Test Bank for
Introduction to Statistics and Data
Analysis 7th Edition By Roxy Peck,
Chris Olsen
(All Chapters 1-16, 100% Original
Verified, A+ Grade)
All Chapters Arranged Reverse: 16-1
This is the Original Test Bank for 7th
Edition, All Other Files in the Market
are Wrong/Old Questions.
,Name Clas Dat
: s: e:
Chapter 16 - Nonparametric (Distribution-Free) Statistical Methods
INSTRUCTIONS:
The following questions are in a True/False format. The answers to these questions will frequently depend on
remembering facts, understanding of the concepts, and knowing the statistical vocabulary. Before answering these
questions, be sure to read them carefully!
1. In a signed-rank sum test for a set of n pairs of observations, the differences in pairs are calculated, these differences are
ranked from smallest to largest, and the sum of ranks is calculated.
a. True
b. Fals
e
ANSWER: False
2. If the sample size is large enough (n > 20), the distribution of the signed-rank sum statistic when H0 is true is well
approximated by the normal distribution with a mean of 0 and standard deviation of n(n+1)/4.
a. True
b. Fals
e
ANSWER: False
3. To conduct the Kruskal-Wallis test for comparing three different methods of treatment, one needs to state the null
hypothesis as H0: μ1 = μ2 = μ3 and alternative hypothesis as Ha: μ1 ≠ μ2 ≠ μ3.
a. True
b. Fals
e
ANSWER: False
4. If l is not too small and H0 is true Fr has approximately a chi-squared distribution with df = k – 1. The null hypothesis is
rejected if Fr > chi-square critical value for the given level of significance α.
a. True
b. Fals
e
ANSWER: True
5. Under what conditions can a rank-sum test be performed on two samples? (More than one answer may be correct.)
a. The samples must be of the same size.
b. The samples must be independent random samples.
c. The samples must be taken from the same population or treatment response set.
d. The population or treatment response distributions must be at least approximately
normal.
e. The population or treatment response distributions must be symmetric.
f. The population or treatment response distributions must have the same shape.
g. The population or treatment response distributions must have the same variability.
h. The population or treatment response distributions must have the same mean value.
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,Name Clas Dat
: s: e:
Chapter 16 - Nonparametric (Distribution-Free) Statistical Methods
ANSWER: b, f,
g
6. Two sport cars complete 6 laps on a track, the lap times in seconds are given below.
Car 1 103.481 101.35 103.513 103.112 102.552 103.402
Car 2 103.581 102.336 104.284 103.221 104.378 103.698
Is there enough evidence that Car 1 is faster than Car 2? Use a level 0.05 rank-sum test.
a. Yes. The rank-sum for the Car 1 lap time versus Car 2 lap time is 29 that is greater
than the critical value for n1 = 6, n2 = 6, Ha: μ1 < μ2. Thus, there is significant evidence
that Car 1 is faster than Car 2.
b.No. The rank-sum for the Car 1 lap time versus Car 2 lap time is 29 that is greater than
the critical value for n1 = 6, n2 = 6, Ha: μ1 < μ2. Thus, there is no significant evidence
that Car 1 is faster than Car 2.
c. Yes. The rank-sum for the Car 1 lap time versus Car 2 lap time is 29 that is less than
the critical value for n1 = 6, n2 = 6, Ha: μ1 < μ2. Thus, there is significant evidence that
Car 1 is faster than Car 2.
d.No. Rank-sum for the Car 1 lap time versus Car 2 lap time is 29 that is less than the
critical value for n1 = 6, n2 = 6, Ha: μ1 < μ2. Thus, there is no significant evidence that
Car 1 is faster than Car 2.
e. No. The rank-sum for the Car 1 lap time versus Car 2 lap time is 49 that is less than
the critical value for n1 = 6, n2 = 6, Ha: μ1 < μ2. Thus, there is no significant evidence
that Car 1 is faster than Car 2.
f. Yes. The rank-sum for the Car 1 lap time versus Car 2 lap time is 49 that is greater
than the critical value for n1 = 6, n2 = 6, Ha: μ1 < μ2. Thus, there is significant evidence
that Car 1 is faster than Car 2.
