the following data:a) Prepare a scatterplot of Price against Capacity.b) What can you
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 of
2. Association II Suppose you were to collect data for each pair of variables. 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, form, and
1. Association Suppose you were to collect data for each pair of variables. 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, form, and
#!# a) Find the 5-number summary.b) Draw a boxplot for these data.c) Find the mean and standard deviation.d) Describe the distribution of profits for these corporations. 099 99 -0 1234 0 111123444 0 5555679 1 00113 1 2 2 2 5 Profits (% of sales) (-03 means a loss of 3%)
38. Profits Here is a stem-and-leaf display showing 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%.
37. Some assembly required 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 postpurchase surveys the company has learned that only 25% of its customers succeeded in building the desk in
36. Bike safety 2005 The Bicycle Helmet Safety Institute website includes a report on the number of bicycle fatalities per year in the United States. The table below shows the counts for the years 1994–2005.Year Bicycle Fatalities 1994 802 1995 833 1996 765 1997 814 1998 760 1999 754 2000 693
35. Age and party 2011 II Consider again the Pew Research Center results on age and political party in Exercise 33.a) What is the marginal distribution of party affiliation?b) Create segmented bar graphs displaying the conditional distribution of party affiliation for each age group.c) Summarize
34. Pay According to the 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 likely to
33. Age and party 2011 The Pew Research Center conducts surveys regularly asking respondents which political party they identify with or lean toward. Among their results is the following table relating preferred political party and age. (http://people-press.org/files/legacydetailed_
32. Engines, again Horsepower is another measure commonly used to describe auto engines. Here are the summary statistics and histogram displaying horsepowers of the same group of 38 cars discussed in Exercise 31.a) Describe the shape, center, and spread of this distribution.b) What is the
31. Engines One measure of the size of an automobile engine is its “displacement,” the total volume (in liters or cubic inches) of its cylinders. Summary statistics for several models of new cars are shown. These displacements were measured in cubic inches.Summary of Displacement Count 38 Mean
30. Birth order revisited Consider again the data on birth order and college majors in Exercise 28.a) What is the marginal distribution of majors?b) What is the conditional distribution of majors for the oldest children?c) What is the conditional distribution of majors for the children born
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 major? A Statistics professor at a large university polled his students to find out what their majors were and what position they held in the family birth order. The results are summarized in the table.a) What percent of these students
27. Mail Here are the number of pieces of mail received at a school office for 36 days.a) Plot these data.b) Find appropriate summary statistics.c) Write a brief description of the school’s mail deliveries.d) What percent of the days actually lie within one standard deviation of the mean?
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 steps 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 second.a) Use
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) set a new standard of 70 in 1998. Listed below are the home run totals for each season McGwire
23. Sample 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 5 years later. Only 416 of the original group participated in the 5-year follow-up study. This made researchers concerned that the
22. Winter Olympics 2010 speed skating The top 34 women’s 500-m speed skating times are listed in the table in the next column.a) The mean finishing time was 40.72 seconds, with a standard deviation of 9.82 seconds. If the Normal model is appropriate, what percent of the times should be within
21. Liberty’s nose Is the Statue of Liberty’s nose too long?Her nose measures 46, but she is a large statue, after all. Her arm is 42 feet long. That means her arm is 42>45 = 9.3 times as long as her nose. Is that a reasonable ratio? Shown in the table are arm and nose lengths of 18 girls in
20. Teen drivers 2008 In its Teen Driver Crashes Report to Congress 2008, the National Highway Traffic Safety Administration reported that 6.3% of licensed drivers were between the ages of 15 and 20, yet this age group was behind the wheel in 12.9% of all fatal crashes. Use these statistics to
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. # of Eruptions 30 30 20 10 1.6 2.6 3.6 4.6 5.6 Eruption Duration
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. 40 # of Inter-eruption Intervals 10 10 30 30 20 40.0
17. Seasons Average daily temperatures in January and July for 60 large U.S. cities are graphed in the histograms below.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 regions.a) 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. Let’s play cards You pick a card from a deck and record its denomination (7, say) and its suit (maybe spades).a) Is the variable suit categorical or quantitative?b) Name a game you might be playing for which you would consider the variable denomination to be categorical. Explain.c) Name a
12. e-Books A study by the Pew Internet & American Life Project found that 78% of U.S residents over 16 years old read a book in the past 12 months. They also found that 21% had read an e-book using a reader or computer during that period. A newspaper reporting on these findings concluded that 99%
11. Cramming One Thursday, researchers gave students enrolled in a section of basic Spanish 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 sets of test
10. Streams As part of the course work, a class at an upstate NY 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), and
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 the Shenandoah Mountains 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 of
7. State University Public relations staff at State U.phoned 850 local residents. After identifying themselves, the callers asked the survey participants their ages, whether they had attended college, and whether they had a favorable opinion of the university. The official report to the
d) For these data, the mean was 103 loaves sold per day, with a standard deviation of 9 loaves. Do these statistics suggest that Clarksburg Bakery should expect to sell between 94 and 112 loaves on about 68% of the days? Explain.
