CHAPTER 1 EXERCISES

Question 1.145

image 1.145 Sources of energy consumed. Energy consumed in the United States can be classified as coming from one of three sources: fossil fuels, nuclear and electric power, and renewable energy. In 2014, the energy from these three sources was 80.3, 8.3, and 9.6 quadrillion Btu, respectively. In 2004, the corresponding amounts were 85.8, 8.2, and 6.1.37 Write a description of the changes from 2004 to 2014 expressed in these data. Illustrate your summary with appropriate graphical summaries. Be sure to discuss both the amounts of energy from each source as well as the percents.

Question 1.146

1.146 CO2 emissions in vehicles. Natural Resources Canada tests new vehicles each year and reports several variables related to fuel consumption for vehicles in different classes.38 For 2015, it provides data for 526 vehicles that use regular fuel. Two variables reported are carbon dioxide (CO2) emissions and highway fuel consumption. CO2 is measured in grams per kilometer (g/km), and highway fuel consumption measured in liters per 100 kilometers (L/km). Use graphical and numerical summaries to describe the distribution of CO2 emissions for these vehicles. Be sure to justify your choice of summaries.

CANFREG

Question 1.147

1.147 Highway fuel consumption. Refer to the previous exercise. Use graphical and numerical summaries to describe the distribution of highway fuel consumption for these vehicles. Be sure to justify your choice of summaries.

CANFREG

Question 1.148

1.148 Jobs for business majors. What types of jobs are available for students who graduate with a business degree? The website careerbuilder.com lists job opportunities classified in a variety of ways. A recent posting had 25,120 jobs. The following table gives types of jobs and the numbers of postings listed under the classification “business administration” on a recent day:39

BUSJOBS

Type Number
Management 10916
Sales 5981
Information technology 4605
Customer service 4116
Marketing 3821
Finance 2339
Health care 2231
Accounting 2175
Human resources 1685

Describe these data using the methods you learned in this chapter, and write a short summary about jobs that are available for those who have a business degree. Include comments on the limitations that should be kept in mind when interpreting this particular set of data.

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Question 1.149

1.149 Flopping in the 2014 World Cup. Soccer players are often accused of spending an excessive amount of time dramatically falling to the ground followed by other activities, suggesting that a possible injury is very serious. It has been suggested that these tactics are often designed to influence the call of a referee or to take extra time off the clock. Recordings of the first 32 games of the 2014 World Cup were analyzed, and there were 302 times when the referee interrupted the match because of a possible injury. The number of injuries and the total time, in minutes, spent flopping for each of the 32 teams who participated in these matches was recorded.40 Here are the data:

FLOPS

Country Injuries Time
Brazil 17 3.30
Chile 16 6.97
Honduras 15 7.67
Nigeria 15 6.42
Mexico 15 3.97
Costa Rica 13 3.80
USA 12 6.40
Ecuador 12 4.55
France 10 7.32
South Korea 10 4.52
Algeria 10 4.05
Iran 9 5.43
Russia 9 5.27
Ivory Coast 9 4.63
Croatia 9 4.32
Colombia 9 4.32
Uruguay 9 4.12
Greece 9 2.65
Cameroon 8 3.15
Germany 8 1.97
Spain 8 1.82
Belgium 7 3.38
Japan 7 2.08
Italy 7 1.60
Switzerland 7 1.35
England 7 3.13
Argentina 6 2.80
Ghana 6 1.85
Australia 6 1.83
Portugal 4 1.82
Netherlands 4 1.65
Bosnia and
Herzegovina
2 0.40

Describe these data using the methods you learned in this chapter, and write a short summary about flopping in the 2014 World Cup based on your analysis.

Question 1.150

1.150 Twitter accounts. Twitter has more than 52,900,000 million users in the United States. A study of Twitter accounts classified users by age. Here are the numbers of users (in millions) for six age groups:41

TWIT

Age Number Age Number
18–24 11.7 45–54 6.7
25–34 13.3 55–64 4.1
35–44 8.7 65 and over 2.7

Describe these data using the methods you learned in this chapter, and write a short summary about the age distribution of Twitter users based on your analysis.

Question 1.151

1.151 What graph would you use? What type of graph or graphs would you plan to make in a study of each of the following issues?

  1. (a) What makes of cars do students drive? How old are their cars?

  2. (b) How many hours per week do students study? How does the number of study hours change during a semester?

  3. (c) Which radio stations are most popular with students?

  4. (d) When many students measure the concentration of the same solution for a chemistry course laboratory assignment, do their measurements follow a Normal distribution?

