Statistics for business and economics 13th edition mcclave solutions manual

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Chapter 2 Methods for Describing Sets of Data

2 First, we find the frequency of the grade A. The sum of the frequencies for all five grades must be 200.
Therefore, subtract the sum of the frequencies of the other four grades from 200. The frequency for grade
A is:
200  (36 + 90 + 30 + 28) = 200  184 = 16

To find the relative frequency for each grade, divide the frequency by the total sample size, 200. The
relative frequency for the grade B is 36/200 = .18. The rest of the relative frequencies are found in a
similar manner and appear in the table:

Grade on Statistics Exam Frequency Relative Frequency
A: 90  100 16.
B: 80  89 36.
C: 65  79 90.
D: 50  64 30.
F: Below 50 28.
Total 200 1.

2 a. To find the frequency for each class, count the number of times each letter occurs. The frequencies
for the three classes are:

Class Frequency
X 8
Y 9
Z 3
Total 20

b. The relative frequency for each class is found by dividing the frequency by the total sample size. The
relative frequency for the class X is 8/20 = .40. The relative frequency for the class Y is 9/20 = .45.
The relative frequency for the class Z is 3/20 = .15.

Class Frequency Relative Frequency
X 8.
Y 9.
Z 3.
Total 20 1.

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Methods for Describing Sets of Data 11

c. The frequency bar chart is:

C la s s

Frequency

ZYX

9 8 7 6 5 4 3 2 1 0

d. The pie chart for the frequency distribution is:

2 a.

####### 107

####### .

####### U 174

p 

####### 57

####### .

####### S 174

p 

####### 10

####### .

####### R 174

p 

d. .615 360øù221, .328 360øù118, .057 360øù20.

XY
Z

Category
15%Z

45%Y

40%X

Pie Chart of Class

Methods for Describing Sets of Data 13

b. Using MINITAB, the pie chart is:

2 a. The type of graph is a bar graph.

b. The variable measured for each of the robots is type of robotic limbs.

c. From the graph, the design used the most is the ìlegs onlyî design.

d. The relative frequencies are computed by dividing the frequencies by the total sample size. The total
sample size is n = 106. The relative frequencies for each of the categories are:

Type of Limbs Frequency Relative Frequency
None 15 15/106 =.
Both 8 8 / 106 =.
Legs ONLY 63 63/106 =.
Wheels ONLY 20 20/106 =.
Total 106 1.

e. Using MINITAB, the Pareto diagram is:

Type

Relative Frequency

BothNoneWheelsLegs

Percent within all data.

Cable TVCord cutterCategory
Cord cutter16%

83%Cable TV

Pie Chart of Subscribe

14 Chapter 2

2 a. Region is qualitative because it is not measured using numbers.

b.
48
.
A P 150
p  ,
10
.
C 150
p ,
34
.
E 150
p ,
29
.
LA 150
p , /
3
.
ME A 150
p ,

26
.
US 150
p 

c. Using MINITAB, the plot is

d. The regions that most of the top 150 credit card users serve are Asia-Pacific, Europe, Latin America,
and the United States.

2 a. Using MINITAB, the pie chart is:

Explorer had the lowest proportion of security issues with the proportion
6
.
50

####### .

EuropeCanadaAsia-Pacific Latin AmericaMiddle East/AfricaUnited States

30
25

20
15

5
0
Region

Percent

Percent is calculated within all data.

OfficeWindows
Explorer

Category
Explorer12%

Windows64%

24%Office

Pie Chart of Product

16 Chapter 2

The network type that suffered the most jamming attacks is WLAN with more than half. The
network type that suffered the least number of jamming attacks is AHN.

2 Using MINITAB, the pie chart is:

A little of half of the successful candidates had a First (Bachelorís) degree, while a little more than a third
of the successful candidates had no degree. Only about 10% of the successful candidates had graduate
degrees.

2 Using MINITAB, the bar graphs of the 2 waves is:

Job Status

Percent

Sch

NoWorkBusSchNoWorkGrad

WorkMBA
WorkNoMBA

90
8070
60
5040
30
2010
0

WorkNoMBAWorkMBANoWorkBusSchNoWorkGradSch
1 2

Panel variable: Wave; Percent within all data.

Chart of Job Status

In wave 1, most of those taking the GMAT were workingøù2657 / 3244 .819 and none had MBAís. About

20% were not working but were in either a 4-year institution or other graduate school

øù36 551 / 3244 .181. In wave 2, almost all were now workingøù1787 1372 / 3244 .974. Of those

working, more than half had MBAís øù1787 / 1787 1372  .566. Of those not working, most were in

another graduate school.

