Type:
Solution Manual
Resource:
Business Statistics A First Course
Edition:
5th Edition
Author(s):
David M. Levine Timothy C. Krehbiel Mark L. Berenson
Solutions to End-of-Section and Chapter Review Problems 79
CHAPTER 1 1.1
The types of beverages sold yield categorical or “qualitative” responses because they have values that can only be placed into categories.
1.2
Three sizes of French fries are classified into distinct categories—small, medium, and large—in which order is implied.
1.3
(a) (b)
1.4
(a) (b) (c) (d)
The time it takes to download a video clip from the Internet yields numerical or “quantitative” responses. The download time is a ratio scaled variable because the true zero point in the measurement is zero units of time. numerical, discrete, ratio scale numerical, continuous, ratio scale categorical, nominal scale categorical, nominal scale
1.5
(a) numerical, continuous, ratio scale * (b) numerical, discrete, ratio scale (c) categorical, nominal scale (d) categorical, nominal scale *Some researchers consider money as a discrete numerical variable because it can be “counted.” 1.6
(a) (b) (c) (d)
categorical, nominal scale numerical, continuous, ratio scale numerical, discrete, ratio scale numerical, discrete, ratio scale
1.7
(a) numerical, continuous, ratio scale * (b) categorical, nominal scale (c) categorical, nominal scale (d) numerical, discrete, ratio scale *Some researchers consider money as a discrete numerical variable because it can be “counted.” 1.8
(a) numerical, continuous, ratio scale * (b) numerical, discrete, ratio scale (c) numerical, continuous, ratio scale * (d) categorical, nominal *Some researchers consider money as a discrete numerical variable because it can be “counted.” 1.9
(a) (b)
The population is “all working women from the metropolitan area. A systematic or random sample could be taken of women from the metropolitan area. The director might wish to collect both numerical and categorical data. Three categorical questions might be occupation, marital status, type of clothing. Numerical questions might be age, average monthly hours shopping for clothing, income.
80
Chapter 1: Introduction and Data Collection
1.10
A population contains all the items of interest whereas a sample contains only a portion of the items in the population.
1.11
A statistic is a summary measure describing a sample whereas a parameter is a summary measure describing an entire population.
1.12
Descriptive statistical methods deal with the collection, presentation, summarization, and analysis of data whereas inferential statistical methods deal with decisions arising from the projection of sample information to the characteristics of a population.
1.13
Categorical random variables yield categorical responses, such as yes or no answers. Numerical random variables yield numerical responses such as your height in inches.
1.14
Discrete random variables produce numerical responses that arise from a counting process. Continuous random variables produce numerical responses that arise from a measuring process.
1.15
An operational definition is a universally accepted meaning that is clear to all associated with an analysis. Without an operational definition, confusion can occur.
Answers for 1.16 through 1.19 provided below are just some of the many different possible answers. 1.16
Microsoft Excel could be used to perform various statistical computations that were possible only with a slide-rule or hand-held calculator in the old days.
1.17
The answers to this question vary day-to-day according to the top analyses of a particular day.
1.18
The answers to this question depend on which data set is being selected.
1.19
(a) (b) (c)
1.20
(a) (b) (c)
(d)
1.21
1.22
(a)
The answer to the question: “What is the sex of Owner 1?” is a categorical variable. The answer to the question: “What was Owner 1’s age as of December 31, 2002?” is a numerical variable. Age measured in number of years is a discrete variable. The population of interest was all the people living in the United States, and age 18 and older when the interviews were performed. The sample consisted of the 1,102 people that were interviewed. A parameter of interest can be the proportion of people living in the United States, age 18 and older during March 6-9, 2008 who have made major changes in their shopping and living habits over the last five years to help protect the environment. The statistic used to describe the parameter in (c) was the 28% of respondents who had made major changes in their shopping and living habits over the last five years to help protect the environment.
(b) (c)
The population of interest was the collection of all business students at Northern Kentucky University when the study was conducted. The sample consisted of the 96 students that were involved in the study. class: categorical; age: numerical; gender: categorical; major: categorical
(a) (b)
Population: U.S. cat owners (1) categorical (3) numerical, discrete
Solutions to End-of-Section and Chapter Review Problems 81
(2) 1.23
(a) (b) (c)
1.24
(a) (b) (c)
categorical
(4) categorical
Categorical variables: gender, class, major, grad school, employment status, satisfaction advisement. Numerical variables: age, height, GPA, expected salary, annual salary in 5 years, number of affiliations spending. Discrete numerical variables: age (in years), height( in inches), expected salary (in thousands of dollars), annual salary in 5 years (in thousands of dollars), number of affiliations, satisfaction advisement. Categorical variables: gender, major, undergrad specialization, employment status, satisfaction advisement. Numerical variables: age, height, graduate GPA, undergrad GPA, GMAT, number of jobs, expected salary, anticipated salary in 5 years, spending. Discrete numerical variables: age (in years), height (in inches), GMAT, number of jobs, expected salary (in thousands of dollars), anticipated salary in 5 years (in thousands of dollars), spending (in dollars).
82
Chapter 2: Presenting Data in Tables and Charts
CHAPTER 2 2.1 (a) Category
Frequency 11 30 9
A B C
Percentage 22% 60 18
(b)
Bar Graph
A
B
C
0
10
20
30
40
Percentage (%)
(c)
Pie Graph A 22%
C 18%
B 60%
50
60
70
Solutions to End-of-Section and Chapter Review Problems 2.1 cont.
(d)
70
100 90 80 70 60 50 40 30 20 10 0
Percentage (%)
60 50 40 30 20 10 0 B
2.2
A
(a)
(b) A 12%
Pie Chart
D 26%
B 29%
C 33%
C
Cumulative %
Pareto Chart
83
84
Chapter 2: Presenting Data in Tables and Charts
2.2 cont.
