Chapter 3:
3.1
A Gallup poll surveyed
499 women and 502 men to assess the importance of family life in the United States.
The results shown in the table are responses to the question, “How would you
rate the importance of having a good family life?”
Very Important
|
Somewhat Important
|
Very Unimportant
|
No Opinion
|
|
Women
|
459
|
35
|
0
|
5
|
Men
|
432
|
70
|
0
|
0
|
a.
Define the sample and
the population of interest to the researchers.
For me, the sample and the population interest to the researchers are
seems to be very important to both men and women.
b.
Describe the variables
that have been measured in this survey. Are the variables qualitative or
quantitative? Are the data univariate or
bivariate?
For me, there are 2 qualitative variables that have been measured in this
study;
- Variable#1 is the opinion of the subject for the question, “How would
you rate the importance of having a good family life?”
- Variable#2 is the gender, since the researchers will compare the
responses of women and men.
The data are bivariate.
c.
What do the entries in
the cells represent?
The entries represent the
opinions of men and women.
d.
Use comparative pie charts to compare the responses for men and women.
Figure 1 (Responses of Women)
Figure 2 (Responses of Men)
e.
What other graphical
techniques could be used to describe the data? Would any of these techniques be
more informative than the pie charts constructed in part d?
We can also use comparative bar charts to describe the data. Pie charts
and bar charts differ in graphics but they will give us the same level of
information for this survey.
3.2
Does education really make a difference in how much
money you will earn? A study summarized in American
Demographics reports the percentage of people classified as “marginally
rich,” “comfortably rich,” or “super rich” according to their educational
attainment.
Education |
Marginally Rich
($70–99 K)
|
Comfortably Rich ($100–249 K)
|
Super Rich ($250 K or more)
|
No college
|
32.0%
|
20.5%
|
23.4%
|
At least an
undergraduate
degree
|
43.3%
|
59.3%
|
60.3%
|
Postgraduate
study/degree
|
12.3%
|
12.9%
|
16.2%
|
a.
The percentages in each of the
three categories should sum to 100%. What category has been left out? Add that
category to the table.
For me, the missing category is Vocational.
Education |
Marginally Rich ($70–99 K)
|
Comfortably Rich
($100–249 K)
|
Super Rich ($250 K or more)
|
No college
|
32.0%
|
20.5%
|
23.4%
|
Vocational
|
12.4%
|
7.3%
|
0.1%
|
At least an
undergraduate
degree
|
43.3%
|
59.3%
|
60.3%
|
Postgraduate
study/degree
|
12.3%
|
12.9%
|
16.2%
|
b.
Create side-by-side pie charts
to display the data.
c.
Create a side-by-side
comparative bar chart to display the data.
3.3
A study in Psychological
Reports explored the relationship of mental health services (as reflected
in per-capita expenditures on psychiatric hospitals, number of beds per 1000
population, and length of stay in days) to the gross domestic product (GDP) for
selected countries. A portion of the results are shown here:
Country
|
GDP per Capita
|
Expenditures per
Capita
|
Beds/1000 Population
|
Length of Stay
|
Finland
|
18,045.00
|
83.53
|
2.6
|
27.2
|
The Netherlands
|
14,449.80
|
71.38
|
1.7
|
35.6
|
Denmark
|
19,842.15
|
64.79
|
0.9
|
11.3
|
USA
|
17,670.15
|
41.21
|
0.7
|
12.3
|
Spain
|
7,563.70
|
9.17
|
0.8
|
156.8
|
Japan
|
19,763.63
|
54.98
|
2.8
|
310.8
|
a.
What variables have
been measured in this study?
There are 5 variables that have been measured in this study; Country, GDP
per Capita, Expenditures per Capita, Beds/1000 Population and Length of Stay.
b.
Draw a scatterplot to
examine the relationship between per-capita gross domestic product and
expenditures on psychiatric hospitals for these six countries. Describe the
relationship.
Let:
1- Finland
2- The Netherlands
3- Denmark
4- USA
5- Spain
6- Japan
c.
Draw a scatterplot to
examine the relationship between beds per 1000 population and length of stay
for these six countries. Describe the relationship. Are there any observations
that seem unusual?
Let:
1- Finland
2- The Netherlands
3- Denmark
4- USA
5- Spain
6- Japan
d.
Comment on the values
of r given in the Minitab
output in light of parts b and c.
The values of r given in the
Minitab output in light of parts b and c are both linear.
Minitab Output for Exercise 3.3
Correlations (Pearson)
Correlation of Beds and Stay = 0.477
Correlation of GDP and Expend = 0.708
Therefore, the
relationship is linear since
-1 ≤ (0.477 and 0.708) ≤
1.
