Solution and Answer Guide: Ellingson and Panorska, Probability and Statistics for Engineering and the Sciences, 10e, 2027, 9798214023823; Chapter 1: Overview and
Descriptive Statistics
Solution and Answer Guide
ELLINGSON AND PANORSKA, PROBABILITY AND STATISTICS FOR ENGINEERING AND THE SCIENCES,
10E, 2027, 9798214023823; CHAPTER 1: OVERVIEW AND DESCRIPTIVE STATISTICS
TABLE OF CONTENTS
Section 1.1.....................................................................................................................1
Section 1.2.....................................................................................................................3
Section 1.3...................................................................................................................18
Section 1.4...................................................................................................................24
SECTION 1.1
1.
Solutions:
a. Los Angeles Times, Chicago Tribune, Gainesville Sun, Washington Post
b. France, Sweden, Denmark, Malta
c. Alice Johnson, Catherine Miller, Emma Davis, Ken Lee
d. 2.97, 3.56, 2.20, 2.97
2.
Solutions:
a. 45.3 m, 52.7 m, 60.1 m, 48.9 m
b. 432 pp, 196 pp, 184 pp, 321 pp
c. 4.5, 4.9, 5.6, 6.4
d. 0.07 g, 1.58 g, 7.1 g, 27.2 g
3.
Solutions:
a. How likely is it that more than half of the sampled computers will need or have needed warranty
service? What is the expected number among the 100 that need warranty service? How likely is it that
the number needing warranty service will exceed the expected number by more than 10?
b. Suppose that 15 of the 100 sampled needed warranty service. How confident can we be that the
proportion of all such computers needing warranty service is between .08 and .22? Does the sample
provide compelling evidence for concluding that more than 10% of all such computers need warranty
service?
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 1
accessible website, in whole or in part.
,Solution and Answer Guide: Ellingson and Panorska, Probability and Statistics for Engineering and the Sciences, 10e, 2027, 9798214023823; Chapter 1: Overview and
Descriptive Statistics
4.
Solutions:
a. Concrete populations: all living citizens of U.S., all the mutual funds currently marketed in U.S., all the
books that were published in 1980. Hypothetical populations: All GPAs of the University of California
undergraduates in the next academic year, page lengths of all books that will be published next year,
the batting averages of all major league players in the next baseball season.
b. (Concrete) Probability: In a sample of 5 mutual funds, what is the chance that all
5 have rates of return which exceeded 10% last year? Statistics: If previous year rates-of-return for 5
mutual funds were 9.6, 14.5, 8.3, 9.9 and 10.2, can we conclude that the average rate for all funds was
below 10%? (Hypothetical) Probability: In a sample of 10 books to be published next year, how likely
is it that the average number of pages for the 10 is between 200 and 250? Statistics: If the sample
average number of pages for 10 books is 227, can we be highly confident that the average for all books
is between 200 and 245?
5.
Solutions:
a. No. All students taking a large statistics course who participate in an SI program of this sort.
b. The advantage to randomly allocating students to the two groups is that the two groups should then be
fairly comparable before the study. If the two groups perform differently in the class, we might
attribute this to the treatments (SI and control). If students were allowed to choose, stronger or more
motivated students might prefer SI, which could bias the results.
c. If all students were put in the treatment group, there would be no firm basis for assessing the
effectiveness of SI (nothing to which the SI scores could reasonably be compared).
6.
Solution:
One could take a simple random sample of students from all students in the California State University
system and ask each student in the sample to report the distance from their hometown to campus.
Alternatively, the sample could be generated by taking a stratified random sample by taking a simple
random sample from each of the 23 campuses and again asking each student in the sample to report the
distance from their hometown to campus. Certain problems might arise with self-reporting of distances,
such as recording error or poor recall. This study is enumerative because there exists a finite, identifiable
population of objects from which to sample.
7.
Solution:
One could generate a simple random sample of all single-family homes in the city, or a stratified random sample
by taking a simple random sample from each of the 10 district neighborhoods. From each of the selected homes,
values of all desired variables would be determined. This is an enumerative study as there is a finite, well-defined
population of objects that can be used as a sample.
8.
Solutions:
a. Number observations equal
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 2
accessible website, in whole or in part.
,Solution and Answer Guide: Ellingson and Panorska, Probability and Statistics for Engineering and the Sciences, 10e, 2027, 9798214023823; Chapter 1: Overview and
Descriptive Statistics
b. This could be called an analytic study because the data would be collected on an existing process.
There is no sampling frame.
9.