None
First
Post

Category
10%
Post

52%
First

36%

None

Pie Chart of Degree

Methods for Describing Sets of Data 17

2 Using MINITAB, the Pareto diagram for the data is:

Tenants

Percent

AnchorMajorLargeSmallStandardSmall

Chart of Tenants

Percent within all data.

Most of the tenants in UK shopping malls are small or small standard. They account for approximately

84% of all tenantsøù711 819 / 1,821 .84. Very few (less than 1%) of the tenants are anchors.

2 Using MINITAB, the side-by-side bar graphs are:

Acquisitions

Percent

YesNo
100
75
50
25
0

YesNo

100
75
50
25
0

1980 1990

2000

Panel variable: Year; Percent within all data.

Chart of Acquisitions

In 1980, very few firms had acquisitionsøù18 / 1, 963 .009. By 1990, the proportion of firms having

acquisitions increased to350 / 2,197 .159. By 2000, the proportion of firms having acquisitions increased
to748 / 2,778 .269.

Methods for Describing Sets of Data 19

d. In all cities, most customers rated the iphone 6 as ëgoodí, while very few rated the iphone 6 as
excellent.

2 Using MINITAB, a pie chart of the data is:

Since the sizes of the slices are close to each other, it appears that the researcher is correct. There is a large
amount of variation within the museum community with regard to performance measurement and
evaluation.

2 a. The variable measured by Performark is the length of time it took for each advertiser to respond back.

b. The pie chart is:

c. Twenty-one percent or 17,000 3,570of the advertisers never respond to the sales lead.

d. The information from the pie chart does not indicate how effective the "bingo cards" are. It just
indicates how long it takes advertisers to respond, if at all.

Big Shows
Funds RaisedMembers
Paying visitors
Total visitors

Category

Total visitors26%

16%
Paying visitors

13%
Members

23%Funds Raised

20%Big Shows

Pie Chart of Measure

Never responded>120 days
60-120 days13-59 days

Category

13-59 days25%

60-120 days37%

13%>120 days

23%Never responded

Pie Chart of Response Time

20 Chapter 2

2 Using MINITAB, the side-by-side bar graphs are:

Dive

Percent

RightMiddleLeft
80
60
40
20
0

RightMiddleLeft

80
60
40
20
0

Ahead Behind

Tied

Chart of Dive

Panel variable: Situation; Percent within all data.

From the graphs, it appears that if the team is either tied or ahead, the goal-keepers tend to dive either right
or left with equal probability, with very few diving in the middle. However, if the team is behind, then the
majority of goal-keepers tend to dive right (71%).

2 a. Using MINITAB, bar charts for the 3 variables are:

Well Class

Count

PublicPrivate

120

100

Chart of Well Class

22 Chapter 2

c. Using MINITAB, the side-by-side bar chart is:

Detection

Percent

Below Limit Detect

70
60
50
40
30
20
10
0

Below Limit Detect
Bedrock Unconsoli

Chart of Detection

Panel variable: Aquifer; Percent within all data.

d. From the bar charts in parts a-c, one can infer that most aquifers are bedrock and most levels of
MTBE were below the limit( 2 / 3) . Also the percentages of public wells verses private wells are
relatively close. Approximately 80% of private wells are not contaminated, while only about 60% of
public wells are not contaminated. The percentage of contaminated wells is about the same for both
types of aquifers( 30%) .

2 Using MINITAB, the relative frequency histogram is:

Class

Relative Frequency

16.514.512.510.58.56.54.52.

Methods for Describing Sets of Data 23

2 To find the number of measurements for each measurement class, multiply the relative frequency by the
total number of observations, n = 500. The frequency table is:

Measurement Class Relative Frequency Frequency
.5  2 .10 500(.10) = 50
2  4 .15 500(.15) = 75
4  6 .25 500(.25) = 125
6  8 .20 500(.20) = 100
8  10 .05 500(.05) = 25
10  12 .10 500(.10) = 50
12  14 .10 500(.10) = 50
14  16 .05 500(.05) = 25
500

Using MINITAB, the frequency histogram is:

Class

Frequency

16.514.612.510.58.56.54.52.

140

120

100

2 a. The original data set has 1 + 3 + 5 + 7 + 4 + 3 = 23 observations.

b. For the bottom row of the stem-and-leaf display:

The stem is 0.
The leaves are 0, 1, 2.
Assuming that the data are up to two digits, rounded off to the nearest whole number, the
numbers in the original data set are 0, 1, and 2.

c. Again, assuming that the data are up to two digits, rounded off to the nearest whole number, the dot
plot corresponding to all the data points is:

2 a. This is a frequency histogram because the number of observations is graphed for each interval rather
than the relative frequency.

b. There are 14 measurement classes.

