,Contents
1. Introduction .................................................................................................................................... 1
2. Descriptive Statistics ..................................................................................................................... 5
3. Probability .................................................................................................................................... 27
4. Discrete Random Variables .......................................................................................................... 43
5. Continuous Random Variables..................................................................................................... 63
6. Bivariate Probability Distributions and Sampling Distributions .....................................................97
7. Estimation Using Confidence Intervals ...................................................................................... 131
8. Tests of Hypotheses .................................................................................................................... 157
9. Categorical Data Analysis ........................................................................................................... 185
10. Simple Linear Regression..............................................................................................................205
11. Multiple Regression Analysis ........................................................................................................ 245
12. Model Building............................................................................................................................. 295
13. Principles of Experimental Design.............................................................................................. 327
14. The Analysis of Variance for Designed Experiments ................................................................... 331
15. Nonparametric Statistics ............................................................................................................. 373
16. Statistical Process and Quality Control ........................................................................................403
17. Product and System Reliability .....................................................................................................433
Appendix A: Matrix Algebra ................................................................................................................. 449
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,1
Introduction
1.1 a. The population of interest to the researchers is the population of all young women who
recently participated in a STEM program.
b. The sample is the set of 159 young women who were recruited to complete an on-line survey.
c. We could infer that approximately 27% of all young women who recently participated in a
STEM program felt that participation in the STEM program increased their interest in science.
1.3 There are two populations – male students at Griffin University who were video game
players and male students at Griffin University who were not video game players. There
were two samples — those male students in the 65 chosen who were video game players and
those male students in the 65 chosen who were not video game players.
1.5 a. The experimental units for this study are the earthquakes.
b. The data from the 15 earthquakes represent a sample. There are many more than 15
earthquakes from around the world. Only 15 of the many were studied.
1.7 a. The variable measured is the level of carbon monoxide gas in the atmosphere. The experimental
unit is the atmosphere at the Cold Bay, Alaska, weather sta- tion each week.
b. If we are interested in only the weekly carbon monoxide values at the Cold Bay station for
the years 2000-2002, then this data represents the population because all that data were
collected.
1.9 a. Sampling method would be qualitative.
b. Effective stress level would be quantitative.
c. Damping ratio would be quantitative.
1.11 a. Town where sample was collected is qualitative.
b. Type of water supply is qualitative.
c. Acidic level is quantitative.
d. Turbidity level is quantitative.
e. Temperature is quantitative.
f. Number of fecal coliforms per 100 milliliters is quantitative.
g. Free chlorine-residual is quantitative.
h. Presence of hydrogen sulfide is qualitative.
1.13 a. The experimental units are the smokers.
b. Two variables measured on each smoker are screening method and age at which
scanning method first detects a tumor.
c. Screening method is qualitative and age is quantitative.
d. The inference is which screening method (CT or X-ray) is more effective in pinpointing
small tumors.
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,2 Statistics for Engineering and the Sciences, Sixth Edition Student Solutions Manual
1.15 Answers will vary. First, we number the wells from 1 to 223. We will use Table 1, Appendix B to select
the sample of 5. Start in column 8, row 11, and look at the first 3 digits. We proceed down the
column until we select 5 numbers between 1 and 223: 58, 176, 136, 47, and 153. Thus, wells
numbered 47, 58, 136, 153, and 176 will be selected.
1.17 Answers will vary. First, we number the weeks from 1 to 590. Using the MINITAB random sample
procedure, the following sample is selected:
Weeks Sample Weeks Sample
1 568 9 192
2 584 10 590
3 329 11 81
4 379 12 67
5 54 13 230
6 104 14 56
7 171 15 154
8 439
The 15 weeks with the numbers listed in the Sample column will be selected.
1.19 a. The population of interest is all computer security personnel at all U.S. corpo- rations and
government agencies.
b. The data-collection method is a survey of 5,412 firms. Only 351 computer secu- rity personnel
responded. Since this was a survey, the computer security person- nel elected to either respond
or not. Because only 351 of the 5,412 firms survey responded, there could be a nonresponse
bias. In addition, the security person- nel chose whether to respond or not.
c. The variable measured is whether or not unauthorized use of the computer sys- tem occurred at
the firm during the year. This variable is qualitative because the response would be yes or no.
d. Because 41% of the sample admitted that there was unauthorized use of their computer
system, we can infer that approximately 41% of all firms had unau- thorized use of their
computer systems during the year.
