Chapter 1 – Overview and Descriptive Statistics
SHORT ANSWER
1. Give one possible sample of size 4 from each of the following populations:
a. All daily newspapers published in the United States
b. All companies listed on the New York Stock Exchange
c. All students at your college or university
d. All grade point averages of students at your college or university
ANS:
a. Houston Chronicle, Des Moines Register, Chicago Tribune, Washington Post
b. Capital One, Campbell Soup, Merrill Lynch, Pulitzer
c. John Anderson, Emily Black, Bill Carter, Kay Davis
d. 2.58. 2.96, 3.51, 3.69
PTS: 1
2. A Southern State University system consists of 23 campuses. An administrator wishes to make an inference
about the average distance between the hometowns of students and their campuses. Describe and discuss
several different sampling methods that might be employed. Would this be an enumerative or an analytic
study? Explain your reasoning.
ANS:
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.
, PTS: 1
3. A Michigan city divides naturally into ten district neighborhoods. How might a real estate appraiser select a
sample of single-family homes that could be used as a basis for developing an equation to predict appraised
value from characteristics such as age, size, number of bathrooms, and distance to the nearest school, and
so on? Is the study enumerative or analytic?
ANS:
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
homes in the sample the necessary variables would be collected. This would be an enumerative study
because there exists a finite, identifiable population of objects from which to sample.
PTS: 1
4. An experiment was carried out to study how flow rate through a solenoid valve in an automobile’s
pollution-control system depended on three factors: armature lengths, spring load, and bobbin depth.
Two different levels (low and high) of each factor were chosen, and a single observation on flow was made
for each combination of levels.
a. The resulting data set consisted of how many observations?
b. Is this an enumerative or analytic study? Explain your reasoning.
ANS:
a. Number observations equal 2 2 2=8
b. This could be called an analytic study because the data would be collected on an existing process.
There is no sampling frame.
PTS: 1
5. The accompanying data specific gravity values for various wood types used in construction .
, .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
display.
ANS:
One method of denoting the pairs of stems having equal values is to denote the stem by L, for ‘low’ and the
second stem by H, for ‘high’. Using this notation, the stem-and-leaf display would appear as follows:
3L 1 stem: tenths
3H 56678 leaf: hundredths
4L 000112222234
5L 144
5H 58
6L 2
6H 6678
7L
7H 5
The stem-and-leaf display on the previous page shows that .45 is a good representative value for the data.
In addition, the display is not symmetric and appears to be positively skewed. The spread of the data is .75
- .31 = .44, which is .44/.45 = .978 or about 98% of the typical value of .45. This constitutes a reasonably
large amount of variation in the data. The data value .75 is a possible outlier.
PTS: 1
, 6. Temperature transducers of a certain type are shipped in batches of 50. A sample of 60 batches was
selected, and the number of transducers in each batch not conforming to design specifications was
determined, resulting in the following data:
0 4 2 1 3 1 1 3 4 1 2 3 2 2 8 4 5 1
3 1
2 1 2 4 0 1 3 2 0 5 3 3 1 3 2 4 7 0
2 3
5 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 6 1
2 3
a. Determine frequencies and relative frequencies for the observed values of x = number of
nonconforming transducers in a batch.
b. What proportion of batches in the sample has at most four nonconforming transducers? What proportion
has fewer than four? What proportion has at least four nonconforming units?
ANS:
a.
Number Nonconforming Frequency Relative Frequency
0 7 0.117
1 12 0.200
2 13 0.217
3 14 0.233
4 6 0.100
5 3 0.050
6 3 0.050
7 1 0.017
8 1 0.017
1.001
SHORT ANSWER
1. Give one possible sample of size 4 from each of the following populations:
a. All daily newspapers published in the United States
b. All companies listed on the New York Stock Exchange
c. All students at your college or university
d. All grade point averages of students at your college or university
ANS:
a. Houston Chronicle, Des Moines Register, Chicago Tribune, Washington Post
b. Capital One, Campbell Soup, Merrill Lynch, Pulitzer
c. John Anderson, Emily Black, Bill Carter, Kay Davis
d. 2.58. 2.96, 3.51, 3.69
PTS: 1
2. A Southern State University system consists of 23 campuses. An administrator wishes to make an inference
about the average distance between the hometowns of students and their campuses. Describe and discuss
several different sampling methods that might be employed. Would this be an enumerative or an analytic
study? Explain your reasoning.
ANS:
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.
, PTS: 1
3. A Michigan city divides naturally into ten district neighborhoods. How might a real estate appraiser select a
sample of single-family homes that could be used as a basis for developing an equation to predict appraised
value from characteristics such as age, size, number of bathrooms, and distance to the nearest school, and
so on? Is the study enumerative or analytic?
ANS:
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
homes in the sample the necessary variables would be collected. This would be an enumerative study
because there exists a finite, identifiable population of objects from which to sample.
PTS: 1
4. An experiment was carried out to study how flow rate through a solenoid valve in an automobile’s
pollution-control system depended on three factors: armature lengths, spring load, and bobbin depth.
Two different levels (low and high) of each factor were chosen, and a single observation on flow was made
for each combination of levels.
a. The resulting data set consisted of how many observations?
b. Is this an enumerative or analytic study? Explain your reasoning.
ANS:
a. Number observations equal 2 2 2=8
b. This could be called an analytic study because the data would be collected on an existing process.
There is no sampling frame.
PTS: 1
5. The accompanying data specific gravity values for various wood types used in construction .
, .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
display.
ANS:
One method of denoting the pairs of stems having equal values is to denote the stem by L, for ‘low’ and the
second stem by H, for ‘high’. Using this notation, the stem-and-leaf display would appear as follows:
3L 1 stem: tenths
3H 56678 leaf: hundredths
4L 000112222234
5L 144
5H 58
6L 2
6H 6678
7L
7H 5
The stem-and-leaf display on the previous page shows that .45 is a good representative value for the data.
In addition, the display is not symmetric and appears to be positively skewed. The spread of the data is .75
- .31 = .44, which is .44/.45 = .978 or about 98% of the typical value of .45. This constitutes a reasonably
large amount of variation in the data. The data value .75 is a possible outlier.
PTS: 1
, 6. Temperature transducers of a certain type are shipped in batches of 50. A sample of 60 batches was
selected, and the number of transducers in each batch not conforming to design specifications was
determined, resulting in the following data:
0 4 2 1 3 1 1 3 4 1 2 3 2 2 8 4 5 1
3 1
2 1 2 4 0 1 3 2 0 5 3 3 1 3 2 4 7 0
2 3
5 0 2 3 2 1 0 6 4 2 1 6 0 3 3 3 6 1
2 3
a. Determine frequencies and relative frequencies for the observed values of x = number of
nonconforming transducers in a batch.
b. What proportion of batches in the sample has at most four nonconforming transducers? What proportion
has fewer than four? What proportion has at least four nonconforming units?
ANS:
a.
Number Nonconforming Frequency Relative Frequency
0 7 0.117
1 12 0.200
2 13 0.217
3 14 0.233
4 6 0.100
5 3 0.050
6 3 0.050
7 1 0.017
8 1 0.017
1.001