ANSWER: b
7. As a new model of the internal combustion engine enters the market, its manufacturer claims that the new engine is
more fuel-efficient than the older model by 1.1 miles per gallon. Two samples below represent fuel efficiency, in miles per
gallon, for the cars of the same model equipped with different engines.
New engine 26.5 25.9 26.8 23.1 23.6 24.8 25.3
Old engine 22.1 21.4 22.4 22.6 23.4
Does a level 0.05 rank-sum test performed on these samples supports the manufacturer's claim?
a. The rank-sum value for the new engine fuel efficiency versus old engine fuel
efficiency is 62 that is greater than the critical value for n1 = 7, n2 = 5. The test
supports the manufacturer's claim.
b.The rank-sum value for the new engine fuel efficiency versus old engine fuel
efficiency is 62 that is less than the critical value for n1 = 7, n2 = 5. The test does not
support the manufacturer's claim.
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, Name Clas Dat
: s: e:
Chapter 16 - Nonparametric (Distribution-Free) Statistical Methods
c. The rank-sum value for the new engine fuel efficiency versus old engine fuel
efficiency shifted by +1.1 is 57 that is greater than the critical value for n1 = 7, n2 = 5.
The test supports the manufacturer's claim.
d.The rank-sum value for the new engine fuel efficiency versus old engine fuel
efficiency shifted by +1.1 is 57 that is less than the critical value for n1 = 7, n2 = 5. The
test does not support the manufacturer's claim.
e. The 95% confidence interval for the difference in fuel efficiency is (1.0, 4.4). The
value of 1.1 lies within the 95% confidence interval so the test supports the
manufacturer's claim.
f. The 95% confidence interval for the difference in fuel efficiency is (1.0, 4.4). The
value of 1.1 lies within the 95% confidence interval so the test does not support the
manufacturer's claim.
ANSWER: c
8. The ratio between concentrations of radioactive and stable isotopes of carbon (radioactive carbon-14, 14C, and stable
carbon-12, 12C) is used to determine the age of organic materials. The older the specimen, the lower the concentration of
radioactive carbon-14 in it, while the concentration of stable carbon-12 does not significantly change. The ratio of 14C/12C
is usually expressed as a fraction of the modern one.
A scientist takes two sets of probes of charcoal from two specimens at the same excavation site and suspects they are of
14 12
different age. The table below represents the ratio of C/ C in the probes. Does a rank-sum test provide enough evidence
that the age is different? Use α = 0.05.
Specimen 1 0.187 0.203 0.210 0.195 0.220 0.213 0.216 0.156
Specimen 2 0.191 0.199 0.174 0.194 0.156 0.192 0.173 0.188
a. Yes. The rank-sum value for probe set 1 is 87 that is within the limits for a two-tailed rank
sum test, the null hypothesis (the specimens are of the same age) can be rejected at α = 0.05,
i.e. the specimen are of different age.
b.No. The rank-sum value for probe set 1 is 86.5 that is within the limits for a two-tailed rank
sum test, the null hypothesis (the specimens are of the same age) cannot be rejected at α =
0.05.
c. Yes. The rank-sum value for probe set 1 is 86.5 that is greater than the limit for an upper-
tailed rank sum test, the null hypothesis (the specimens are of the same age) can be rejected
at α = 0.05 with Ha: μ1 > μ2, i.e. specimen 1 is younger than specimen 2.
d.No. The rank-sum value for probe set 1 is 87 that is less than the limit for an upper-tailed
rank sum test, the null hypothesis (the specimens are of the same age) cannot be rejected at
α = 0.05.
e. No. The rank-sum value for probe set 1 is 86 that is within the limits for a two-tailed rank
sum test, the null hypothesis (the specimens are of the same age) cannot be rejected at α =
0.05.
f. Yes. The rank-sum value for probe set 1 is 86 that is greater than the limit for an upper-tailed
rank sum test, the null hypothesis (the specimens are of the same age) can be rejected at α =
0.05 with Ha: μ1 > μ2, i.e. specimen 1 is younger than specimen 2.