1.21 First, suppose we number all of the intersections from 1 to 5,000. Then, we will use a random
number generator to select 50 numbers between 1 and 5,000. The intersections with the 50
numbers selected will then be used for digging.
Second, we will number the rows from 1 to 100 and the columns from 1 to 50. We will then
use a random number generator to select 50 rows from 1 to 100 (rows can be selected more
than once) and 50 columns from 1 to 50 (columns can be selected more than once). We will
then combine the rows and columns
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,Introduction 3
selected to get the intersections used for the digs. For instance, the first row selected might
be row 10 and the first column selected might be 47. Then the intersection of row 10 and
column 47 will be the first intersection selected.
1.23 a. The population of interest is the set of all computer components (e.g. the hard disk drives).
b. The sample is the 100 computer components tested.
c. The data are quantitative because the lifelength of the component is a numeri- cal value.
d. The mean lifelength of the computer components tested could be used to esti- mate the mean
lifelength of all computer components.
1.25 a. The experimental units are the 2-ml portions of the newly developed cleaning solution.
b. The variable measured is the amount of hydrochloric acid necessary to achieve neutrality of 2-
ml of the newly developed cleaning solution.
c. The population of interest is the set of all amounts of hydrochloric acid neces- sary to
neutralize all 2-ml portions of the newly developed cleaning solution.
d. The sample is the set of amounts of hydrochloric acid necessary to neutralize the five 2-ml
portions of the newly developed cleaning solution.
1.27 a. The experimental units are the undergraduate engineering students at Penn State.
b. The population of interest is the set of all undergraduate engineering at Penn State. The
sample is the set of 21 undergraduate engineering students in a first- year, project-based design
course.
c. The data collected are the Perry scores which are quantitative.
d. We estimate that the mean Perry score for all undergraduate engineering stu- dents at Penn
State is 3.27.
e. Answers will vary. First, we number the students from 1 to 21. Using the MINITAB
random sample procedure, the following sample is selected:
Aftershock Sample
1 14
2 3
3 16
The 3 students with the numbers listed in the Sample column will be selected.
1.29 a. The variable of interest is the status of bridges in the United States.
b. The variable is qualitative with values structurally deficient, functionally obsolete, and
safe.
c. The data set is a population since all of the bridges in the United States were inspected.
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,4 Statistics for Engineering and the Sciences, Sixth Edition Student Solutions Manual
d. The data for the study were obtained from the FHWA inspection ratings.
e. Answers will vary. First, number the bridges from 1 to 600,000. Using the MINITAB
random sample procedure, the following sample is selected:
Sample Sample
369,891 69,324
481,030 28,952
58,902 365,481
301,594 187,834
538,562 569,846
255,565 566,258
350,835 250,030
267,191 325,747
470,533 528,693
482,519 400,430
403,882 252,044
202,888 191,159
360,439
The 25 bridges with the numbers listed in the Sample column will be selected.
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,2
Descriptive Statistics
2.1 a. The graph used is a bar chart.
b. The variable measured is the type of robotic limbs on social robots.
c. The social robot design that is currently used the most is legs only.
d. The relative frequencies are found by dividing the frequencies by the sample size, n 106.
Robotic Limbs Frequency Relative Frequency
None 15 15/106 = 0.1415
Both 8 8/106 = 0.0755
Legs only 63 63/106 = 0.5943
Wheels only 20 20/106 = 0.1887
e. Using MINITAB, the Pareto chart is:
60
50
40
Percent
30
20
10
0
Legs only Wheels only None Both
Robotic Limbs
2.3 Using MINITAB, the pie chart is:
Pie Chart of Location
Rural
5.7%
Category
Urban
Suburban
Rural
Suburban
32.8%
Urban
61.5%
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,6 Statistics for Engineering and the Sciences, Sixth Edition Student Solutions Manual
The majority of young women who recently participated in a STEM program are from urban
areas (61.5%) and very few are from rural areas (5.7%).