Solutions:
a. The measurements might vary for different reasons. Some of these include measurement error resulting
from mechanical or technical changes across measurements, recording errors, differences in weather
conditions at the time of measurements, etc.
b. No, because there is no sampling frame.
SECTION 1.2
10.
Solutions:
a.
5 9
6 33588
7 00234677889
8 127
9 077 stem: ones
10 7 leaf: tenths
11 368
A representative strength for these beams is around 7.8 MPa, but there is a reasonably large amount of
variation around that representative value.
(What constitutes large or small variation usually depends on context, but variation is usually
considered large when the range of the data – the difference between the largest and smallest value – is
comparable to a representative value. Here, the range is which is similar in
size to the representative value of 7.8 MPa. So, most researchers would call this a large amount of
variation.)
b. The data display is not perfectly symmetric around some middle/representative value. There is some
positive skewness in this data.
c. Outliers are data points that appear to be very different from the pack. Looking at the stem-and-leaf
display in part (a), there appear to be no outliers in this data.
(A later section gives a more precise definition of what constitutes an outlier.)
d. From the stem-and-leaf display in part (a), there are 4 values greater than 10. Therefore, the proportion
of data values that exceed 10 is or, about 15%.
11.
Solution:
3L 1
3H 56678
4L 000112222234
4H 5667888 stem: tenths
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 3
accessible website, in whole or in part.
,Solution and Answer Guide: Ellingson and Panorska, Probability and Statistics for Engineering and the Sciences, 10e, 2027, 9798214023823; Chapter 1: Overview and
Descriptive Statistics
5L 144 leaf: hundredths
5H 58
6L 2
6H 6678
7L
7H 5
The stem-and-leaf plot shows that .45 is a good representative value for the data. It also shows that the plot
is not symmetric and it is positively skewed. The range of the data is which is comparable
to the typical value of .45. This constitutes a reasonably large amount of variation in the data. The data
value .75 is a possible outlier.
12.
Solutions:
The sample size for this data set is .
a. The first four intervals correspond to observations less than 5, so the proportion of values less than 5 is
b. The last four intervals correspond to observations at least 6, so the proportion of values at least 6 is
c. The relative frequency and density histograms are shown below. The distribution of particle
sizes is not symmetric, but are positively skewed. Notice that the relative frequency and density
histograms are essentially identical, other than the vertical axis labeling, because the bin widths are all
the same.
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 4
accessible website, in whole or in part.
Descriptive Statistics
Solution and Answer Guide
ELLINGSON AND PANORSKA, PROBABILITY AND STATISTICS FOR ENGINEERING AND THE SCIENCES,
10E, 2027, 9798214023823; CHAPTER 1: OVERVIEW AND DESCRIPTIVE STATISTICS
TABLE OF CONTENTS
Section 1.1.....................................................................................................................1
Section 1.2.....................................................................................................................3
Section 1.3...................................................................................................................18
Section 1.4...................................................................................................................24
SECTION 1.1
1.
Solutions:
a. Los Angeles Times, Chicago Tribune, Gainesville Sun, Washington Post
b. France, Sweden, Denmark, Malta
c. Alice Johnson, Catherine Miller, Emma Davis, Ken Lee
d. 2.97, 3.56, 2.20, 2.97
2.
Solutions:
a. 45.3 m, 52.7 m, 60.1 m, 48.9 m
b. 432 pp, 196 pp, 184 pp, 321 pp
c. 4.5, 4.9, 5.6, 6.4
d. 0.07 g, 1.58 g, 7.1 g, 27.2 g
3.
Solutions:
a. How likely is it that more than half of the sampled computers will need or have needed warranty
service? What is the expected number among the 100 that need warranty service? How likely is it that
the number needing warranty service will exceed the expected number by more than 10?
b. Suppose that 15 of the 100 sampled needed warranty service. How confident can we be that the
proportion of all such computers needing warranty service is between .08 and .22? Does the sample
provide compelling evidence for concluding that more than 10% of all such computers need warranty
service?
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 1
accessible website, in whole or in part.
,Solution and Answer Guide: Ellingson and Panorska, Probability and Statistics for Engineering and the Sciences, 10e, 2027, 9798214023823; Chapter 1: Overview and
Descriptive Statistics
4.