(c)
35
100 90 80 70 60 50 40 30 20 10 0
Percentage
30 25 20 15 10 5 0 C
D
A
(a) Bar Chart
Within limits
Use of the Internet at Work
2.3
B
Cumulative %
Pareto Diagram
Very little
Too much
More than I should
Do not use
0
10
20
30
40
50
60
70
Solutions to End-of-Section and Chapter Review Problems
(a)
Pie Chart
Do not use 26%
More than I should 4%
Within limits 60%
Too much 5% Very little 5%
Pareto Diagram 70%
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%
60% 50% 40% 30% 20% 10% More than I should
Very little
Too much
Do not use
0% Within limits
2.3 cont.
85
Use of the Internet at Work
(b)
(c)
The Pareto diagram is the best to portray these data because it not only sorts the frequencies in descending order, it also provides the cumulative polygon on the same scale. From the Pareto diagram, it is obvious that “within limits” and “do not use” have made up more than 80% of the use of Internet at work. * * Note: This is one of the many possible solutions for the question. We can conclude that at least 80% of the workers use the Internet “within limits” or “do not use” the Internet at work.
2.4
Chapter 2: Presenting Data in Tables and Charts (a)
Bar Chart Salespeople Retail websites
Shopping Advisers
86
Other Online user reviews News media Manufacturer websites Friends/family Advertising 0
100
200
300
400
500
Pie Chart
Salespeople Retail websites 1% Advertising 4% 7% Other 14%
Online user reviews 13% Friends/family 45%
News media 11% Manufacturer websites 5%
600
Solutions to End-of-Section and Chapter Review Problems 2.4 cont.
87
(a)
Pareto Diagram 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0%
Salespeople
Retail websites
Manufacturer websites
Advertising
News media
Online user reviews
Other
Friends/family
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%
Shopping Advisers
(b) . (c)
(a)
Bar Chart Work/Family Balance
Other
Perks
2.5
The Pareto diagram is better than the pie chart to portray these data because it not only sorts the frequencies in descending order, it also provides the cumulative polygon on the same scale. From the Pareto diagram, it is obvious that “Friends/Family” is the women’s most trusted source of shopping advisers at 45%.
More Money
Better Retirement
Better Healthcare
0
10
20
30
40
50
88
Chapter 2: Presenting Data in Tables and Charts
2.5 cont.
(a)
Work/Family Balance 10%
Pie Chart Better Healthcare 20%
Other 16%
Better Retirement 12%
More Money 42%
Pareto Diagram 45%
100%
40%
90%
35%
80%
70%
30%
60%
25%
50%
20%
40%
15%
30%
10%
20%
5%
10%
0%
0% More Money
Better Healthcare
Other
Better Work/Family Retirement Balance
Perks (b)
(c)
The Pareto diagram is better than the pie chart or the bar chart because it not only sorts the frequencies in descending order, it also provides the cumulative polygon on the same scale. From the Pareto diagram, it is obvious that more than 40% of the workers want “more money”. So “more money” is the perk workers want most.
Solutions to End-of-Section and Chapter Review Problems (a)
Pareto Diagram 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%
50% 45% 40% 35% 30% 25% 20% 15% 10% 5% Wind
Other
Hydropower
Natural gas
Nuclear
0% Coal
2.6
89
Source
(b) (c)
Approximately 85% of power is derived from coal, nuclear energy or natural gas.
Other 1%
Pie Chart Wind 1%
Nuclear 19%
Coal 47%
Natural gas 19%
Hydropower 13%
(d)
The Pareto diagram is better than the pie chart because it not only sorts the frequencies in descending order, it also provides the cumulative polygon on the same scale. From the Pareto diagram, it is obvious that almost 90% of the electricity is derived from coal, nuclear energy or natural gas. * * Note: This is one of the many possible solutions for the question.
2.7
Chapter 2: Presenting Data in Tables and Charts (a)
Bar Chart Amount of Internet Search Results Scanned
90
More than first three pages
First two pages
First three pages
First page of search results
A few search results
0
200
400
600
800
1000
% More than first Pie Chart three pages 10%
A few search results 23%
First two pages 19%
First three pages 9% First page of search results 39%
(b)
(c)
The bar chart is more suitable if the purpose is to compare the categories. The pie chart is more suitable if the main objective is to investigate the portion of the whole that is in a particular category. * * Note: This is one of the many possible solutions for the question. You can conclude that most of the people (39%) scan Internet search results according to the “first page of search results”, followed by “a few search results” (23%) and “first two pages” (19%).
Solutions to End-of-Section and Chapter Review Problems 2.8
91
(a) Bar Chart TV Radio Outdoor
Media
Other Newspapers Magazines Internet Direct mail Cinema 0
10
20
30
40
50
60
Amount ($ billions)
Pie Chart
TV 21.60%
Cinema 0.16%
Direct mail 17.35%
Internet 3.90% Radio 8.03%
Magazines 9.32%
Outdoor 2.22% Other 17.86%
(b)
2.9
Newspapers 19.57%
The bar chart is more suitable if the purpose is to compare the categories. The pie chart is more suitable if the main objective is to investigate the portion of the whole that is in a particular category. * * Note: This is one of the many possible solutions for the question.
Ordered Array: 63, 69, 75, 78, 83, 89, 93
92
Chapter 2: Presenting Data in Tables and Charts
2.10
Stem-and-leaf of Finance Scores 5 46 6 7 7 5 8 0 9 18 n=7
2.11
Ordered array: 72 78 78 78 86 88 91
2.12 2.13
Ordered array: 50 74 74 78 81 83 95 (a) Ordered array: 9.1 9.5 9.8 10.0 10.2 10.2 10.5 10.9 11.1 11.2 11.5 11.5 11.6 11.6 11.7 11.7 12.2 12.2 12.3 12.4 12.8 11.6 12.9 13.0 13.3 (b) The stem-and-leaf display conveys more information than the ordered array. We can more readily determine the arrangement of the data from the stem-and-leaf display than we can from the ordered array. We can also obtain a sense of the distribution of the data from the stem-and-leaf display. (c) The most likely gasoline purchase is between 11 and 11.9 gallons.