3.4
Investors are becoming more and more concerned about
securities fraud, especially involving initial public offerings (IPOs). During a
6-year period, the number of federal securities-fraud class action suits
has continued to increase:
Year
|
1996
|
1997
|
1998
|
1999
|
2000
|
2001
|
Suits
|
110
|
178
|
236
|
205
|
211
|
282
|
a.
Plot the data using a
scatterplot. How would you describe the
relationship between year and number of class action suits?
b.
Find the least squares
regression line relating the number of class action suits to the year being
measured.
Y = 26.51x - 52785
c.
If you were to predict the
number of class action suits in the year 2002, what problems might arise with
your predictions?
The problems may arise with my predictions are hidden class action suits.
If I can’t see those visually, they will not
be included in my number of data.
3.5
Is it harder for single parents to make ends meet than
it is for two working parents? The
monthly expenses for families with two children in Riverside,
San Bernardino, Orange,
and Ventura, California, are displayed in the
side-by-side bar chart.
a.
What variables have been
measured in this study? Are the
variables qualitative or quantitative?
The variables are single parents and two single parents which means,
qualitative.
b.
Describe the population of
interest. Do these data represent a
population or a sample drawn from the population?
The population of interest represents a sample drawn from population.
c.
What type of graphical
presentation has been used? What other
type could have been used?
Side-by-side bar chart has been used, and other type could be the stacked
bar chart.
d.
If you wanted to make the
increase in the expenses for families with two working parents look as dramatic
as possible, what changes would you make in the graphical presentation?
I
would change the expenses for miscellaneous.
3.6
LCD
TVs, again
In Exercise 2.10, Consumer Reports
gave the prices for the top ten LCD standard definition TVs in the 14- to
20-inch category. Does the price of an
LCD TV depend on the size of the screen?
The table below shows the ten costs again, along with the screen size in
inches.
Brand
|
Price
|
Size
|
Sharp
LC-20E1U
Sony
KLV-15SR1
Panasonic
TC-20LA1
Panasonic
TC-17LA1
Gateway
GTW-L18M103
Panasonic
TC-14LA1
Gateway
GTW-L17M103
Toshiba
14VL43U
Toshiba
20VL43U
Sharp
LC-15E1U
|
$1200
800
1050
750
700
500
600
670
1200
650
|
20
15
20
17
18
14
17
14
20
15
|
a.
Which of the two variables (price
and size) is the independent variable, and which is the dependent variable?
The
independent variable is the size and the dependent is the price.
b.
Construct a scatterplot for the
data. Does the relationship appear to be
linear?
No, it does not!
3.7
LCD
TVs, continued
Refer to Exercise 3.6. Suppose we
assume that the relationship between x
and y is linear.
a.
Find the correlation coefficient,
r.
What does this value tell you about the strength and direction of the
relationship between size and price?
Positive
linear relationship.
b.
What is the equation of the
regression line used to predict the price of the TV based on the size of the
screen?
y = 85.92x - 648.7
c.
The Sony Corporation is
introducing a new 18” LCD TV. What would
you predict its price to be?
It would be more than 800 dollars.
d.
Would it be reasonable to try to
predict the price of a 30” LCD TV?
Explain.
Yes, it would be reasonable.
3.8
Movie
Money
Does the opening weekend adequately predict the success or failure of a
new movie? In a recent summer, 36 movies
were investigated in Entertainment Weekly,
and the following variables were recorded.
·
The movie’s first weekend’s gross
earnings (in millions)
·
The movie’s total gross earnings
in the United States
(in millions)
a.
How would you describe the
relationship between the first weekend’s gross and the total gross?
Positive linear – strong.
b.
Are there any outliers? If so, explain how they do not fit the
pattern of the other movies.
Yes there are outliers.
c.
Which dot represents the movie
with the best opening weekend? Did it
also have the highest total gross?
Pearl Harbor. No, since
the highest total gross was from the movie Rush Hour 2.
d.
The film Pearl Harbor opened on a
3-day weekend (Memorial Day). Does that
help to explain its position in relation to the other data points?
Yes, it would help.
3.9
Movie
Money, continued
The data from Exercise 3.8 were entered into a MINITAB
worksheet, and the following output was obtained.
Covariances: 1st
Gross, Total Gross
1st
Gross
|
Total Gross
|
|
1st
Gross
|
412.528
|
|
Total Gross
|
1232.231
|
4437.109
|
a.
Use the MINITAB output
or the original data to find the correlation between first weekend and total
gross.
b.
Which of the two variables would
you classify as the independent variable?
The dependent variable?
The independent variable is the 1st
gross and the dependent is the total gross.
c.
If the average first weekend
gross is 25.66 million dollars and the average total gross is 86.71 million
dollars, find the regression line for predicting total gross as a function of
the first weekend’s gross.
d.
If another film was released and
grossed $30 million on the first weekend, what would you predict that its total
gross earnings will be?
