TestBank ForProbabilityAnd StatisticsForEngineering And
s ss s s ss s s ss
, ss The Sciences 8th Ed by Jay L. Devore.
ss ss ss ss ss ss ss
Chapter 1 – Overview and Descriptive Statistics
ss ss ss ss ss ss
SHORT ANSWER
s s
1. Give one possible sample of size 4 from each of the following populations:
s s s s s s s s s s s s s s s s s s s s s s s s
a. All daily newspapers published in the United States
s s s s s s s s s s s s s s
b. All companies listed on the New York Stock Exchange
s s s s s s s s s s s s s s s s
c. All students at your college or university
s s s s s s s s s s s s
d. All grade point averages of students at your college or university
s s s s s s s s s s s s s s s s s s s s
ANS:
a. Houston Chronicle, Des Moines Register, Chicago Tribune, Washington Post
s s s s ss s s s s s s ss s s
b. Capital One, Campbell Soup, Merrill Lynch, Pulitzer
s s s s s s s s s s s s
c. John Anderson, Emily Black, Bill Carter, Kay Davis
s s s s s s s s s s s s
d. 2.58. 2.96, 3.51, 3.69 s s s s s s
PTS: 1
2. A Southern State University system consists of 23 campuses.
s s s s An administrator wishes to
s s s s s s s s s s s s s s s s s s s s
s s make an inference about the average distance between the hometowns of students and their
s s s s s s s s s s s s s s s s s s s s s s s s s s
s s campuses. Describe and discuss several different sampling methods that might be employed.
s s s s ss s s s s s s s s s s s s s s s s
s s Would this be an enumerative or an analytic study? Explain your reasoning.
s s s s s s s s s s s s ss s s s s s s s s
ANS:
One could take a simple random sample of students from all students in the California State
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
University system and ask each student in the sample to report the distance from their
s s ss s s s s s s s s s s s s s s s s s s s s s s s s s s
hometown to campus.
s s s s s s
Alternatively, the sample could be generated by taking a stratified random sample by taking
s s s s s s s s s s s s s s s s s s s s s s s s s s
a simple random sample from each of the 23 campuses and again asking each student in
s s s s ss s s s s s s s s s s s s s s s s s s s s s s s s s s
the sample to report the distance from their hometown to campus.
s s s s s s s s s s ss s s s s s s s s s s
Certain problems might arise with self reporting of distances, such as recording error or poor
s s s s s s s s s s s s s s s s s s s s s s s s s s s s
recall. This study is enumerative because there exists a finite, identifiable population of
s s s s ss s s s s s s s s s s s s s s s s s s s s
objects from which to sample.
s s s s s s s s s s
PTS: 1
3. A Michigan city divides naturally into ten district neighborhoods. How might a real estate
s s s s s s s s s s s s s s s s s s s s s s s s s s
s s appraiser select a sample of single-family homes that could be used as a basis for
s s ss s s s s s s s s s s s s s s s s s s s s s s s s
s s developing an equation to predict appraised value from characteristics such as age, size,
s s s s s s s s ss s s s s s s s s s s s s s s
s s number of bathrooms, and distance to the nearest school, and so on? Is the study
s s s s s s s s s s s s s s ss s s s s s s s s s s
s s enumerative or analytic? s s s s
ANS:
One could generate a simple random sample of all single family homes in the city or a
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
stratified random sample by taking a simple random sample from each of the 10 district
s s s s ss s s s s s s s s s s s s s s s s s s s s s s s s
neighborhoods. From each of the homes in the sample the necessary variables would be
s s s s s s s s s s ss s s s s s s s s s s s s s s s s
collected. This would be an enumerative study because there exists a finite, identifiable
s s s s s s s s s s s s s s ss s s s s s s s s s s
population of objects from which to sample.
s s s s s s s s s s s s s s
, PTS: 1
4. An experiment was carried out to study how flow rate through a solenoid valve in an
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
s s automobile‘s pollution-control system depended on three factors:
ss armature lengths, spring s s s s s s s s s s s s s s
s s load, and bobbin depth. Two different levels (low and high) of each factor were chosen,
s s s s s s ss s s s s s s s s s s s s s s s s s s s s
s s and a single observation on flow was made for each combination of levels.
s s s s s s s s s s s s ss s s s s s s s s s s
a. The resulting data set consisted of how many observations?
ss s s s s s s s s s s s s s s
b. Is this an enumerative or analytic study? Explain your reasoning.