Solutions:
a. Concrete populations: all living citizens of U.S., all the mutual funds currently marketed in U.S., all the
books that were published in 1980. Hypothetical populations: All GPAs of the University of California
undergraduates in the next academic year, page lengths of all books that will be published next year,
the batting averages of all major league players in the next baseball season.
b. (Concrete) Probability: In a sample of 5 mutual funds, what is the chance that all
5 have rates of return which exceeded 10% last year? Statistics: If previous year rates-of-return for 5
mutual funds were 9.6, 14.5, 8.3, 9.9 and 10.2, can we conclude that the average rate for all funds was
below 10%? (Hypothetical) Probability: In a sample of 10 books to be published next year, how likely
is it that the average number of pages for the 10 is between 200 and 250? Statistics: If the sample
average number of pages for 10 books is 227, can we be highly confident that the average for all books
is between 200 and 245?
5.
Solutions:
a. No. All students taking a large statistics course who participate in an SI program of this sort.
b. The advantage to randomly allocating students to the two groups is that the two groups should then be
fairly comparable before the study. If the two groups perform differently in the class, we might
attribute this to the treatments (SI and control). If students were allowed to choose, stronger or more
motivated students might prefer SI, which could bias the results.
c. If all students were put in the treatment group, there would be no firm basis for assessing the
effectiveness of SI (nothing to which the SI scores could reasonably be compared).
6.
Solution:
One could take a simple random sample of students from all students in the California State University
system and ask each student in the sample to report the distance from their hometown to campus.
Alternatively, the sample could be generated by taking a stratified random sample by taking a simple
random sample from each of the 23 campuses and again asking each student in the sample to report the
distance from their hometown to campus. Certain problems might arise with self-reporting of distances,
such as recording error or poor recall. This study is enumerative because there exists a finite, identifiable
population of objects from which to sample.
7.
Solution:
One could generate a simple random sample of all single-family homes in the city, or a stratified random sample
by taking a simple random sample from each of the 10 district neighborhoods. From each of the selected homes,
values of all desired variables would be determined. This is an enumerative study as there is a finite, well-defined
population of objects that can be used as a sample.
8.
Solutions:
a. Number observations equal
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 2
accessible website, in whole or in part.
,Solution and Answer Guide: Ellingson and Panorska, Probability and Statistics for Engineering and the Sciences, 10e, 2027, 9798214023823; Chapter 1: Overview and
Descriptive Statistics
b. This could be called an analytic study because the data would be collected on an existing process.
There is no sampling frame.
9.
Solutions:
a. The measurements might vary for different reasons. Some of these include measurement error resulting
from mechanical or technical changes across measurements, recording errors, differences in weather
conditions at the time of measurements, etc.
b. No, because there is no sampling frame.
SECTION 1.2
10.
Solutions:
a.
5 9
6 33588
7 00234677889
8 127
9 077 stem: ones
10 7 leaf: tenths
11 368
A representative strength for these beams is around 7.8 MPa, but there is a reasonably large amount of
variation around that representative value.
(What constitutes large or small variation usually depends on context, but variation is usually
considered large when the range of the data – the difference between the largest and smallest value – is
comparable to a representative value. Here, the range is which is similar in
size to the representative value of 7.8 MPa. So, most researchers would call this a large amount of
variation.)
b. The data display is not perfectly symmetric around some middle/representative value. There is some
positive skewness in this data.
c. Outliers are data points that appear to be very different from the pack. Looking at the stem-and-leaf
display in part (a), there appear to be no outliers in this data.
(A later section gives a more precise definition of what constitutes an outlier.)
d. From the stem-and-leaf display in part (a), there are 4 values greater than 10. Therefore, the proportion
of data values that exceed 10 is or, about 15%.
11.
Solution:
3L 1
3H 56678
4L 000112222234
4H 5667888 stem: tenths
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 3
accessible website, in whole or in part.
,Solution and Answer Guide: Ellingson and Panorska, Probability and Statistics for Engineering and the Sciences, 10e, 2027, 9798214023823; Chapter 1: Overview and
Descriptive Statistics
5L 144 leaf: hundredths
5H 58
6L 2
6H 6678
7L
7H 5
The stem-and-leaf plot shows that .45 is a good representative value for the data. It also shows that the plot
is not symmetric and it is positively skewed. The range of the data is which is comparable
to the typical value of .45. This constitutes a reasonably large amount of variation in the data. The data
value .75 is a possible outlier.
12.
Solutions:
The sample size for this data set is .
a. The first four intervals correspond to observations less than 5, so the proportion of values less than 5 is
b. The last four intervals correspond to observations at least 6, so the proportion of values at least 6 is
c. The relative frequency and density histograms are shown below. The distribution of particle
sizes is not symmetric, but are positively skewed. Notice that the relative frequency and density
histograms are essentially identical, other than the vertical axis labeling, because the bin widths are all
the same.
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 4
accessible website, in whole or in part.