2.14
(d)
Yes, the third row is the most frequently occurring stem in the display and it is located in the center of the distribution.
(a)
Ordered array: Cost($)137, 140, 142, 146, 148, 151, 157, 160, 164, 165, 166, 166, 167, 184, 190, 191, 192, 196, 200, 202, 207, 215, 215, 217, 229, 230, 251, 252, 260, 321 PHStat output:
(b)
Stem-and-Leaf Display Stem unit:
10 13 7 14 0 2 6 8 15 1 7 16 0 4 5 6 6 7 17 18 4 19 0 1 2 6 20 0 2 7 21 5 5 7 22 9 23 0 24 25 1 2 26 0 27 28 29 30 31 32 1
Solutions to End-of-Section and Chapter Review Problems 2.14
(c)
cont.
(d) 2.15
(a) (b)
93
The stem-and-leaf display provides more information because it not only
orders observations from the smallest to the largest into stems and leaves, it also conveys information on how the values distribute and cluster over the range of the observations in the data set. The costs of attending a baseball game is concentrating around $160 for six of the teams have costs in the $160s. Ordered array: 31, 33.75, 35.05, 36.15, 40.25, 43 Stem-and-Leaf Display for Price Stem unit: 1 31 32 33 34 35 36 37 38 39 40 41 42 43
0 8 1 2
3
0
(c)
The stem-and-leaf display conveys more information than the ordered array. We can more readily determine the arrangement of the data from the stem-and-leaf display than we can from the ordered array. We can also obtain a sense of the distribution of the data from the stem-and-leaf display. (d) The price is not concentrated around any particular value. * Note that Excel rounds leaves up to the first decimal place. 2.16
(a) (b)
Ordered array: 4, 5, 7, 8, 16, 19, 19, 20, 20, 23, 24, 25, 29, 29, 30, 30, 30, 30, 40, 56 Stem-and-Leaf Display for Fat Stem unit: 10 0 1 2 3 4 5
(c)
(d)
4578 699 0034599 0000 0 6
The stem-and-leaf display conveys more information than the ordered array. We can more readily determine the arrangement of the data from the stem-and-leaf display. We can also obtain a sense of the distribution of the data from the stem-and-leaf display. The total fat amounts are concentrated around 20 to 29.
94 2.17
Chapter 2: Presenting Data in Tables and Charts (a) (b)
Ordered array: 35, 85, 110, 120, 170, 180, 240, 260, 300, 380, 380, 460 Stem-and-Leaf Display for Life Stem unit: 100 0 1 2 3 4
(c)
(d)
49 1278 46 088 6
The stem-and-leaf display conveys more information than the ordered array. We can more readily determine the arrangement of the data from the stem-and-leaf display than we can from the ordered array. We can also obtain a sense of the distribution of the data from the stem-and-leaf display. The battery life clusters around the high 100s and high 300s.
* Note that Excel rounds leaves up to the tens. 2.18
(a)
The class boundaries of the 9 classes can be "10 to less than 20", "20 to less than 30", "30 to less than 40", "40 to less than 50", "50 to less than 60", "60 to less than 70", "70 to less than 80", "80 to less than 90", and "90 to less than 100".
(b)
The class-interval width is
(c)
The nine class midpoints are: 15, 25, 35, 45, 55, 65, 75, 85, and 95.
2.19
(a)
4%
2.20
(a)
Electricity Costs $80 up to $99 $100 up to $119 $120 up to $139 $140 up to $159 $160 up to $179 $180 up to $199 $200 up to $219
(b) 36%
98.6 − 11.2 = 9.71 10 . 9
(c) 40%
(d) 100%
Frequency 4 7 9 13 9 5 3
Percentage 8% 14 18 26 18 10 6
Solutions to End-of-Section and Chapter Review Problems (b) Histogram 14 12
Frequency
2.20 cont.
10 8 6 4 2 0 90
110
130
150
170
190
210
Midpoints
Monthly Electricity Costs Percentage Polygon 30% 25% 20% 15% 10% 5% 0% 70
90
110
130
150
170
190
210
Monthly Electricity Costs
230
95
96 2.20 cont.
Chapter 2: Presenting Data in Tables and Charts (c) Electricity Costs
Frequency
$99 $119 $139 $159 $179 $199 $219
4 7 9 13 9 5 3
Percentage 8% 14% 18% 26% 18% 10% 6%
Cumulative % 8% 22% 40% 66% 84% 94% 100%
Cumulative Percentage Polygon 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 79
(d)
99
119
139
159
179
199
219
239
Monthly electricity costs are most concentrated between $140 and $160 a month, with better than one-fourth of the costs falling in that interval.
2.21
The costs of attending a baseball game is concentrating around $160 for six of the teams have costs centered around $160.
2.22
The property taxes per capita appear to be right-skewed with approximately 90% fall between $399 and $1,700, and the remaining 10% fall between $1,700 and $2,100. The center is at about $1,000.
Solutions to End-of-Section and Chapter Review Problems 2.23
97
(a) Error Frequency Cumulative % Percentage -0.00350 -- -0.00201 13 13% 13% -0.00200 -- -0.00051 26 39% 26% -0.00050 -- 0.00099 32 71% 32% 0.00100 -- 0.00249 20 91% 20% 0.00250 -- 0.00399 8 99% 8% 0.00400 -- 0.00549 1 100% 1%
%
Histogram 35.00% 30.00% 25.00% 20.00% 15.00% 10.00% 5.00% 0.00%
0.0047
0.0032
0.0017
0.0002
-0.0013
-0.0028
---
Midpoints (b)
2.24
Yes, the steel mill is doing a good job at meeting the requirement as there is only one steel part out of a sample of 100 that is as much as 0.005 inches longer than the specified requirement.