Question 1.152

image 1.152 Canadian international trade. The government organization Statistics Canada provides data on many topics related to Canada’s population, resources, economy, society, and culture. Go to the web page statcan.gc.ca/start-debut-eng.html . Under the “Subject” tab, choose “International trade.” Pick some data from the resources listed and use the methods that you learned in this chapter to create graphical and numerical summaries. Write a report summarizing your findings that includes supporting evidence from your analyses.

Question 1.153

image 1.153 Travel and tourism in Canada. Refer to the previous exercise. Under the “Subject” tab, choose “Travel and tourism.” Pick some data from the resources listed and use the methods that you learned in this chapter to create graphical and numerical summaries. Write a report summarizing your findings that includes supporting evidence from your analyses.

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Question 1.154

1.154 Leisure time for college students. You want to measure the amount of “leisure time” that college students enjoy. Write a brief discussion of two issues:

  1. (a) How will you define “leisure time”?

  2. (b) Once you have defined leisure time, how will you measure it?

Question 1.155

image 1.155 How much vitamin C do you need? The U.S. Food and Nutrition Board of the Institute of Medicine, working in cooperation with scientists from Canada, have used scientific data to answer this question for a variety of vitamins and minerals.42 Their methodology assumes that needs, or requirements, follow a distribution. They have produced guidelines called dietary reference intakes for different gender-by-age combinations. For vitamin C, there are three dietary reference intakes: the estimated average requirement (EAR), which is the mean of the requirement distribution; the recommended dietary allowance (RDA), which is the intake that would be sufficient for 97% to 98% of the population; and the tolerable upper level (UL), the intake that is unlikely to pose health risks. For women aged 19 to 30 years, the EAR is 60 milligrams per day (mg/d), the RDA is 75 mg/d, and the UL is 2000 mg/d.43

  1. (a) The researchers assumed that the distribution of requirements for vitamin C is Normal. The EAR gives the mean. From the definition of the RDA, let’s assume that its value is the 97.72 percentile. Use this information to determine the standard deviation of the requirement distribution.

  2. (b) Sketch the distribution of vitamin C requirements for 19- to 30-year-old women. Mark the EAR, the RDA, and the UL on your plot.

Question 1.156

image 1.156 How much vitamin C do men need? Refer to the previous exercise. For men aged 19 to 30 years, the EAR is 75 milligrams per day (mg/d), the RDA is 90 mg/d, and the UL is 2000 mg/d. Answer the questions in the previous exercise for this population.

Question 1.157

image 1.157 How much vitamin C do women consume? To evaluate whether or not the intake of a vitamin or mineral is adequate, comparisons are made between the intake distribution and the requirement distribution. Here is some information about the distribution of vitamin C intake, in milligrams per day, for women aged 19 to 30 years:44

Percentile (mg/d)
Mean 1st 5th 19th 25th 50th 75th 90th 95th 99th
84.1 31 42 48 61 79 102 126 142 179
  1. (a) Use the 5th, the 50th, and the 95th percentiles of this distribution to estimate the mean and standard deviation of this distribution assuming that the distribution is Normal. Explain your method for doing this.

  2. (b) Sketch your Normal intake distribution on the same graph with a sketch of the requirement distribution that you produced in part (b) of Exercise 1.155.

  3. (c) Do you think that many women aged 19 to 30 years are getting the amount of vitamin C that they need? Explain your answer.

Question 1.158

image 1.158 How much vitamin C do men consume? To evaluate whether or not the intake of a vitamin or mineral is adequate, comparisons are made between the intake distribution and the requirement distribution. Here is some information about the distribution of vitamin C intake, in milligrams per day, for men aged 19 to 30 years:

Percentile (mg/d)
Mean 1st 5th 19th 25th 50th 75th 90th 95th 99th
122.2 39 55 65 85 114 150 190 217 278
  1. (a) Use the 5th, the 50th, and the 95th percentiles of this distribution to estimate the mean and standard deviation of this distribution assuming that the distribution is Normal. Explain your method for doing this.

  2. (b) Sketch your Normal intake distribution on the same graph with a sketch of the requirement distribution that you produced in Exercise 1.156.

  3. (c) Do you think that many men aged 19 to 30 years in the United States are getting the amount of vitamin C that they need? Explain your answer.

Question 1.159

1.159 Time spent studying. Do women study more than men? We asked the students in a large first-year college class how many minutes they studied on a typical weeknight. Here are the responses of random samples of 30 women and 30 men from the class:

STUDY

Women Men
170 120 180 360 240 80 120 30 90 200
120 180 120 240 170 90 45 30 120 75
150 120 180 180 150 150 120 60 240 300
200 150 180 150 180 240 60 120 60 30
120 60 120 180 180 30 230 120 95 150
90 240 180 115 120 0 200 120 120 180
  1. (a) Examine the data. Why are you not surprised that most responses are multiples of 10 minutes? We eliminated one student who claimed to study 30,000 minutes per night. Are there any other responses that you consider suspicious?