6. Bread Clarksburg 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 62 tall, and a woman over 510. The National Health Survey suggests that heights of adults may be Normally distributed, with mean heights of 69.1 for men and 64.0 for women. The respective standard
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 16 72 12 49 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 on the next page, broken down by the level of prenatal care the mother had received.a) Is the overall rate the average of the
1. Bananas Here are the prices (in cents per pound) of bananas reported from 15 markets surveyed by the U.S.Department of Agriculture.51 52 45 48 53 52 50 49 52 48 43 46 45 42 50a) Display these data with an appropriate graph.b) Report appropriate summary statistics.c) Write a few sentences about
52. Stereograms, revisited Because of the skewness of the distributions of fusion times described in Exercise 51, 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
51. 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
50. Rainmakers The table lists the amount of rainfall (in acre-feet) from the 26 clouds seeded with silver iodide discussed in Exercise 40: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
49. Assets again Here are the same data you saw in Exercise 47 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
46. Drunk driving 2008 Accidents involving drunk drivers account for about 40% of all deaths on the nation’s highways. The table in the next column tracks the number of alcohol-related fatalities for 26 years.(www.alcoholalert.com)a) Create a stem-and-leaf display or a histogram of these data.b)
c) When did the number of fruit flies alive stop changing very much from day to day?
proportion of flies die?
45. Fruit flies Researchers tracked a population of 1,203,646 fruit flies, counting how many died each day for 171 days.Here are three timeplots offering different views of these data. One shows the number of flies alive on each day, one the number who died that day, and the third the mortality
44. Baseball 2011 American League baseball teams play their games with the designated hitter rule, meaning that pitchers do not bat. The League believes that replacing the pitcher, typically a weak hitter, with another player in the batting order produces more runs and generates more interest among
43. MPG A consumer organization wants to compare gas mileage figures for several models of cars made in the United States with autos manufactured in other countries.The data for a random sample of cars classified as “midsize”are shown in the table.a) Create graphical displays for these two
42. 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 5 years and then stopped. Create appropriate graphical displays for both groups, and write a brief
41. 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
40. 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). Here are the summary statistics:a) Which of the summary statistics
39. Reading scores A class of fourth graders takes a diagnostic reading test, and the scores are reported by reading grade level. The 5-number summaries for the 14 boys and 11 girls are shown:a) Which group had the highest score?b) Which group had the greater range?c) Which group had the greater
38. 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.) Construct a boxplot for these data, and write a few sentences
37. Derby speeds 2011 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 about 86% of the winning
36. SAT scores Here are the summary statistics for Verbal SAT scores for a high school graduating class:a) Create side-by-side boxplots comparing the scores of boys and girls as best you can from the information given.b) Write a brief report on these results. Be sure to discuss the shape, center,
35. Caffeine A student study of the effects of caffeine asked volunteers to take a memory test 2 hours after drinking soda. Some drank caffeine-free cola, some drank regular cola (with caffeine), and others drank a mixture of the two (getting a half-dose of caffeine). Here are the 5-number
34. Vineyards Here are summary statistics for the sizes(in acres) of Finger Lakes vineyards:a) Would you describe this distribution as symmetric or skewed? Explain.b) Are there any outliers? Explain.c) Create a boxplot of these data.d) Write a few sentences about the sizes of the vineyards. Count
33. Graduation? A survey of major universities asked what percentage of incoming freshmen usually graduate “on time” in 4 years. Use the summary statistics given to answer the questions that follow.a) Would you describe this distribution as symmetric or skewed? Explain.b) Are there any
32. Eye and hair color A survey of 1021 school-age children was conducted by randomly selecting children from several large urban elementary schools. Two of the questions concerned eye and hair color. In the survey, the following codes were used:The Statistics students analyzing the data were asked
31. Test scores Three Statistics classes all took the same test.Histograms and boxplots of the scores for each class are shown below. Match each class with the corresponding boxplot. 2 # of Students 6 8 of Students 30 30 60 Class 1 90 60 Class 3 Scores 100 100 80 40 I g # of Students 2 4 30 30 60
30. Ozone Ozone levels (in parts per billion, ppb) were recorded at sites in New Jersey monthly between 1926 and 1971. Here are boxplots of the data for each month (over the 46 years), lined up in order(January = 1):a) In what month was the highest ozone level ever recorded?b) Which month has the