(a) Width 8.310 -- 8.329 8.330 -- 8.349 8.350 -- 8.369 8.370 -- 8.389 8.390 -- 8.409 8.410 -- 8.429 8.430 -- 8.449 8.450 -- 8.469 8.470 -- 8.489 8.490 -- 8.509
Frequency
Percentage 3 2 1 4 5 16 5 5 6 2
6.12% 4.08% 2.04% 8.16% 10.20% 32.65% 10.20% 10.20% 12.24% 4.08%
2.24 cont.
Chapter 2: Presenting Data in Tables and Charts (b)
Histogram Frequency
98
20 15 10 5 0 8.52 8.5 8.48 8.46 8.44 8.42 8.4 8.38 8.36 8.34 8.32 ---
Midpoints Percentage Polygon 35% 30% 25% 20% 15% 10% 5% 0% --- 8.32 8.34 8.36 8.38 8.4 8.42 8.44 8.46 8.48 8.5 8.52
(c) Cumulative Percentage Polygon 120% 100% 80% 60% 40% 20% 0% 8.5299
8.5099
8.4899
8.4699
8.4499
8.4299
8.4099
8.3899
8.3699
8.3499
8.3299
8.3099
(d)
All the troughs will meet the company’s requirements of between 8.31 and 8.61 inches wide.
Solutions to End-of-Section and Chapter Review Problems (a) Strength 1500 -- 1549 1550 -- 1599 1600 -- 1649 1650 -- 1699 1700 -- 1749 1750 -- 1799 1800 -- 1849 1850 -- 1899
Frequency 1 2 2 7 5 7 3 3
Percentage 3.33% 6.67% 6.67% 23.33% 16.67% 23.33% 10.00% 10.00%
(b) %Histogram 25.00% 20.00% 15.00%
10.00% 5.00% 0.00% 1525 1575 1625 1675 1725 1775 1825 1875 Midpoints
(b)
Percentage Polygon 25% 20% 15% 10% 5%
1925
1875
1825
1775
1725
1675
1625
1575
1525
0% 1475
2.25
99
100 2.25 cont.
Chapter 2: Presenting Data in Tables and Charts (c)
Cumulative Percentage Polygon 100% 90% 80% 70% 60% 50% 40% 30% 20% 10%
(d) 2.26
1949
1899
1849
1799
1749
1699
1649
1599
1549
1499
1449
0%
The strength of all the insulators meets the company’s requirement of at least 1500.
(a) Bulb Life (hrs) 650 -- 749 750 -- 849 850 -- 949 950 -- 1049 1050 -- 1149
Bulb Life (hrs) 650 – 749 750 – 849 850 – 949 950 – 1049 1050 – 1149 1150 – 1249
Frequency Manufacturer A 3 5 20 9 3 Percentage, Mfgr A 7.5% 12.5 50.0 22.5 7.5 0.0
Bulb Life (hrs) 750 -- 849 850 -- 949 950 -- 1049 1050 -- 1149 1150 -- 1249 Percentage, Mfgr B 0.0% 5.0 20.0 40.0 22.5 12.5
Frequency Manufacturer B 2 8 16 9 5
Solutions to End-of-Section and Chapter Review Problems (b)
Percentage
Percentage Histogram (Manufacturer A) 60 50 40 30 20 10 0 749
849
949
1049
1149
1249
Bin
Percentage Histogram (Manufacturer B)
Percentage
50 40 30 20 10 0 749
849
949
1049
1149
1249
Bin
Percentage Polygon
Percentage
2.26 cont.
60 50 40 30 20 10 0
Manufacturer A Manufacturer B
600 700 800 900 1000 1100 1200 Mid-points
101
(c)
Frequency Less Than, Mfgr A 3 8 28 37 40 40 Percentage Less Than, Mfgr A 7.5% 20.0 70.0 92.5 100.0 100.0
Bulb Life (hrs) 650 – 749 750 – 849 850 – 949 950 – 1049 1050 – 1149 1150 – 1249
Bulb Life (hrs) 650 – 749 750 – 849 850 – 949 950 – 1049 1050 – 1149 1150 – 1249
Frequency Less Than, Mfgr B 0 2 10 26 35 40 Percentage Less Than, Mfgr B 0.0% 5.0 25.0 65.0 87.5 100.0
Ogives 100 80 60
Manufacturer A
40
Manufacturer B
20
1250
1150
1050
950
850
750
0
650
2.26 cont.
Chapter 2: Presenting Data in Tables and Charts
Percentage
102
Life (Hours)
(d)
Manufacturer B produces bulbs with longer lives than Manufacturer A. The cumulative percentage for Manufacturer B shows 65% of their bulbs lasted 1049 hours or less contrasted with 70% of Manufacturer A’s bulbs which lasted 949 hours or less. None of Manufacturer A’s bulbs lasted more than 1149 hours, but 12.5% of Manufacturer B’s bulbs lasted between 1150 and 1249 hours. At the same time, 7.5% of Manufacturer A’s bulbs lasted less than 750 hours, while all of Manufacturer B’s bulbs lasted at least 750 hours.
Solutions to End-of-Section and Chapter Review Problems (a)
Amount of Soft Drink Frequency 1.850 – 1.899 1 1.900 – 1.949 5 1.950 – 1.999 18 2.000 – 2.049 19 2.050 – 2.099 6 2.100 – 2.149 1
Percentage 2% 10 36 38 12 2
(b) Histogram
Frequency
20 15 10 5 0 1.875
1.925
1.975
2.025
2.075
2.125
Amout of Soft Drink
Percentage Polygon 40 Percentage
2.27
30 20 10 0 1.825 1.875 1.925 1.975 2.025 2.075 2.125 2.175 Mid-points
103
104 2.27 cont.
