. Test Bank For Probability And Statistics For Engineering
And The Sciences 9th Ed by Jay L. Devore
Chapter 1 – Overview and Descriptive Statistics
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SHORT ANSWER
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1. Give one possible sample of size 4 from each of the following populations:
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a. All daily newspapers published in the United States w w w w w w w
b. All companies listed on the New York Stock Exchange w w w w w w w w
c. All students at your college or university w w w w w w
d. All grade point averages of students at your college or university
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ANS:
a. Houston Chronicle, Des Moines Register, Chicago Tribune, Washington Post
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b. Capital One, Campbell Soup, Merrill Lynch, Pulitzer
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c. John Anderson, Emily Black, Bill Carter, Kay Davis
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d. 2.58. 2.96, 3.51, 3.69
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PTS: 1 w w
2. A Southern State University system consists of 23 campuses. An administrator wishes to make an infere
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nce about the average distance between the hometowns of students and their campuses. Describe and dis
w w w w w w w w w w w w w w w
cuss several different sampling methods that might be employed. Would this be an enumerative or an an
w w w w w w w w w w w w w w w w
alytic study? Explain your reasoning.
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ANS:
One could take a simple random sample of students from all students in the California State University sy
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stem and ask each student in the sample to report the distance from their hometown to campus. Alternati
w w w w w w w w w w w w w w w w w
vely, the sample could be generated by taking a stratified random sample by taking a simple random sam
w w w w w w w w w w w w w w w w w
ple from each of the 23 campuses and again asking each student in the sample to report the distance fro
w w w w w w w w w w w w w w w w w w w
m their hometown to campus.
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Certain problems might arise with self reporting of distances, such as recording error or poor recall. This stud
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y is enumerative because there exists a finite, identifiable population of objects from which to sample.
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PTS: 1 w w
3. A Michigan city divides naturally into ten district neighborhoods. How might a real estate appraiser sele
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ct a sample of single-
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family homes that could be used as a basis for developing an equation to predict appraised value from c
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haracteristics such as age, size, number of bathrooms, and distance to the nearest school, and so on? Is t
w w w w w w w w w w w w w w w w w w
he study enumerative or analytic?
w w w w
ANS:
One could generate a simple random sample of all single family homes in the city or a stratified random s
w w w w w w w w w w w w w w w w w w w
ample by taking a simple random sample from each of the 10 district neighborhoods. From each of the h
w w w w w w w w w w w w w w w w w w
omes in the sample the necessary variables would be collected. This would be an enumerative study beca
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,use there exists a finite, identifiable population of objects from which to sample.
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, PTS: 1 w w
4. An experiment was carried out to study how flow rate through a solenoid valve in an automobile’s pollut
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ion-
control system depended on three factors: armature lengths, spring load, and bobbin depth. Two differe
w w w w w w w w w w w w w w
nt levels (low and high) of each factor were chosen, and a single observation on flow was made for each
w w w w w w w w w w w w w w w w w w w w
combination of levels. w w
a. The resulting data set consisted of how many observations?
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b. Is this an enumerative or analytic study? Explain your reasoning.
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ANS:
a. Number observations equal 2 2 2=8 w w w ww ww
b. This could be called an analytic study because the data would be collected on an existin
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g process. There is no sampling frame.
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PTS: 1 w w
5. The accompanying data specific gravity values for various wood types used in construction .
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.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- w w
leaf display using repeated stems and comment on any interesting features of the display.
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ANS:
One method of denoting the pairs of stems having equal values is to denote the stem by L, for ‘low’ and t
w w w w w w w w w w w w w w w w w w w w w
he second stem by H, for ‘high’. Using this notation, the stem-and-leaf display would appear as follows:
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3L 1 stem: tenth w
s
3H 56678 leaf: hundredths w
4L 00011222223
4
5L 144
5H 58
6L 2
6H 6678
7L
7H 5
The stem-and- w
leaf display on the previous page shows that .45 is a good representative value for the data. In addition, t
w w w w w w w w w w w w w w w w w w w
he display is not symmetric and appears to be positively skewed. The spread of the data is .75 -
w w w w w w w w w w w w w w w w w w
w.31 = .44, which is .44/.45 = .978 or about 98% of the typical value of .45. This constitutes a reasonably
w w w w w w w w w w w w w w w w w w w w
wlarge amount of variation in the data. The data value .75 is a possible outlier.
w w w w w w w w w w w w w w
PTS: 1 w w
6. Temperature transducers of a certain type are shipped in batches of 50. A sample of 60 batches was se
w w w w w w w w w w w w w w w w w w
lected, and the number of transducers in each batch not conforming to design specifications was deter
w w w w w w w w w w w w w w w
mined, resulting in the following data:
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, 0 4 2 1 3 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
w w w w w w
2 1 2 4 0 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
w w w w w w
5 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3
w w w w w w
And The Sciences 9th Ed by Jay L. Devore
Chapter 1 – Overview and Descriptive Statistics
w w w w w w
SHORT ANSWER
w
1. Give one possible sample of size 4 from each of the following populations:
w w w w w w w w w w w w
a. All daily newspapers published in the United States w w w w w w w
b. All companies listed on the New York Stock Exchange w w w w w w w w
c. All students at your college or university w w w w w w
d. All grade point averages of students at your college or university
w w w w w w w w w w
ANS:
a. Houston Chronicle, Des Moines Register, Chicago Tribune, Washington Post
w w w w w w w w
b. Capital One, Campbell Soup, Merrill Lynch, Pulitzer
w w w w w w
c. John Anderson, Emily Black, Bill Carter, Kay Davis
w w w w w w w
d. 2.58. 2.96, 3.51, 3.69
w w w
PTS: 1 w w
2. A Southern State University system consists of 23 campuses. An administrator wishes to make an infere
w w w w w w w w w w w w w w w
nce about the average distance between the hometowns of students and their campuses. Describe and dis
w w w w w w w w w w w w w w w
cuss several different sampling methods that might be employed. Would this be an enumerative or an an
w w w w w w w w w w w w w w w w
alytic study? Explain your reasoning.