2.5 a. The variable beach condition is qualitative, nearshore bar condition is qualita- tive, and long-
term erosion rate is quantitative.
b. Using MINITAB, the pie chart for beach condition is:
Pie Chart of Beach Condition
Bluff/scarp
16.7% Category
Single dune
Bluff/scarp
33.3%
No dunes/flat
Not observed
Single dune
No dunes/flat
33.3%
Not observed
16.7%
c. Using MINITAB, the pie chart of nearshore bar condition is:
Pie Chart of Nearshore Bar Condition
Other
Single/parallel 33.3%
33.3% Category
Other
Planar
Single/parallel
Planar
33.3%
d. The sample size for this study is only 6. It would be very risky to use the information
from this sample to make inferences about all beach hotspots. The data were collected using
an online questionnaire. It is very doubtful that this sample is representative of the population
of all beach hot spots.
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,Descriptive Statistics 7
2.7 Using MINITAB, pie charts to compare the two ownership sectors of LEO and GEO satellites
are:
Pie Chart of Satellites
Category
LEO GEO
Government
Civil Civil Military
9.2% 0.2% Government Commercial
13.7% Civil
Government
Commerical 45.6%
23.5% Military
21.1%
Military Commerical
21.7% 65.0%
Most LEO satellites are owned by entities in the government (45.6%) while most GEO
satellites are owned by entities in the commercial sector (65.0%). The fewest percentage of
LEO satellites are owned by entities in the civil sec- tor (9.2%). The fewest percentage of GEO
satellites are also owned by entities in the civil sector (0.2%), but the percentage is much smaller
than that for the LEO satellites.
2.9 a. Using MINITAB, the Pareto chart is:
16
14
12
10
Percent
8
6
4
2
0
6 1 4 7 3 2 5 8 9
First Digit
Percent is calculated within all data.
b. Yes and no. The graph does support Benford’s Law in that certain digits are more likely to
occur than others. In this set of data, the number 6 occurs first 15.7% of the time while
the number 9 occurs first only 5.8% of the time. However, Benford’s Law also states that
the number 1 is the most likely to occur at 30% of the time. In this set of data, the number
1 is not the most fre- quent number to occur first, and it also only occurs as the first significant
digit 14.7% of the time, not the 30% specified by Benford’s Law.
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TO DOWNLOAD THE FULL PDF
CLICK ON THE L.I.N.K
ON THE NEXT PAGE
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1. Introduction .................................................................................................................................... 1
2. Descriptive Statistics ..................................................................................................................... 5
3. Probability .................................................................................................................................... 27
4. Discrete Random Variables .......................................................................................................... 43
5. Continuous Random Variables..................................................................................................... 63
6. Bivariate Probability Distributions and Sampling Distributions .....................................................97
7. Estimation Using Confidence Intervals ...................................................................................... 131
8. Tests of Hypotheses .................................................................................................................... 157
9. Categorical Data Analysis ........................................................................................................... 185
10. Simple Linear Regression..............................................................................................................205
11. Multiple Regression Analysis ........................................................................................................ 245
12. Model Building............................................................................................................................. 295
13. Principles of Experimental Design.............................................................................................. 327
14. The Analysis of Variance for Designed Experiments ................................................................... 331
15. Nonparametric Statistics ............................................................................................................. 373
16. Statistical Process and Quality Control ........................................................................................403
17. Product and System Reliability .....................................................................................................433
Appendix A: Matrix Algebra ................................................................................................................. 449
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,1
Introduction
1.1 a. The population of interest to the researchers is the population of all young women who
recently participated in a STEM program.
b. The sample is the set of 159 young women who were recruited to complete an on-line survey.
c. We could infer that approximately 27% of all young women who recently participated in a
STEM program felt that participation in the STEM program increased their interest in science.
1.3 There are two populations – male students at Griffin University who were video game
players and male students at Griffin University who were not video game players. There
were two samples — those male students in the 65 chosen who were video game players and
those male students in the 65 chosen who were not video game players.
1.5 a. The experimental units for this study are the earthquakes.
b. The data from the 15 earthquakes represent a sample. There are many more than 15
earthquakes from around the world. Only 15 of the many were studied.
1.7 a. The variable measured is the level of carbon monoxide gas in the atmosphere. The experimental
unit is the atmosphere at the Cold Bay, Alaska, weather sta- tion each week.
b. If we are interested in only the weekly carbon monoxide values at the Cold Bay station for
the years 2000-2002, then this data represents the population because all that data were
collected.
1.9 a. Sampling method would be qualitative.
b. Effective stress level would be quantitative.
c. Damping ratio would be quantitative.