Chapter 2: Presenting Data in Tables and Charts (c)
Amount of Soft Drink 1.85 – 1.89 1.90 – 1.94 1.95 – 1.99 2.00 – 2.04 2.05 – 2.09 2.10 – 2.14
Frequency Less Than 1 6 24 43 49 50
Percentage Less Than 2% 12 48 86 98 100
Cumulative Percentage Polygon 100
Percentage
80 60 40 20 0 1.85
1.9
1.95
2
2.05
2.1
2.15
Amount of Soft Drink
2.28
(d)
The amount of soft drink filled in the two liter bottles is most concentrated in two intervals on either side of the two-liter mark, from 1.950 to 1.999 and from 2.000 to 2.049 liters. Almost three-fourths of the 50 bottles sampled contained between 1.950 liters and 2.049 liters.
(a)
Table frequencies for all student responses Student Major Categories Gender A C M Totals Male 14 9 2 25 Female 6 3 6 15 Totals 20 12 8 40 Table percentages based on overall student responses Student Major Categories Gender A C M Totals Male 35.0% 22.5% 5.0% 62.5% Female 15.0% 7.5% 15.0% 37.5% Totals 50.0% 30.0% 20.0% 100.0% Table based on row percentages Student Major Categories Gender A C M Totals Male 56.0% 36.0% 8.0% 100.0% Female 40.0% 20.0% 40.0% 100.0% Totals 50.0% 30.0% 20.0% 100.0% Table based on column percentages Student Major Categories Gender A C M Totals Male 70.0% 75.0% 25.0% 62.5% Female 30.0% 25.0% 75.0% 37.5% Totals 100.0% 100.0% 100.0% 100.0%
(b)
(c)
(d)
Solutions to End-of-Section and Chapter Review Problems 2.29
105
(a) Table of total percentages
Nonconforming Conforming Total
Shift Day Evening 1.8% 2.7% 4.5% 64.2% 31.3% 95.5% 66% 34% 100%
Table of row percentages Day Evening Nonconforming 40.0% 60.0% 100% Conforming 67.2% 32.8% 100% Total 66% 34% 100%
Table of column percentages Shift Day Evening Nonconforming 2.7% 7.9% 4.5% Conforming 97.3% 92.1% 95.5% Total 100% 100% 100%
(b)
(c)
The row percentages allow us to block the effect of disproportionate group size and show us that the pattern for day and evening tests among the nonconforming group is very different from the pattern for day and evening tests among the conforming group. Where 40% of the nonconforming group was tested during the day, 67% of the conforming group was tested during the day. The director of the lab may be able to cut the number of nonconforming tests by reducing the number of tests run in the evening, when there is a higher percent of tests run improperly.
106 2.30
Chapter 2: Presenting Data in Tables and Charts (a)
Table of total percentages Enjoy Shopping for Clothing Yes No Total
Gender Male 25.2% 20.8% 46%
Female 46.8% 7.2% 54%
Total 72% 28% 100%
Table of row percentages Enjoy Shopping for Clothing Yes No Total
Gender Male 35% 74.3% 46%
Female 65% 25.7% 54%
Total 100% 100% 100%
Table of column percentages Enjoy Shopping for Clothing Yes No Total (b)
2.31
Gender Male 54.8% 45.2% 100%
Female 86.7% 13.3% 100%
Total 72% 28% 100%
The percentage of shoppers who enjoy shopping for clothing is higher among females than males.
(a)
Contingency Table Condition of Die Quality No Particles Particles Totals Good 320 14 334 Bad 80 36 116 Totals 400 50 450 Table of Total Percentages Condition of Die Quality No Particles Particles Totals Good 71% 3% 74% Bad 18% 8% 26% Totals 89% 11% 100%
Table of Row Percentages Condition of Die Quality No Particles Particles Totals Good 96% 4% 100% Bad 69% 31% 100% Totals 89% 11% 100%
Solutions to End-of-Section and Chapter Review Problems 2.31 cont.
107
(a) Table of Column Percentages Condition of Die Quality No Particles Particles Totals Good 80% 28% 74% Bad 20% 72% 26% Totals 100% 100% 100% (b) Side-by-side Bar Chart
Condition of Die
36 Particles 14 Bad Good 80 No Particles 320
0
100
200
300
400
Frequency
(c)
2.32
The data suggests that there is some association between condition of the die and the quality of wafer because more good wafers are produced when no particles are found in the die and more bad wafers are produced when there are particles found in the die.
The number of MBA and undergraduate students who choose the lowest cost fund and the second-lowest cost fund is about the same. More MBA students choose the third-lowest cost fund while more undergraduate students choose the highest cost fund.
2.33 Side-by-side Bar Chart Internet
Media
Local Newspaper 50+ 36-50 Under 36
Radio National TV Local TV 0
20
40
60
80
100
120
140
Frequencies
Among the three groups, the “under 36” group has the lowest number of occurrences who get their news from local newspaper and the highest frequency who get their news from the Internet. The “50+” group has the highest frequency who get their news from national TV, local TV, radio, and local newspaper.
108 2.34
Chapter 2: Presenting Data in Tables and Charts (a)
Scatter Plot 40 35 30 Y
25 20 15 10 5 0 0
5
10
15
20
X
(b) (a)
Time-Series Plot of Annual Sales Income (millions of dollars)
2.35
Yes, there appears to be a positive linear relationship between X and Y.
25 20 15 10 5 0 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Year
(b) Annual sales appear to be increasing in the earlier years before 1998 but start to decline after 2002.