ANSWER: b
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Introduction to Statistics and Data
Analysis 7th Edition By Roxy Peck,
Chris Olsen
(All Chapters 1-16, 100% Original
Verified, A+ Grade)
All Chapters Arranged Reverse: 16-1
This is the Original Test Bank for 7th
Edition, All Other Files in the Market
are Wrong/Old Questions.
,Name Clas Dat
: s: e:
Chapter 16 - Nonparametric (Distribution-Free) Statistical Methods
INSTRUCTIONS:
The following questions are in a True/False format. The answers to these questions will frequently depend on
remembering facts, understanding of the concepts, and knowing the statistical vocabulary. Before answering these
questions, be sure to read them carefully!
1. In a signed-rank sum test for a set of n pairs of observations, the differences in pairs are calculated, these differences are
ranked from smallest to largest, and the sum of ranks is calculated.
a. True
b. Fals
e
ANSWER: False
2. If the sample size is large enough (n > 20), the distribution of the signed-rank sum statistic when H0 is true is well
approximated by the normal distribution with a mean of 0 and standard deviation of n(n+1)/4.
a. True
b. Fals
e
ANSWER: False
3. To conduct the Kruskal-Wallis test for comparing three different methods of treatment, one needs to state the null
hypothesis as H0: μ1 = μ2 = μ3 and alternative hypothesis as Ha: μ1 ≠ μ2 ≠ μ3.
a. True
b. Fals
e
ANSWER: False
4. If l is not too small and H0 is true Fr has approximately a chi-squared distribution with df = k – 1. The null hypothesis is
rejected if Fr > chi-square critical value for the given level of significance α.
a. True
b. Fals
e
ANSWER: True
5. Under what conditions can a rank-sum test be performed on two samples? (More than one answer may be correct.)
a. The samples must be of the same size.
b. The samples must be independent random samples.
c. The samples must be taken from the same population or treatment response set.
d. The population or treatment response distributions must be at least approximately
normal.
e. The population or treatment response distributions must be symmetric.
f. The population or treatment response distributions must have the same shape.
g. The population or treatment response distributions must have the same variability.
h. The population or treatment response distributions must have the same mean value.
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,Name Clas Dat
: s: e:
Chapter 16 - Nonparametric (Distribution-Free) Statistical Methods
ANSWER: b, f,
g
6. Two sport cars complete 6 laps on a track, the lap times in seconds are given below.
Car 1 103.481 101.35 103.513 103.112 102.552 103.402
Car 2 103.581 102.336 104.284 103.221 104.378 103.698
Is there enough evidence that Car 1 is faster than Car 2? Use a level 0.05 rank-sum test.
a. Yes. The rank-sum for the Car 1 lap time versus Car 2 lap time is 29 that is greater
than the critical value for n1 = 6, n2 = 6, Ha: μ1 < μ2. Thus, there is significant evidence
that Car 1 is faster than Car 2.
b.No. The rank-sum for the Car 1 lap time versus Car 2 lap time is 29 that is greater than
the critical value for n1 = 6, n2 = 6, Ha: μ1 < μ2. Thus, there is no significant evidence
that Car 1 is faster than Car 2.
c. Yes. The rank-sum for the Car 1 lap time versus Car 2 lap time is 29 that is less than
the critical value for n1 = 6, n2 = 6, Ha: μ1 < μ2. Thus, there is significant evidence that
Car 1 is faster than Car 2.
d.No. Rank-sum for the Car 1 lap time versus Car 2 lap time is 29 that is less than the
critical value for n1 = 6, n2 = 6, Ha: μ1 < μ2. Thus, there is no significant evidence that
Car 1 is faster than Car 2.
e. No. The rank-sum for the Car 1 lap time versus Car 2 lap time is 49 that is less than
the critical value for n1 = 6, n2 = 6, Ha: μ1 < μ2. Thus, there is no significant evidence
that Car 1 is faster than Car 2.
f. Yes. The rank-sum for the Car 1 lap time versus Car 2 lap time is 49 that is greater
than the critical value for n1 = 6, n2 = 6, Ha: μ1 < μ2. Thus, there is significant evidence
that Car 1 is faster than Car 2.
