Chapter 2 Review Exercises

section 2.1

Question 2.331

1. Parts of Speech. The accompanying bar graph summarizes the frequencies for the various parts of speech in a sample of English words. Should we be interested in determining whether this graph is symmetric or skewed? Clearly explain why or why not.

image

2.99.1

No, because the variable is categorical.

For Exercises 2–6, refer to the bar graph from Exercise 1 to construct the following for the variable parts of speech.

Question 2.332

2. Relative frequency bar graph

Question 2.333

3. Frequency distribution

2.99.3

Part of speech Frequency Relative frequency
Adjective 1 0.0323
Adverb 2 0.0645
Article 3 0.0968
Conjunction 3 0.0968
Preposition 9 0.2903
Pronoun 7 0.2258
Verb 6 0.1935
Total 31

Question 2.334

4. Relative frequency distribution

Question 2.335

5. Frequency pie chart

2.99.5

image

Question 2.336

6. Relative frequency pie chart

Happiness in Marriage. The General Social Survey tracks trends in American society through annual surveys. Use the following contingency table for Exercises 7–11.

Happiness of marriage
Respondents'
gender		 Very
happy		 Pretty
happy		 Not too
happy		 Total
Male 242 115 9 366
Female 257 149 17 423
Total 499 264 26 789

Question 2.337

7. What proportion of the males responded that they were very happy in their marriage?

2.99.7

0.6612

104

Question 2.338

8. What proportion of the females responded that they were very happy in their marriage?

Question 2.339

9. What proportion of the males responded that they were not too happy in their marriage?

2.99.9

0.0246

Question 2.340

10. What proportion of the females responded that they were not too happy in their marriage?

Question 2.341

11. Construct a clustered bar graph of the data.

2.99.11

Answers will vary. May have clustered bar graph by happiness of marriage or clustered bar graph by sex.

section 2.2

Student-Run Café Business. Use the Minitab relative frequency distribution of potato chip sales for Exercises 12–14. The distribution shows the number of days each number of chips was sold. For example, four bags of chips were sold on three different days.

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Minitab relative frequency distribution of potato chip sales

Question 2.342

12. Construct a relative frequency distribution of 4 classes, each of class width 7. Let the leftmost class be: 0 to < 7.

Question 2.343

13. Use the relative frequency distribution to construct a histogram of potato chip sales.

2.99.13

image

Question 2.344

14. For what percentage of days were more than 20 bags of chips sold?

Student-Run Café Business. Use the data in the following table for Exercises 15–20. The data represent the total sales (in dollars) for the first 20 days of sales for the Student-Run café. You will construct a histogram of the sales data, with 8 classes, each with class width 25.

Table 2.107:

totalsales20

Total sales for the first 20 days
199.95 186.94 172.31 181.43
195.74 120.18 137.65 125.57
102.68 228.78 197.56 180.63
162.88 88.02 70.00 75.87
101.76 119.57 97.00 150.51

Question 2.345

15. Find the class limits, and draw the horizontal axis. Let the leftmost lower class limit equal 50.

2.99.15

image

Question 2.346

16. Determine the frequencies, and draw the vertical axis.

Question 2.347

17. Draw the rectangles.

2.99.17

image

Question 2.348

18. What percentage of days had sales over $200?

Question 2.349

19. What proportion of days had sales of at most $149.99?

2.99.19

0.5

Question 2.350

20. Find the percentage of days with sales between $150 and $199.99 inclusive.

section 2.3

Question 2.351

21. Fraud Cases in Brooklyn. Use the data from Table 31 on page 82 of Section 2.2 to

  1. construct a cumulative frequency distribution.
  2. construct a cumulative relative frequency distribution.

2.99.21

(a) and (b)

Frauds Frequency Relative frequency Cumulative frequency Cumulative relative frequency
8 8 0.3478
13 21 0.9130
1 22 0.9565
1 23 1.0000
Total 23 1.0000

Question 2.352

22. Fraud Cases in Brooklyn. Use the data from Table 31 on page 82 of Section 2.2 to

  1. construct a frequency ogive.
  2. construct a relative frequency ogive.

Question 2.353

tradedeficits

23. Trade Deficit. Table 47 presents the annual trade deficits (imports minus exports) for the United States from 1991 to 2013, in billions of dollars.

  1. Construct a time series plot of the data.
  2. Describe any trends that you see.
Table 2.109: TABLE 47 U.S. trade deficits
Year Trade deficit
in $ billions		 Year Trade deficit
in $ billions
1991 31 2003 494
1992 39 2004 609
1993 70 2005 714
1994 98 2006 759
1995 96 2007 702
1996 104 2008 698
1997 108 2009 374
1998 166 2010 495
1999 264 2011 548
2000 379 2012 538
2001 364 2013 476
2002 421
Table 2.109: Source: U.S. Census Bureau.

2.99.23

(a)

image

(b) The trade deficit generally increased from 1991 to 2006, then it generally decreased from 2006 until 2009, then it increased from 2009 until 2011, and then it decreased from 2011 to 2013.

section 2.4

Question 2.354

24. Carbon Dioxide Emissions. The following table contains the energy-related carbon dioxide emissions (in millions of metric tons), by end-use sector, as reported by the U.S. Energy Information Administration.

co2emissions

Sector Emissions
Residential 1213.9
Commercial 1034.1
Industrial 1736.0
Transportation 1939.2

105

  1. Construct a bar graph that overemphasizes the differences among the sectors.
  2. Which of the common methods for making misleading graphics are you using in (a)?
  3. Construct a bar graph that underemphasizes the differences among the sectors.
  4. Which of the common methods for making graphics misleading are you using in (c)?
  5. Construct a bar graph that fairly represents the data.