Solutions to End-of-Section and Chapter Review Problems 2.36
(a)
Current Government Standard Mileage
Scatter Diagram 60.0 50.0 40.0 30.0 20.0 10.0 0.0 0.0
20.0
40.0
60.0
Owner Mileage (b) (a)
Scatter Plot 60
Fat (grams per serving)
2.37
There is a positive relationship between owner mileage and current government standard mileage.
50 40 30 20 10 0 0
200
400
600
800
1000
Calories (b) There is a positive relationship between calories and total fat in chicken sandwiches.
109
110 2.38
Chapter 2: Presenting Data in Tables and Charts (a)
Yes, schools with higher revenues will also have higher coach’s salaries.
Salary ($ millions)
Scatter Diagram 2.00 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 0.00
5.00
10.00
15.00
20.00
Revenue ($ millions) (b) (c) (a)
Scatter Plot 100
Graduation %
2.39
There appears to be a positive relationship between coaches’ salary and revenue. The scatter plot confirms the answer to (a).
80 60 40 20 0 0
10
20
30
40
Wonderlic Score (b)
There is a positive relationship between Wonderlic score and graduation rate.
Solutions to End-of-Section and Chapter Review Problems 2.40
(a)
111
Excel output:
Time-Series Plot 7
Unemployment Rate
6 5 4 3 2
1
2000 January 2000 April 2000 July 2000 October 2001 January 2001 April 2001 July 2001 October 2002 January 2002 April 2002 July 2002 October 2003 January 2003 April 2003 July 2003 October 2004 January 2004 April 2004 July 2004 October 2005 January 2005 April 2005 July 2005 October 2006 January 2006 April 2006 July 2006 October 2007 January 2007 April 2007 July 2007 October
0
Year/Month
(b)
(a)
Time-Series Plot 120 100
Revenues (billions $)
80 60
40 20 0
2001-1 2001-2 2001-3 2001-4 2002-1 2002-2 2002-3 2002-4 2003-1 2003-2 2003-3 2003-4 2004-1 2004-2 2004-3 2004-4 2005-1 2005-2 2005-3 2005-4 2006-1 2006-2 2006-3 2006-4 2007-1 2007-2 2007-3 2007-4 2008-1 2008-2 2008-3 2008-4
2.41
The unemployment rate was quite stable at around 4% from January 2000 to around January 2001. Then it trended upward and leveled off at around 6% by December 2001. Around October 2003, it started to trend downward and reached about 4.5% by December 2006. It started to trend up again in January 2007.
Quarters
(b)
The quarterly revenues are highest in the fourth quarter and lowest in the first quarter of each year. There is a long-term upward trend in the quarterly revenues.
112 2.42
Chapter 2: Presenting Data in Tables and Charts (a)
Excel output:
Time-Series Plot for Number of TV Channels Received 120
100 80 60
40 20 0
1985
1990
1995
2000
2005
Year
(b) (c)
2.43
There is an obvious upward trend in the average number of TV channels that the U. S. home received from 1985 to 2005. With extrapolation, you would predict the average number of TV channels that the U. S. home will receive in 2010 to be around 140.
(a)
Time-series Plot Subscribers (in millions)
6 5 4 3 2 1 0 1998
2000
2002
2004
2006
Year (b)
The number of subscribers is increasing but the rate of growth is decreasing because the slope of the line segments that join the data points is decreasing over the years.
2.53
A histogram uses bars to represent each class while a polygon uses a single point. The histogram should be used for only one group, while several polygons can be plotted on a single graph.
2.54
A summary table allows one to determine the frequency or percentage of occurrences in each category.
Solutions to End-of-Section and Chapter Review Problems
113
2.55
A bar chart is useful for comparing categories. A pie chart is useful when examining the portion of the whole that is in each category. A Pareto diagram is useful in focusing on the categories that make up most of the frequencies or percentages.
2.56
The bar chart for categorical data is plotted with the categories on the vertical axis and the frequencies or percentages on the horizontal axis. In addition, there is a separation between categories. The histogram is plotted with the class grouping on the horizontal axis and the frequencies or percentages on the vertical axis. This allows one to more easily determine the distribution of the data. In addition, there are no gaps between classes in the histogram.
2.57
A time-series plot is a type of scatter diagram with time on the x-axis.
2.58
Because the categories are arranged according to frequency or importance, it allows the user to focus attention on the categories that have the greatest frequency or importance.
2.59
Percentage breakdowns according to the total percentage, the row percentage, and/or the column percentage allow the interpretation of data in a two-way contingency table from several different perspectives.
2.60
(a)
Bar Chart
Revenue Categories
Publisher
Freight
Bookstore
Author
0
10
20
30
40
%
50
60
70
114 2.60 cont.
Chapter 2: Presenting Data in Tables and Charts (a)
Pie Chart
Author 11.6%
Bookstore 22.4% Publisher 64.8%
Freight 1.2%
Pareto Diagram 70%
100% 90%
60%
80% 50%
70%
40%
60% 50%
30%
40%
20%
30% 20%
10%
10%
0%
0% Publisher
Bookstore
Author
Revenue Categories
Freight
Solutions to End-of-Section and Chapter Review Problems (b)
Bar Chart Pretax profit
Revenue Categories
2.60 cont.
Operations Marketing and promotion Manufacturing costs Freight Employee salaries and benefits Author After-tax profit Administrative costs and taxes 0
5
10
15
20
%
Pie Chart Pretax profit 4.5% Operations 6.6% Marketing and promotion 15.4%
Administrative costs and taxes 10.0% After-tax profit 7.1%
Author 11.6%
Employee salaries and benefits 11.3% Manufacturing costs 32.3%
Freight 1.2%
25
30
35
115
116
Chapter 2: Presenting Data in Tables and Charts
2.60 cont.