1.11 a. Town where sample was collected is qualitative.
b. Type of water supply is qualitative.
c. Acidic level is quantitative.
d. Turbidity level is quantitative.
e. Temperature is quantitative.
f. Number of fecal coliforms per 100 milliliters is quantitative.
g. Free chlorine-residual is quantitative.
h. Presence of hydrogen sulfide is qualitative.
1.13 a. The experimental units are the smokers.
b. Two variables measured on each smoker are screening method and age at which
scanning method first detects a tumor.
c. Screening method is qualitative and age is quantitative.
d. The inference is which screening method (CT or X-ray) is more effective in pinpointing
small tumors.
@
@sseeisismmicicisisoolalatitoionn 1
,2 Statistics for Engineering and the Sciences, Sixth Edition Student Solutions Manual
1.15 Answers will vary. First, we number the wells from 1 to 223. We will use Table 1, Appendix B to select
the sample of 5. Start in column 8, row 11, and look at the first 3 digits. We proceed down the
column until we select 5 numbers between 1 and 223: 58, 176, 136, 47, and 153. Thus, wells
numbered 47, 58, 136, 153, and 176 will be selected.
1.17 Answers will vary. First, we number the weeks from 1 to 590. Using the MINITAB random sample
procedure, the following sample is selected:
Weeks Sample Weeks Sample
1 568 9 192
2 584 10 590
3 329 11 81
4 379 12 67
5 54 13 230
6 104 14 56
7 171 15 154
8 439
The 15 weeks with the numbers listed in the Sample column will be selected.
1.19 a. The population of interest is all computer security personnel at all U.S. corpo- rations and
government agencies.
b. The data-collection method is a survey of 5,412 firms. Only 351 computer secu- rity personnel
responded. Since this was a survey, the computer security person- nel elected to either respond
or not. Because only 351 of the 5,412 firms survey responded, there could be a nonresponse
bias. In addition, the security person- nel chose whether to respond or not.
c. The variable measured is whether or not unauthorized use of the computer sys- tem occurred at
the firm during the year. This variable is qualitative because the response would be yes or no.
d. Because 41% of the sample admitted that there was unauthorized use of their computer
system, we can infer that approximately 41% of all firms had unau- thorized use of their
computer systems during the year.
1.21 First, suppose we number all of the intersections from 1 to 5,000. Then, we will use a random
number generator to select 50 numbers between 1 and 5,000. The intersections with the 50
numbers selected will then be used for digging.
Second, we will number the rows from 1 to 100 and the columns from 1 to 50. We will then
use a random number generator to select 50 rows from 1 to 100 (rows can be selected more
than once) and 50 columns from 1 to 50 (columns can be selected more than once). We will
then combine the rows and columns
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,Introduction 3
selected to get the intersections used for the digs. For instance, the first row selected might
be row 10 and the first column selected might be 47. Then the intersection of row 10 and
column 47 will be the first intersection selected.
1.23 a. The population of interest is the set of all computer components (e.g. the hard disk drives).
b. The sample is the 100 computer components tested.
c. The data are quantitative because the lifelength of the component is a numeri- cal value.
d. The mean lifelength of the computer components tested could be used to esti- mate the mean
lifelength of all computer components.
1.25 a. The experimental units are the 2-ml portions of the newly developed cleaning solution.
b. The variable measured is the amount of hydrochloric acid necessary to achieve neutrality of 2-
ml of the newly developed cleaning solution.
c. The population of interest is the set of all amounts of hydrochloric acid neces- sary to
neutralize all 2-ml portions of the newly developed cleaning solution.
d. The sample is the set of amounts of hydrochloric acid necessary to neutralize the five 2-ml
portions of the newly developed cleaning solution.
1.27 a. The experimental units are the undergraduate engineering students at Penn State.
b. The population of interest is the set of all undergraduate engineering at Penn State. The
sample is the set of 21 undergraduate engineering students in a first- year, project-based design
course.
c. The data collected are the Perry scores which are quantitative.
d. We estimate that the mean Perry score for all undergraduate engineering stu- dents at Penn
State is 3.27.
e. Answers will vary. First, we number the students from 1 to 21. Using the MINITAB
random sample procedure, the following sample is selected:
Aftershock Sample
1 14
2 3
3 16
The 3 students with the numbers listed in the Sample column will be selected.