  2. (b) Make a back-to-back stemplot of these data. Report the approximate midpoints of both groups. Does it appear that women study more than men (or at least claim that they do)?

  3. (c) Make side-by-side boxplots of these data. Compare the boxplots with the stemplot you made in part (b). Which to you prefer? Give reasons for your answer.

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Question 1.160

1.160 Product preference. Product preference depends in part on the age, income, and gender of the consumer. A market researcher selects a large sample of potential car buyers. For each consumer, she records gender, age, household income, and automobile preference. Which of these variables are categorical and which are quantitative?

Question 1.161

1.161 Two distributions. If two distributions have exactly the same mean and standard deviation, must their histograms have the same shape? If they have the same five-number summary, must their histograms have the same shape? Explain.

Question 1.162

1.162 Spam filters. A university department installed a spam filter on its computer system. During a 21-day period, 6693 messages were tagged as spam. How much spam you get depends on what your online habits are. Here are the counts for some students and faculty in this department (with log-in IDs changed, of course):

ID Count ID Count ID Count ID Count
AA 1818 BB 1358 CC 442 DD 416
EE 399 FF 389 GG 304 HH 251
II 251 JJ 178 KK 158 LL 103

All other department members received fewer than 100 spam messages. How many did the others receive in total? Make a graph and comment on what you learn from these data.

SPAM

Question 1.163

image 1.163 Phish. One of the most favored songs of the band Phish is “Divided Sky.” The band plays this song at many of their concerts. Frequently, after the main theme, Trey, the guitarist, pauses before playing the resolving note.45 The data file PHISH gives the date of each concert where “Divided Sky” was played, the venue, and the length of the pause for 366 concerts. Analyze the data and write a report summarizing what you have found. Be sure to include graphical and numerical summaries. Include the rationale for decisions that you made in performing your analysis. For example, did you give any consideration to the relatively large number of zeros?

PHISH

Question 1.164

image 1.164 Visits to a help room for statistics. A help room staffed by graduate students provides assistance to students taking statistics courses. To justify the cost of providing this service, extensive records are kept. Each time a student visits the help room, the student signs a sheet with several variables. These include the date of the visit, the course number that they are taking, the time they arrived at the room, and the time that they left the room. The length of time that the each student spent in the help room is computed from the two time variables. Data for 1268 visits are given in the file HELP.46 Analyze the data and write a report summarizing what you have found. Be sure to include graphical and numerical summaries. Include the rationale for the choices of methods that you chose for your analysis. There are some missing course numbers. How did you handle these?

HELP

Question 1.165

image 1.165 Blueberries and anthocyanins. Anthocyanins are compounds that have been associated with health benefits associated with the heart, bones, and the brain. Blueberries are a good source of many different anthocyanins. Researchers at the Piedmont Research Station of North Carolina State University have assembled a database giving the concentrations of 18 different anthocyanins for 267 varieties of blueberries.47 Four of the anthocyanins measured are delphinidin-3-arabinoside, malvidin-3-arabinoside, cyanidin-3-galactoside, and delphinidin-3-glucoside, all measured in units of mg/100g of berries. In the data file, we have simplified the names of these anthocyanins to Antho1, Antho2, Antho3, and Antho4. Figure 1.35 gives graphical and numeric summaries from JMP for Antho1. Use this output to write a summary of the distribution of Antho1 using the methods and ideas that you learned in this chapter.

BERRIES

Question 1.166

image 1.166 Blueberries and anthocyanins, Antho2. Refer to the previous exercise. Generate your own output for the analysis of Antho2 and use your output to write a summary of the distribution of Antho2 using the methods and ideas that you learned in this chapter.

BERRIES

Question 1.167

image 1.167 Blueberries and anthocyanins, Antho3. Refer to Exercise 1.165. Figure 1.36 gives the JMP output for Antho3. Use this output to write a summary of the distribution of Antho3 using the methods and ideas that you learned in this chapter.

BERRIES

Question 1.168

image 1.168 Blueberries and anthocyanins, Antho4. Refer to Exercise 1.165. Generate your own output for the analysis of Antho4 and use your output to write a summary of the distribution of Antho4 using the methods and ideas that you learned in this chapter.

BERRIES

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image
Figure 1.35: Figure 1.35 JMP descriptive statistics for Antho1, Exercise 1.165.
image
Figure 1.36: Figure 1.36 JMP descriptive statistics for Antho3, Exercise 1.167.