3.10 Brett Favre, again The number of passes completed and the total
number of passing yards were recorded for Brett Favre for each of the 16
regular season and 2 postseason games in the fall of 2003:
Week
|
Completions
|
Total
Yards
|
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
|
25
15
23
21
19
25
23
18
14
13
10
23
22
23
22
12
26
15
|
248
132
245
179
185
272
268
194
109
92
138
296
210
278
399
116
319
180
|
Source: ESPN.com
a.
Draw a scatterplot to describe
the relationship between number of completions and total passing yards for
Brett Favre.
b.
Describe the plot in part a. Do you see any outliers? Do the rest of the points seem to form a
pattern?
I see an outlier. The rest of the
points seem to form a pattern.
c.
Calculate the correlation
coefficient, r, between the number of
completions and total passing yards.
y = 13.52x - 47.76
d.
What is the regression line for
predicting total number of passing yards y
based on the total number of completions x?
e.
If Brett Favre had 20 pass
completions in his next game, what would you predict his total number of
passing yards to be?
3.11 Happy in the Air? Of the 6,229 consumer complaints against
major U.S.
airlines in a recent year, the distribution by airline is shown in the table,
along with the system wide passenger boardings (millions of passengers).
Airline
|
Number
of Complaints
|
Passengers
(millions)
|
United
American
West
Northwest
Continental
Delta
American
U.S.
Airways
Alaska
American
Eagle
Southwest
|
1172
318
765
563
1231
1212
532
129
71
236
|
68.6
19.5
52.8
40.0
89.9
94.1
47.2
14.2
11.8
72.5
|
a.
Construct a scatterplot for the
data.
b.
Describe the form, direction, and
strength of the pattern in the scatterplot.
Positive linear relationship.
c.
Are there any outliers in the
scatterplot? If so, which airline does
this outlier represent?
Yes, American Eagle Southwest airline.
d. Does
the outlier from part c indicate that this airline is doing better or worse
than the other airlines with respect to customer satisfaction?
It indicates that the airline is doing
better.
3.12 CD Players The table below shows the prices of eight
portable CD players along with their overall score (on a scale of 0-100) in a
consumer rating survey presented by Consumer
Reports.
Brand
and Model
|
Price
|
Overall
Score
|
Sony
D-EJ611
Panasonic
SL-SX280
Aiwa
XP-V713
Aiwa
XP-SP911
Panasonic
SL-CT470
Phillips
AZ9213
GPX
C3948B1
RCA
RP-2360FM
|
$80
50
70
80
100
80
60
65
|
70
66
60
65
59
60
47
42
|
a.
Calculate the correlation
coefficient r between price and
overall score. How would you describe
the relationship between price and overall score?
Xmean = 73.125
Ymean = 58.625
σx = 15.3884
σy = 9.5609
r = 0.2478
The relationship is linear.
b. Use
the applet called Correlation and the
Scatterplot to plot the eight data points.
What is the correlation coefficient shown on the applet? Compare with the value you calculated in part
a.
c.
Describe the pattern that you see
in the scatterplot. Are there any
clusters or outliers? If so, how would
you explain them?
Linear. There are outliers but not too far, the cheapest and the expensive cd players.
3.13 SAT Scores Is there a correlation between Math and
Verbal SAT test scores? That is, do
students who do well on the Math portion typically do well on the Verbal
portion of the test? The data below
(score – 400) show the average scores on standardized math and verbal tests for
seven high schools in Southern California.
School
|
Verbal
|
Math
|
Centennial
Norco
Moreno
Valley
Valley
View
Ramona
San Bernardino
Canyon
Springs
North
|
64
74
27
75
20
38
68
85
|
84
95
45
71
50
27
85
98
|
a.
Calculate the correlation
coefficient r between verbal and math
scores. How would you describe the
relationship between verbal and math scores?
Xmean = 49.67
Ymean = 62
σx = 24.3694
σy = 25.7371
r = 0.7959
The relationship is linear.
b.
Use the applet called Correlation and the Scatterplot to plot
the eight data points. What is the
correlation coefficient shown on the applet?
Compare with the value you calculated in part a.
c.
Describe the pattern that you see
in the scatterplot. Are there any
clusters or outliers? If so, how would
you explain them?
Well, it seems that these high school students are good
in math than in verbal. There are 3 outliers in the group. The reason may be is
they are not mathematically and verbally intelligent or they are better in
other subjects.
---
hahahaha!!!!!!!!!!!
I am rolling on the floor... weh?
Haahahahaha!!
My answers here are out of the question...
I want more vacation days!!!
Hmm, fine! I don't know what must be the answer.
Our instructor didn't discuss those. :(
Comment for the correct answers!
Throw me potato chips!
Throw me fruits!
Throw me rotten veggies..
If you are not satisfied..
Sweet,
LRJG