w w w w
ANS:
One could take a simple random sample of students from all students in the California State University sy
w w w w w w w w w w w w w w w w w
stem and ask each student in the sample to report the distance from their hometown to campus. Alternati
w w w w w w w w w w w w w w w w w
vely, the sample could be generated by taking a stratified random sample by taking a simple random sam
w w w w w w w w w w w w w w w w w
ple from each of the 23 campuses and again asking each student in the sample to report the distance fro
w w w w w w w w w w w w w w w w w w w
m their hometown to campus.
w w w w
Certain problems might arise with self reporting of distances, such as recording error or poor recall. This stud
w w w w w w w w w w w w w w w w w
y is enumerative because there exists a finite, identifiable population of objects from which to sample.
w w w w w w w w w w w w w w w
PTS: 1 w w
3. A Michigan city divides naturally into ten district neighborhoods. How might a real estate appraiser sele
w w w w w w w w w w w w w w w
ct a sample of single-
w w w w
family homes that could be used as a basis for developing an equation to predict appraised value from c
w w w w w w w w w w w w w w w w w w
haracteristics such as age, size, number of bathrooms, and distance to the nearest school, and so on? Is t
w w w w w w w w w w w w w w w w w w
he study enumerative or analytic?
w w w w
ANS:
One could generate a simple random sample of all single family homes in the city or a stratified random s
w w w w w w w w w w w w w w w w w w w
ample by taking a simple random sample from each of the 10 district neighborhoods. From each of the h
w w w w w w w w w w w w w w w w w w
omes in the sample the necessary variables would be collected. This would be an enumerative study beca
w w w w w w w w w w w w w w w w
,use there exists a finite, identifiable population of objects from which to sample.
w w w w w w w w w w w w
, PTS: 1 w w
4. An experiment was carried out to study how flow rate through a solenoid valve in an automobile’s pollut
w w w w w w w w w w w w w w w w w
ion-
control system depended on three factors: armature lengths, spring load, and bobbin depth. Two differe
w w w w w w w w w w w w w w
nt levels (low and high) of each factor were chosen, and a single observation on flow was made for each
w w w w w w w w w w w w w w w w w w w w
combination of levels. w w
a. The resulting data set consisted of how many observations?
w w w w w w w w
b. Is this an enumerative or analytic study? Explain your reasoning.
w w w w w w w w w
ANS:
a. Number observations equal 2 2 2=8 w w w ww ww
b. This could be called an analytic study because the data would be collected on an existin
w w w w w w w w w w w w w w w
g process. There is no sampling frame.
w w w w w w
PTS: 1 w w
5. The accompanying data specific gravity values for various wood types used in construction .
w w w w w w w w w w w w w
.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- w w
leaf display using repeated stems and comment on any interesting features of the display.
w w w w w w w w w w w w w
ANS:
One method of denoting the pairs of stems having equal values is to denote the stem by L, for ‘low’ and t
w w w w w w w w w w w w w w w w w w w w w
he second stem by H, for ‘high’. Using this notation, the stem-and-leaf display would appear as follows:
w w w w w w w w w w w w w w w w
3L 1 stem: tenth w
s
3H 56678 leaf: hundredths w
4L 00011222223
4
5L 144
5H 58
6L 2
6H 6678
7L
7H 5
The stem-and- w
leaf display on the previous page shows that .45 is a good representative value for the data. In addition, t
w w w w w w w w w w w w w w w w w w w
he display is not symmetric and appears to be positively skewed. The spread of the data is .75 -
w w w w w w w w w w w w w w w w w w
w.31 = .44, which is .44/.45 = .978 or about 98% of the typical value of .45. This constitutes a reasonably
w w w w w w w w w w w w w w w w w w w w
wlarge amount of variation in the data. The data value .75 is a possible outlier.
w w w w w w w w w w w w w w
PTS: 1 w w
6. Temperature transducers of a certain type are shipped in batches of 50. A sample of 60 batches was se
w w w w w w w w w w w w w w w w w w
lected, and the number of transducers in each batch not conforming to design specifications was deter
w w w w w w w w w w w w w w w
mined, resulting in the following data:
w w w w w
, 0 4 2 1 3 1 1 3 4 1 2 3 2 2 8 4 5 1 3 1
w w w w w w
2 1 2 4 0 1 3 2 0 5 3 3 1 3 2 4 7 0 2 3
w w w w w w
5 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 6 1 2 3
w w w w w w