(b)
Pareto Diagram 35%
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%
30% 25% 20% 15% 10% 5% Freight
Pretax profit
Operations
After-tax profit
Administrative costs and taxes
Employee salaries and benefits
Author
Marketing and promotion
Manufacturing costs
0%
Revenue Categories (c)
The publisher gets the largest portion (64.8%) of the revenue. About half (32.2%) of the revenue received by the publisher is used for manufacturing costs. Publisher’s marketing and promotion account for the next larger share of the revenue at 15.4%. Author, bookstore employee salaries and benefits, and publisher administrative costs and taxes each accounts for around 10% of the revenue while the publisher after-tax profit, bookstore operations, bookstore pretax profit and freight constitute the “trivial few” allocations of the revenue.
2.61 (a) Bar Chart for Payment Method
Payment Method
Cash Debit Card Credit Card Check Other 0
10
20
30
Percentage
40
50
Solutions to End-of-Section and Chapter Review Problems
117
2.61 (a) cont. Pie Chart for Payment Method Cash 35%
Other 1% Check 2%
Debit Card 44%
Credit Card 18%
50 45 40 35 30 25 20 15 10 5 0
100 90 80 70 60 50 40 30 20 10 0 Debit Card
Cash
Credit Card
Check
Cumulative %
Percentage
Pareto Diagram for Payment Method
Other
Payment Method
(b) The large majority (79%) of young adults use a debit card or cash as their payment method. Very few young adults prefer to use a check or some other payment method.
2.62
Chapter 2: Presenting Data in Tables and Charts (a)
PHStat output: Bar Chart Rich media/video
Paid search
Type
118
Other
Display ads
Classified 0
2
Rich media/video 11%
4
6
8
10
Pie Chart Classified 17%
Display ads 20% Paid search 43%
Other 9%
Pareto Diagram 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%
45% 40% 35% 30% 25%
20% 15% 10% 5% 0% Paid search Display ads Classified
Rich media/video
Other
Type
(b)
The Pareto diagram is most appropriate because it not only sorts the frequencies in descending order, it also provides the cumulative polygon on the same scale.
Solutions to End-of-Section and Chapter Review Problems (c) Bar Chart Sneaker pimps*
Sneaker
Search result
2.62 cont.
119
Puma sneaker
Nike sneaker
Jordan sneaker 0
10000 20000 30000 40000 50000 60000 70000
Pie Chart Jordan sneaker 13%
Sneaker pimps* 15%
Nike sneaker 8%
Puma sneaker 7%
Sneaker 57%
Pareto Diagram 70%
100% 90%
60%
80%
50%
70%
40%
60% 50%
30%
40%
20%
30% 20%
10%
10%
0%
0%
Sneaker
Sneaker pimps*
Jordan sneaker
Nike sneaker
Puma sneaker
Search result
(d)
The Pareto diagram is most appropriate because it not only sorts the frequencies in descending order, it also provides the cumulative polygon on the same scale.
120
Chapter 2: Presenting Data in Tables and Charts
2.62 cont.
(e)
2.63
(a)
“Paid search” constitutes the largest category on US online ad spending at 43%. Excluding the generic keyword “sneaker”, searches using the keywords “sneaker pimps” and “Jordan sneaker” make up majority of the search for sneakers on specific brands.
Type of Entrée Beef Chicken Duck Fish Pasta Shellfish Veal Total
Number Served 185 105 24 121 63 74 28 600
% 30.8% 17.5% 4.0% 20.2% 10.5% 12.3% 4.7% 100.0%
(b) Bar Chart for Entrées Veal Shellfish
Entrée
Pasta Fish Duck Chicken Beef 0
50
100
150
Number Served
Pie Chart for Entrées
Shellfish 12%
Veal 4% Beef 31%
Pasta 11%
Fish 20% Duck 4%
Chicken 18%
200
Solutions to End-of-Section and Chapter Review Problems
2.63 cont.
121
(b)
200
100%
150
80% 60%
100 40% 50
20%
0
0%
ef Be
(c) (d)
2.64
sh Fi
a sh en st lfi a l ck i P e h C Sh Type of Entrée
al Ve
k uc D
The Pareto diagram has the advantage of offering the cumulative percentage view of the categories and, hence, enables the viewer to separate the "vital few" from the "trivial many." Beef and fish account for 51% of all entrees ordered by weekend patrons of a continental restaurant. When chicken is included, better than two-thirds of the entrees are accounted for. (a) Gender Dessert Ordered Male Female Total Yes 69.2% 30.8% 100% No 47.1% 52.9% 100% Total 52.5% 47.5% 100% (g) Gender Dessert Ordered Male Female Total Yes 32.1% 15.8% 24.3% No 67.9% 84.2% 75.7% Total 100% 100% 100% (h) Gender Dessert Ordered Male Female Total Yes 16.8% 7.5% 24.3% No 35.7% 40.0% 75.7% Total 52.5% 47.5% 100%
(b)
Cumulative Percentage
Percentage
Pareto Diagram for Entrées
Beef Entrée Dessert Ordered Yes No Total Yes 48.6% 51.4% 100% No 25.1% 74.9% 100% Total 30.8% 69.2% 100% Beef Entrée Dessert Ordered Yes No Total Yes 38.4% 18.1% 24.3% No 61.6% 81.9% 75.7% Total 100% 100% 100% Beef Entrée Dessert Ordered Yes No Total Yes 11.8% 12.5% 24.3% No 19.0% 56.7% 75.7% Total 30.8% 69.2% 100%
If the owner is interested in finding out the percentage of joint occurrence of gender and ordering of dessert or the percentage of joint occurrence of ordering a beef entrée and a dessert among all patrons, the table of total percentages is most informative. If the owner is interested in the effect of gender on ordering of dessert or the effect of ordering a beef entrée on the ordering of dessert, the table of column percentages will be most informative. Since dessert will usually be ordered after the main entree and the owner has no direct control over the gender of patrons, the table of row percentages is not very useful here.
