IOE 366 Fall 2012
Practice
1 of 7
Part 1. Multiple Choice and Fillin the Blanks
1
.
In a singlefactor ANOVA problem involving five populations or treatments, which of the following
statements is true about the alternative hypothesis?
A.
All five
treatment
means are equal.
B.
All five
treatment
means are different.
C.
At least two of the
treatment
means are different.
D.
At least three of the
treatment
means are different.
E.
At most, two of the
treatment
means are equal.
ANSWER:
C
2. In a singlefactor ANOVA problem involving four populations or treatments, the four sample standard
deviations are 25.6, 30.4, 28.7, and 32.50. Then, the mean square for error (MSE) is
3. In a singlefactor ANOVA problem involving 3 treatments, the treatment means were 5, 6, and 9.
If
each observation in the third treatment was increased by 20, the test statistic value
f
would
Answer
: A
̅
is increased by 20 while
̅
is only increased by
, leading to increased MSTr (
i.e
., enlarged
“
betweensamples
”
variation). At the same time,
MSE remains the same. As a result,
increases.
(
cf. p
. 394395)
4. For a multiple regression model,
2
(
)
250
i
y
y
and
2
ˆ
(
)
60
i
i
y
y
, what is the proportion of the
total variation in the observed
i
y
‟s
that is explained by the
regression model is
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IOE 366 Fall 2012
Practice
2 of 7
5. In the twofactor ANOVA model with interaction, assume that there are 3 levels of factor A, 2 levels
of factor B, and 3 observations for each of the six combinations of levels of the two factors. Then the
critical value for testing the null hypothesis of no interaction between the levels of the two factors at
the 0.05 significance level is
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 Winter '08
 GAME
 Statistics, Regression Analysis, Null hypothesis, Statistical hypothesis testing, significance level

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