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