Chapter 2: Presenting Data in Tables and Charts
2.64 cont.
(c)
2.65
(a)
32% of the men sampled ordered desserts compared to 16% of the women. Men are more than twice as likely to order desserts as women. Approximately 38% of the patrons ordering a beef entree ordered dessert compared to 18% of patrons ordering all other entrees. Patrons ordering beef are better than twice as likely to order dessert as patrons ordering any other entree.
Bar Chart (Plasma TV) Samsung Phillips
Company
122
Panasonic Others LGE Hitachi 0
5
10
15
20
%
Pie Chart (Plasma TV)
Samsung 14.4%
Hitachi 7.3% LGE 15.4%
Phillips 13.3%
Others 23.6% Panasonic 26.0%
25
30
Solutions to End-of-Section and Chapter Review Problems (a) Pareto Diagram (Plasma TV) 30%
100% 90%
25%
80% 70%
20%
60% 15%
50% 40%
10%
30% 20%
5%
10% 0%
0% Panasonic
Others
LGE
Samsung
Phillips
Hitachi
25
35
Company Bar Chart (LCD TV) Sony Sharp
Company
2.65 cont.
Samsung Phillips/Magnavox Others LGE 0
5
10
15
20
30
%
Pie Chart (LCD TV)
Sony 14.6%
LGE 6.5%
Sharp 13.6% Others 39.5% Samsung 11.6% Phillips/Magnavo x 14.2%
40
45
123
124 2.65 cont.
Chapter 2: Presenting Data in Tables and Charts (a) Pareto Diagram (LCD TV) 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% LGE
Samsung
Sharp
Phillips/Magnavox
Others
Sony
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%
Company
(b)
(a) Bar Chart (Energy Source) Renewable fuels Petroleum
Energy Source
2.66
Panasonic has the largest market share at 26% in the plasma TV market while the LCD market is not dominated by any manufacturer.
Nuclear electric power Natural gas Hydroelectric Power Coal 0
5
10
15
20
25
%
30
35
40
45
Solutions to End-of-Section and Chapter Review Problems 2.66 cont.
(a) Bar Chart (Renewable Energy Source)
Renewable Energy Source
Wood Wind Waste Solar Geothermal Ethanol 0
10
20
30
40
50
%
Pie Chart (Energy Source)
Renewable fuels 3%
Coal 23%
Hydroelectric Power 3%
Petroleum 41%
Nuclear electric power 8%
Natural gas 22%
60
125
(a) Pie Chart (Renewable Energy Source)
Ethanol 10% Geothermal 11% Solar 2% Wood 55%
Waste 17% Wind 5%
Pareto Diagram 45%
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0%
40% 35% 30% 25% 20% 15% 10% 5%
Energy Source
Hydroelectric Power
Renewable fuels
Nuclear electric power
Natural gas
0% Coal
2.66 cont.
Chapter 2: Presenting Data in Tables and Charts
Petroleum
126
Solutions to End-of-Section and Chapter Review Problems 2.66 cont.
127
(a) Pareto Diagram 60%
100% 90%
50%
80% 70%
40%
60% 30%
50% 40%
20%
30% 20%
10%
10% 0% Solar
Wind
Ethanol
Geothermal
Waste
Wood
0%
Renewable Energy Source
(b)
2.67
In 2005, U.S. relied on petroleum heavily followed by coal and natural gas as major sources of energy while renewable fuels accounted for less than 4% of the total consumption. Wood accounted for more than half of the renewable energy consumption.
(a) Range 0 but less than 25 25 but less than 50 50 but less than 75 75 but less than 100 100 but less than 125 125 but less than 150 150 but less than 175
Frequency Percentage 17 34% 19 38% 5 10% 2 4% 3 6% 2 4% 2 4%
Chapter 2: Presenting Data in Tables and Charts (b)
Histogram
Frequency
128
20 18 16 14 12 10 8 6 4 2 0 0 but less 25 but 50 but 75 but 100 but 125 but 150 but than 25 less than less than less than less than less than less than 50 75 100 125 150 175 Days
Solutions to End-of-Section and Chapter Review Problems 129 2.67 cont.
(b) Percentage Polygon 40% 35% 30% 25% 20%
15% 10% 5% 0% ---
0.53
0.77
0.84
0.89
0.94
0.98
1
(c) Range 0 but less than 25 25 but less than 50 50 but less than 75 75 but less than 100 100 but less than 125 125 but less than 150 150 but less than 175
Cumulative % 34% 72% 82% 86% 92% 96% 100%
Cumulative Percentage Polygon 120% 100% 80% 60% 40% 20% 0% -0.01
(d)
24.99 49.99 74.99 99.99 124.99 149.99 174.99
You should tell the president of the company that over half of the complaints are resolved within a month, but point out that some complaints take as long as three or four months to settle.
130 Chapter 2: Presenting Data in Tables and Charts (a)
40.00% 30.00% 20.00% 10.00% 0.00% --0.35 0.85 1.35 1.85 2.35 2.85 3.35 3.85 4.35 4.85 5.35 5.85 6.35 6.85
Percentage
Percentage Histogram (Alcohol %)
Midpoints
30.00% 20.00%
10.00% 0.00% --70 80 90 100 110 120 130 140 150 160 170 180 190 200
Percentaage
Percentage Histogram (Calories)
Midpoints
Percentage Histogram (Carbohydrates) 25.00% Percentage
2.68
20.00% 15.00% 10.00% 5.00% 0.00% --- 2 4 6 8 10 12 14 16 18 20 22 24 Midpoints