s s s s s s s s ss s s s s s s s s
ANS:
a. Number observations equal 22 2=8 s s s s s s
b. This could be called an analytic study because the data would be collected
s s s s s s s s s s s s s s s s s s s s s s s s
s s on an existing process. There is no sampling frame.
s s s s ss s s s s s s s s s s
PTS: 1
5. The accompanying data specific gravity values for various wood types used in construction .
s s s s s s s s s s s s s s s s s s s s s s s s s s
.41 .41 .42 .42. .42 .42 .42 .43 .44
.54 .55 .58 .62 .66 .66 .67 .68 .75
.31 .35 .36 .36 .37 .38 .40 .40 .40
.45 .46 .46 .47 .48 .48 .48 .51 .54
Construct a stem-and-leaf display using repeated stems and comment on any interesting features of the
s s s s s s s s s s s s s s s s s s s s s s s s s s s s
display.
s s
ANS:
One method of denoting the pairs of stems having equal values is to denote the stem by
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
L, for ‗low‘ and the second stem by H, for ‗high‘.
s s s s s s Using this notation, the stem-and-leaf
s s ss s s s s s s s s s s s s s s s s s s s s
display would appear as follows:
s s s s s s s s s s
3L 1 stem:
tenths s s
3H 56678 leaf: hundredths
4L 000112222234
5L 144
5H 58
6L 2
6H 6678
7L
7H s s 5
The stem-and-leaf display on the previous page shows that .45 is a good representative value
s s s s s s s s s s s s s s s s s s s s s s s s s s s s
for the data. In addition, the display is not symmetric and appears to be positively
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
skewed. s s The spread of the s s s s s s
data is s s s s
.75 - .31 = .44, which is .44/.45 = .978 or about 98% of the typical value of .45.
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
This constitutes a reasonably large amount of s s s s ss s s s s s s
variation in the data.
s s The data value .75 is a possible outlier.
s s s s s s s s s s s s s s s s s s s s
PTS: 1
6. Temperature transducers of a certain type are shipped in batches of 50. A sample of 60
s s s s s s s s s s s s s s s s s s s s s s s s s s s s
s s batches was selected, and the number of transducers in each batch not conforming to
s s ss s s s s s s s s s s s s s s s s s s s s s s
s s design specifications was determined, resulting in the following data:
s s s s ss s s s s s s s s s s
0 4 2 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
1 3
2 1 2 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
, 4 0
5 0 2 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3
3 2
s ss s s ss s s ss
, ss The Sciences 8th Ed by Jay L. Devore.
ss ss ss ss ss ss ss
Chapter 1 – Overview and Descriptive Statistics
ss ss ss ss ss ss
SHORT ANSWER
s s
1. Give one possible sample of size 4 from each of the following populations:
s s s s s s s s s s s s s s s s s s s s s s s s
a. All daily newspapers published in the United States
s s s s s s s s s s s s s s
b. All companies listed on the New York Stock Exchange
s s s s s s s s s s s s s s s s
c. All students at your college or university
s s s s s s s s s s s s
d. All grade point averages of students at your college or university
s s s s s s s s s s s s s s s s s s s s
ANS:
a. Houston Chronicle, Des Moines Register, Chicago Tribune, Washington Post
s s s s ss s s s s s s ss s s
b. Capital One, Campbell Soup, Merrill Lynch, Pulitzer
s s s s s s s s s s s s
c. John Anderson, Emily Black, Bill Carter, Kay Davis
s s s s s s s s s s s s
d. 2.58. 2.96, 3.51, 3.69 s s s s s s
PTS: 1
2. A Southern State University system consists of 23 campuses.
s s s s An administrator wishes to
s s s s s s s s s s s s s s s s s s s s
s s make an inference about the average distance between the hometowns of students and their
s s s s s s s s s s s s s s s s s s s s s s s s s s
s s campuses. Describe and discuss several different sampling methods that might be employed.
s s s s ss s s s s s s s s s s s s s s s s
s s Would this be an enumerative or an analytic study? Explain your reasoning.
s s s s s s s s s s s s ss s s s s s s s s
ANS:
One could take a simple random sample of students from all students in the California State
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
University system and ask each student in the sample to report the distance from their
s s ss s s s s s s s s s s s s s s s s s s s s s s s s s s
hometown to campus.
s s s s s s
Alternatively, the sample could be generated by taking a stratified random sample by taking
s s s s s s s s s s s s s s s s s s s s s s s s s s
a simple random sample from each of the 23 campuses and again asking each student in
s s s s ss s s s s s s s s s s s s s s s s s s s s s s s s s s
the sample to report the distance from their hometown to campus.