ANSWER: b
7. As a new model of the internal combustion engine enters the market, its manufacturer claims that the new engine is
more fuel-efficient than the older model by 1.1 miles per gallon. Two samples below represent fuel efficiency, in miles per
gallon, for the cars of the same model equipped with different engines.
New engine 26.5 25.9 26.8 23.1 23.6 24.8 25.3
Old engine 22.1 21.4 22.4 22.6 23.4
Does a level 0.05 rank-sum test performed on these samples supports the manufacturer's claim?
a. The rank-sum value for the new engine fuel efficiency versus old engine fuel
efficiency is 62 that is greater than the critical value for n1 = 7, n2 = 5. The test
supports the manufacturer's claim.
b.The rank-sum value for the new engine fuel efficiency versus old engine fuel
efficiency is 62 that is less than the critical value for n1 = 7, n2 = 5. The test does not
support the manufacturer's claim.
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, Name Clas Dat
: s: e:
Chapter 16 - Nonparametric (Distribution-Free) Statistical Methods
c. The rank-sum value for the new engine fuel efficiency versus old engine fuel
efficiency shifted by +1.1 is 57 that is greater than the critical value for n1 = 7, n2 = 5.
The test supports the manufacturer's claim.
d.The rank-sum value for the new engine fuel efficiency versus old engine fuel
efficiency shifted by +1.1 is 57 that is less than the critical value for n1 = 7, n2 = 5. The
test does not support the manufacturer's claim.
e. The 95% confidence interval for the difference in fuel efficiency is (1.0, 4.4). The
value of 1.1 lies within the 95% confidence interval so the test supports the
manufacturer's claim.
f. The 95% confidence interval for the difference in fuel efficiency is (1.0, 4.4). The
value of 1.1 lies within the 95% confidence interval so the test does not support the
manufacturer's claim.
ANSWER: c
8. The ratio between concentrations of radioactive and stable isotopes of carbon (radioactive carbon-14, 14C, and stable
carbon-12, 12C) is used to determine the age of organic materials. The older the specimen, the lower the concentration of
radioactive carbon-14 in it, while the concentration of stable carbon-12 does not significantly change. The ratio of 14C/12C
is usually expressed as a fraction of the modern one.
A scientist takes two sets of probes of charcoal from two specimens at the same excavation site and suspects they are of
14 12
different age. The table below represents the ratio of C/ C in the probes. Does a rank-sum test provide enough evidence
that the age is different? Use α = 0.05.
Specimen 1 0.187 0.203 0.210 0.195 0.220 0.213 0.216 0.156
Specimen 2 0.191 0.199 0.174 0.194 0.156 0.192 0.173 0.188
a. Yes. The rank-sum value for probe set 1 is 87 that is within the limits for a two-tailed rank
sum test, the null hypothesis (the specimens are of the same age) can be rejected at α = 0.05,
i.e. the specimen are of different age.
b.No. The rank-sum value for probe set 1 is 86.5 that is within the limits for a two-tailed rank
sum test, the null hypothesis (the specimens are of the same age) cannot be rejected at α =
0.05.
c. Yes. The rank-sum value for probe set 1 is 86.5 that is greater than the limit for an upper-
tailed rank sum test, the null hypothesis (the specimens are of the same age) can be rejected
at α = 0.05 with Ha: μ1 > μ2, i.e. specimen 1 is younger than specimen 2.
d.No. The rank-sum value for probe set 1 is 87 that is less than the limit for an upper-tailed
rank sum test, the null hypothesis (the specimens are of the same age) cannot be rejected at
α = 0.05.
e. No. The rank-sum value for probe set 1 is 86 that is within the limits for a two-tailed rank
sum test, the null hypothesis (the specimens are of the same age) cannot be rejected at α =
0.05.
f. Yes. The rank-sum value for probe set 1 is 86 that is greater than the limit for an upper-tailed
rank sum test, the null hypothesis (the specimens are of the same age) can be rejected at α =
0.05 with Ha: μ1 > μ2, i.e. specimen 1 is younger than specimen 2.
ANSWER: b
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