29. Fuel economy 2012 The Environmental Protection Agency provides fuel economy and pollution information on over 2000 car models. Here is a boxplot of Combined Fuel Economy (using an average of driving conditions)in miles per gallon by vehicle Type (midsize car, standard pickup truck, or SUV) for
28. Fuel economy Describe what these boxplots tell you about the relationship between the number of cylinders a car’s engine has and the car’s fuel economy (mpg). 39 30 25 20 Fuel Efficiency 15 4 HH HIH 5 6 8 Cylinders
27. Marriage age In 1975, did men and women marry at the same age? Here are boxplots of the age at first marriage for a sample of U.S. citizens then. Write a brief report discussing what these data show. 28 26 Age at First Marriage 24 22 22 20 H Women Men
26. Gas prices 2011 Here are boxplots of weekly gas prices for regular gas in the United States as reported by the U.S. Energy Information Administration for 2009, 2010, and 2011.a) Compare the distribution of prices over the three years.b) In which year were the prices least stable? Explain. 4.01
25. Women’s basketball Here are boxplots of the points scored during the first 10 games of the season for both Scyrine and Alexandra:a) Summarize the similarities and differences in their performance so far.b) The coach can take only one player to the state championship. Which one should she
24. Deaths 2009 A National Vital Statistics Report(www.cdc.govchs/) indicated that nearly 290,000 black Americans died in 2009, 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
23. 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 findings in Vital and Health Statistics. Data from a sample of 39 male patients and 35 female patients on length of stay(in days) are displayed
22. Camp sites Shown below are the histogram and summary statistics for the number of camp sites at public parks in Vermont.a) Which statistics would you use to identify the center and spread of this distribution? Why?b) How many parks would you classify as outliers? Explain.c) Create a boxplot for
21. Population growth 2010 On the next page is a “backto-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
20. Tendon transfers People with spinal cord injuries may lose function in some, but not all, of their muscles.The ability to push oneself up is particularly important for shifting position when seated and for transferring into and out of wheelchairs. Surgeons compared two operations to restore the
19. 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)
18. 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
17. 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’
16. Costs To help travelers know what to expect, research ers collected the prices of commodities in 16 cities throughout the world. Here are boxplots comparing the prices of a ride on public transportation, a news paper, and a cup of coffee in the 16 cities (prices are all in $US).a) On average,
15. Pizza prices A company that sells frozen pizza to stores in four markets in the United States (Denver, Baltimore, Dallas, and Chicago) wants to examine the prices that the stores charge for pizza slices. Here are boxplots comparing data from a sample of stores in each market:a) Do prices appear
14. Groups on the Internet Find data on the Internet (or elsewhere) for two or more groups. Make appropriate displays to compare the groups, and interpret what you find.
13. Time on the Internet Find data on the Internet (or elsewhere) that give results recorded over time. Make an appropriate display and discuss what it shows.
12. In the news again Find an article in a newspaper, magazine, or the Internet 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
11. In the news Find an article in a newspaper, magazine, or the Internet that compares two or more groups of data.a) Does the article discuss the W’s?b) Is the chosen display appropriate? Explain.c) Discuss what the display reveals about the groups.d) Does the article accurately describe and
10. 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 22
9. Exoplanets Discoveries of planets beyond our solar system have grown rapidly. Here is a histogram showing the distance from earth (in light-years) of stars having known (as of 2011) planets.Explain why it might be beneficial to re-express these distances. 30 42210 0 1000 3000 Distance (ly) 5000
8. Load factors 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
7. Load factors over time Here is a timeplot of each monthly load factor for domestic flights for 2000 to 2011 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? 83.6- 76.1- 68.6 Domestic 61.1
6. 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? 90 80 70 60 50 Domestic
5. Extraordinary months Look at the boxplots by month in Exercise 3. Two outliers are evident; one in September and one in October. Both of these are for 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
4. Load factors by year Here is a display of the domestic load factors by year.Discuss the patterns you see in this display. Domestic 82.5 75.0 67.5 60.0 2000 01 02 03 '04 '05 '06 '07 '08 '09 '10 '11 Year
3. Load factors by month Here is a display of the international load factors by month for the period from 2000 to 2011.Discuss the patterns you see in this display. International 82.5 75.0 67.5 60.0 1 2 3 4 5 6 7 8 9 10 11 12 Month
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