s s s s s s s s s s ss s s s s s s s s s s
Certain problems might arise with self reporting of distances, such as recording error or poor
s s s s s s s s s s s s s s s s s s s s s s s s s s s s
recall. This study is enumerative because there exists a finite, identifiable population of
s s s s ss s s s s s s s s s s s s s s s s s s s s
objects from which to sample.
s s s s s s s s s s
PTS: 1
3. A Michigan city divides naturally into ten district neighborhoods. How might a real estate
s s s s s s s s s s s s s s s s s s s s s s s s s s
s s appraiser select a sample of single-family homes that could be used as a basis for
s s ss s s s s s s s s s s s s s s s s s s s s s s s s
s s developing an equation to predict appraised value from characteristics such as age, size,
s s s s s s s s ss s s s s s s s s s s s s s s
s s number of bathrooms, and distance to the nearest school, and so on? Is the study
s s s s s s s s s s s s s s ss s s s s s s s s s s
s s enumerative or analytic? s s s s
ANS:
One could generate a simple random sample of all single family homes in the city or a
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
stratified random sample by taking a simple random sample from each of the 10 district
s s s s ss s s s s s s s s s s s s s s s s s s s s s s s s
neighborhoods. From each of the homes in the sample the necessary variables would be
s s s s s s s s s s ss s s s s s s s s s s s s s s s s
collected. This would be an enumerative study because there exists a finite, identifiable
s s s s s s s s s s s s s s ss s s s s s s s s s s
population of objects from which to sample.
s s s s s s s s s s s s s s
, PTS: 1
4. An experiment was carried out to study how flow rate through a solenoid valve in an
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
s s automobile‘s pollution-control system depended on three factors:
ss armature lengths, spring s s s s s s s s s s s s s s
s s load, and bobbin depth. Two different levels (low and high) of each factor were chosen,
s s s s s s ss s s s s s s s s s s s s s s s s s s s s
s s and a single observation on flow was made for each combination of levels.
s s s s s s s s s s s s ss s s s s s s s s s s
a. The resulting data set consisted of how many observations?
ss s s s s s s s s s s s s s s
b. Is this an enumerative or analytic study? Explain your reasoning.
s s s s s s s s ss s s s s s s s s
ANS:
a. Number observations equal 22 2=8 s s s s s s
b. This could be called an analytic study because the data would be collected
s s s s s s s s s s s s s s s s s s s s s s s s
s s on an existing process. There is no sampling frame.
s s s s ss s s s s s s s s s s
PTS: 1
5. The accompanying data specific gravity values for various wood types used in construction .
s s s s s s s s s s s s s s s s s s s s s s s s s s
.41 .41 .42 .42. .42 .42 .42 .43 .44
.54 .55 .58 .62 .66 .66 .67 .68 .75
.31 .35 .36 .36 .37 .38 .40 .40 .40
.45 .46 .46 .47 .48 .48 .48 .51 .54
Construct a stem-and-leaf display using repeated stems and comment on any interesting features of the
s s s s s s s s s s s s s s s s s s s s s s s s s s s s
display.
s s
ANS:
One method of denoting the pairs of stems having equal values is to denote the stem by
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
L, for ‗low‘ and the second stem by H, for ‗high‘.
s s s s s s Using this notation, the stem-and-leaf
s s ss s s s s s s s s s s s s s s s s s s s s
display would appear as follows:
s s s s s s s s s s
3L 1 stem:
tenths s s
3H 56678 leaf: hundredths
4L 000112222234
5L 144
5H 58
6L 2
6H 6678
7L
7H s s 5
The stem-and-leaf display on the previous page shows that .45 is a good representative value
s s s s s s s s s s s s s s s s s s s s s s s s s s s s
for the data. In addition, the display is not symmetric and appears to be positively
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
skewed. s s The spread of the s s s s s s
data is s s s s
.75 - .31 = .44, which is .44/.45 = .978 or about 98% of the typical value of .45.
s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s
This constitutes a reasonably large amount of s s s s ss s s s s s s
variation in the data.
s s The data value .75 is a possible outlier.
s s s s s s s s s s s s s s s s s s s s
PTS: 1
6. Temperature transducers of a certain type are shipped in batches of 50. A sample of 60
s s s s s s s s s s s s s s s s s s s s s s s s s s s s
s s batches was selected, and the number of transducers in each batch not conforming to
s s ss s s s s s s s s s s s s s s s s s s s s s s
s s design specifications was determined, resulting in the following data:
s s s s ss s s s s s s s s s s
0 4 2 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
1 3
2 1 2 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
, 4 0
5 0 2 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3
3 2