1.29 a. The variable of interest is the status of bridges in the United States.
b. The variable is qualitative with values structurally deficient, functionally obsolete, and
safe.
c. The data set is a population since all of the bridges in the United States were inspected.
@
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,4 Statistics for Engineering and the Sciences, Sixth Edition Student Solutions Manual
d. The data for the study were obtained from the FHWA inspection ratings.
e. Answers will vary. First, number the bridges from 1 to 600,000. Using the MINITAB
random sample procedure, the following sample is selected:
Sample Sample
369,891 69,324
481,030 28,952
58,902 365,481
301,594 187,834
538,562 569,846
255,565 566,258
350,835 250,030
267,191 325,747
470,533 528,693
482,519 400,430
403,882 252,044
202,888 191,159
360,439
The 25 bridges with the numbers listed in the Sample column will be selected.
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,2
Descriptive Statistics
2.1 a. The graph used is a bar chart.
b. The variable measured is the type of robotic limbs on social robots.
c. The social robot design that is currently used the most is legs only.
d. The relative frequencies are found by dividing the frequencies by the sample size, n 106.
Robotic Limbs Frequency Relative Frequency
None 15 15/106 = 0.1415
Both 8 8/106 = 0.0755
Legs only 63 63/106 = 0.5943
Wheels only 20 20/106 = 0.1887
e. Using MINITAB, the Pareto chart is:
60
50
40
Percent
30
20
10
0
Legs only Wheels only None Both
Robotic Limbs
2.3 Using MINITAB, the pie chart is:
Pie Chart of Location
Rural
5.7%
Category
Urban
Suburban
Rural
Suburban
32.8%
Urban
61.5%
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,6 Statistics for Engineering and the Sciences, Sixth Edition Student Solutions Manual
The majority of young women who recently participated in a STEM program are from urban
areas (61.5%) and very few are from rural areas (5.7%).
2.5 a. The variable beach condition is qualitative, nearshore bar condition is qualita- tive, and long-
term erosion rate is quantitative.
b. Using MINITAB, the pie chart for beach condition is:
Pie Chart of Beach Condition
Bluff/scarp
16.7% Category
Single dune
Bluff/scarp
33.3%
No dunes/flat
Not observed
Single dune
No dunes/flat
33.3%
Not observed
16.7%
c. Using MINITAB, the pie chart of nearshore bar condition is:
Pie Chart of Nearshore Bar Condition
Other
Single/parallel 33.3%
33.3% Category
Other
Planar
Single/parallel
Planar
33.3%
d. The sample size for this study is only 6. It would be very risky to use the information
from this sample to make inferences about all beach hotspots. The data were collected using
an online questionnaire. It is very doubtful that this sample is representative of the population
of all beach hot spots.
@
@sseeisismmicicisisoolalatitoionn
,Descriptive Statistics 7
2.7 Using MINITAB, pie charts to compare the two ownership sectors of LEO and GEO satellites
are:
Pie Chart of Satellites
Category
LEO GEO
Government
Civil Civil Military
9.2% 0.2% Government Commercial
13.7% Civil
Government
Commerical 45.6%
23.5% Military
21.1%
Military Commerical
21.7% 65.0%
Most LEO satellites are owned by entities in the government (45.6%) while most GEO
satellites are owned by entities in the commercial sector (65.0%). The fewest percentage of
LEO satellites are owned by entities in the civil sec- tor (9.2%). The fewest percentage of GEO
satellites are also owned by entities in the civil sector (0.2%), but the percentage is much smaller
than that for the LEO satellites.
2.9 a. Using MINITAB, the Pareto chart is:
16
14
12
10
Percent
8
6
4
2
0
6 1 4 7 3 2 5 8 9
First Digit
Percent is calculated within all data.
b. Yes and no. The graph does support Benford’s Law in that certain digits are more likely to
occur than others. In this set of data, the number 6 occurs first 15.7% of the time while
the number 9 occurs first only 5.8% of the time. However, Benford’s Law also states that
the number 1 is the most likely to occur at 30% of the time. In this set of data, the number
1 is not the most fre- quent number to occur first, and it also only occurs as the first significant
digit 14.7% of the time, not the 30% specified by Benford’s Law.
@
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, THOSE WERE PREVIEW PAGES
TO DOWNLOAD THE FULL PDF
CLICK ON THE L.I.N.K
ON THE NEXT PAGE
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