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.

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.

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.

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

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.

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:

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.

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

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.

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?

1.152 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.

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.

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:

1.155 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

1.156 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.

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

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:

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:

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?

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.

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):

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.

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?

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?

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.

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.

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.

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.