Methods for Describing Sets of Data 25

b. From the stem-and-leaf display, there are only 6 observations with sanitation scores less than 86. The
proportion of ships with accepted sanitation standards is(195 6) / 195 189 / 195 .97 .

c. The score of 69 is highlighted in the stem-and-leaf display.

2 a. Using MINITAB, a dot plot of the data is:

Acquisitions

8407206004803602401200

Dotplot of Acquisitions

b. By looking at the dot plot, one can conclude that the years 1996-2000 had the highest number of
firms with at least one acquisition. The lowest number of acquisitions in that time frame (748) is
almost 100 higher than the highest value from the remaining years.

2 a. Using MINITAB, a histogram of the current values of the 32 NFL teams is:

3600300024001800

16
14
12
10
8
6
4
2
0
VALUE ($mil)

Frequency

Histogram of VALUE ($mil)

26 Chapter 2

b. Using MINITAB, a histogram of the 1-year change in current value for the 32 NFL teams is:

c. Using MINITAB, a histogram of the debt-to-value ratios for the 32 NFL teams is:

d. Using MINITAB, a histogram of the annual revenues for the 32 NFL teams is:

706050403020

7 6 5 4 3 2 1 0

CHANGE (%)

Frequency

Histogram of CHANGE (%)

5040302010

14
12
10
8
6
4
2
0
DEBT/VALUE (%)

Frequency

Histogram of DEBT/VALUE (%)

600550500450400350300

18
16
14
12
10
8
6
4
2
0
REVENUE ($mil)

Frequency

Histogram of REVENUE ($ mil)

28 Chapter 2

From this graph of the differences, we can see that there are more observations to the right of 0 than
to the left of 0. This indicates that, in general, the scores have improved since 2010.

c. From the graph, the largest improvement score is between 22 and 37. The actual largest score is
34 and it is associated with Wyoming.

2 Using MINITAB, the two dot plots are:

Data

168156144132120108

Arrive
Depart

Dotplot of Arrive, Depart

Yes. Most of the numbers of items arriving at the work center per hour are in the 135 to 165 area. Most of
the numbers of items departing the work center per hour are in the 110 to 140 area. Because the number of
items arriving is larger than the number of items departing, there will probably be some sort of bottleneck.

2 Using MINITAB, the stem-and-leaf display is:

Stem-and-Leaf Display: Dioxide

Stem-and-leaf of Dioxide N = 16
Leaf Unit = 0.

5 0 12234
7 0 55
(2) 1 34
7 1
7 2 44
5 2
5 3 3
4 3
4 4 0000

The highlighted values are values that correspond to water specimens that contain oil. There is a tendency
for crude oil to be present in water with lower levels of dioxide as 6 of the lowest 8 specimens with the
lowest levels of dioxide contain oil.

Methods for Describing Sets of Data 29

2 a. Using MINTAB, the histograms of the number of deaths is:

b. The interval containing the largest proportion of estimates is 0-50. Almost half of the estimates fall
in this interval.

2 Yes, we would agree with the statement that honey may be the preferable treatment for the cough and sleep
difficulty associated with childhood upper respiratory tract infection. For those receiving the honey
dosage, 14 of the 35 children (or 40%) had improvement scores of 12 or higher. For those receiving the
DM dosage, only 9 of the 33 (or 24%) children had improvement scores of 12 or higher. For those
receiving no dosage, only 2 of the 37 children (or 5%) had improvement scores of 12 or higher. In
addition, the median improvement score for those receiving the honey dosage was 11, the median for those
receiving the DM dosage was 9 and the median for those receiving no dosage was 7.

2 a. Using MINITAB, the stem-and-leaf display is as follows, where the stems are the units place and the
leaves are the decimal places:

Stem-and-Leaf Display: Time

Stem-and-leaf of Time N = 49
Leaf Unit = 0.

(26) 1 00001122222344444445555679
23 2 11446799
15 3 002899
9 4 11125
4 5 24
2 6
2 7 8
1 8
1 9
1 10 1

b. A little more than half (26/49 = .53) of all companies spent less than 2 months in bankruptcy. Only
two of the 49 companies spent more than 6 months in bankruptcy. It appears that, in general, the
length of time in bankruptcy for firms using "prepacks" is less than that of firms not using prepacks."

10008006004002000

12
10
8

6
4
2
0
Deaths

Frequency

Histogram of Deaths