Chapter 10 The analysis of variance
SHORT
ANSWER
1. The simplest ANOVA problem is referred to variously as a single-factor, single-classification, or
ANOVA.
ANS:
one-way
PTS: 1
2. In a single-factor ANOVA, the characteristic that differentiates the treatments or populations from one another is
called the under study, and the different treatments or populations are referred to as the of
the factor.
ANS:
factor, levels
PTS: 1
3. An experiment is conducted to study the effectiveness of three teaching methods on student performance. In this
experiment, the factor of interest is , and there are different levels of the factor.
ANS:
teaching method, three
PTS: 1
4. An experiment is conducted to study the effects of the presence of four different sugar solutions (glucose, sucrose,
fructose, and a mixture of the three) on bacterial growth. In this experiment, the factor of interest is , and
there are different levels of the factor.
ANS:
sugar, four
PTS: 1
5. Single-factor ANOVA focuses on a comparison of more than two population or treatment .
ANS:
means
PTS: 1
6. In a one-way ANOVA problem involving four populations or treatments, the null hypothesis of interest is
ANS:
PTS: 1
,7. In single-factor ANOVA, the is a measure of between samples variation, and is denoted by .
ANS:
mean square for treatments, MSTr
PTS: 1
8. In single-factor ANOVA, the is a measure of within-samples variation, and is denoted by .
, ANS:
mean square for error, MSE
PTS: 1
9. In one-factor ANOVA, both mean square for treatments (MSTr) and mean square for error (MSE) are unbiased
estimators for estimating the common population variance when , but MSTr tends to overestimate
when .
ANS:
is true, is false
PTS: 1
10. In single-factor ANOVA, SST – SSTr = .
ANS:
SSE
PTS: 1
11. In one-factor ANOVA, denoted by is the part of total variation that is unexplained by the
truth or falsity of .
ANS:
sum square for error, SSE
PTS: 1
12. In one-factor ANOVA, denoted by is the part of total variation that can be explained by
possible differences in the population means.
ANS:
sum square for treatments, SSTr
PTS: 1
13. Let F =MSTr/MSE be the test statistic in a single-factor ANOVA problem involving four populations or treatments
with a random sample of six observations from each one. When is true and the four population or treatment
distributions are all normal with the same variance then F has an F distribution with degrees of freedom
With f denoting the computed value of F, the rejection region for level .05
test is .
ANS:
3, 20,
PTS: 1
SHORT
ANSWER
1. The simplest ANOVA problem is referred to variously as a single-factor, single-classification, or
ANOVA.
ANS:
one-way
PTS: 1
2. In a single-factor ANOVA, the characteristic that differentiates the treatments or populations from one another is
called the under study, and the different treatments or populations are referred to as the of
the factor.
ANS:
factor, levels
PTS: 1
3. An experiment is conducted to study the effectiveness of three teaching methods on student performance. In this
experiment, the factor of interest is , and there are different levels of the factor.
ANS:
teaching method, three
PTS: 1
4. An experiment is conducted to study the effects of the presence of four different sugar solutions (glucose, sucrose,
fructose, and a mixture of the three) on bacterial growth. In this experiment, the factor of interest is , and
there are different levels of the factor.
ANS:
sugar, four
PTS: 1
5. Single-factor ANOVA focuses on a comparison of more than two population or treatment .
ANS:
means
PTS: 1
6. In a one-way ANOVA problem involving four populations or treatments, the null hypothesis of interest is
ANS:
PTS: 1
,7. In single-factor ANOVA, the is a measure of between samples variation, and is denoted by .
ANS:
mean square for treatments, MSTr
PTS: 1
8. In single-factor ANOVA, the is a measure of within-samples variation, and is denoted by .
, ANS:
mean square for error, MSE
PTS: 1
9. In one-factor ANOVA, both mean square for treatments (MSTr) and mean square for error (MSE) are unbiased
estimators for estimating the common population variance when , but MSTr tends to overestimate
when .
ANS:
is true, is false
PTS: 1
10. In single-factor ANOVA, SST – SSTr = .
ANS:
SSE
PTS: 1
11. In one-factor ANOVA, denoted by is the part of total variation that is unexplained by the
truth or falsity of .
ANS:
sum square for error, SSE
PTS: 1
12. In one-factor ANOVA, denoted by is the part of total variation that can be explained by
possible differences in the population means.
ANS:
sum square for treatments, SSTr
PTS: 1
13. Let F =MSTr/MSE be the test statistic in a single-factor ANOVA problem involving four populations or treatments
with a random sample of six observations from each one. When is true and the four population or treatment
distributions are all normal with the same variance then F has an F distribution with degrees of freedom
With f denoting the computed value of F, the rejection region for level .05
test is .
ANS:
3, 20,
PTS: 1
