Problem 1
: (10pts, 2pt for each question) Note that only one option is allowed to be circled for
each question; any violation will receive zero point for that question.
(1) Which of the following statements is correct regarding the hypothesis testing? ( )
A. A desirable test should be able to control both type I error rate and type II error rate
simultaneously.
B. Increase sample size can help decrease the type II error rate.
C. Reduce the sample variability can increase the Type II error rate.
D None of the above.
(2) At a hazardous intersection, the number of accidents per week
X
follows a poisson distribution
with a mean value of 3 and a variance of 3. If we gather the data from 100 weeks, and obtain
the average weekly accident rate
X,
What is the probability
P
(
X >
3
.
6)? ( )
A. 0.0603
B. 0.0228.
C. 0.0421
D 0.0500.
(3) Here is a ﬁve number summary of a data set: min=1.52, Q1=2.12, Median=2.83, Q3=3.89,
Max=7.86, which one of the following values is an outlier? ( )
A. 1.52
B. 7.86.
C. 2.12
D None of the above.
(4) Which of the following statements are correct? ( )
A. Given a data set, if the (1

α
)% conﬁdence interval for
μ
contains
μ
= 10
,
then the
α
level
hypothesis test for
H
0
:
μ
= 10 versus
H
a
:
μ
6
= 10 will lead to the acceptance of
H
0
.
B. Given a data set, if the (1

α
)% conﬁdence interval for
μ
contains
μ
= 10
,
then the
α
level
hypothesis test for
H
0
:
μ
= 10 versus
H
a
:
μ
6
= 10 will lead to the rejection of
H
0
.
C. There is no direct link between the two procedures.
D Given a data set, if the (1

α
)% conﬁdence interval for
μ
contains
μ
= 10
,
then the
α
level
hypothesis test for
H
0
:
μ
= 10 versus
H
a
:
μ
6
= 10 will sometimes lead to the acceptance of
H
0
and sometimes lead to the rejection of
H
0
.
(5) Which of the following statements are correct? ( )
A. In the analysis of variance table,
SS
treatment
=
SS
total

SS
error
.
B. In the analysis of variance table, the F test is twosided.
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 Spring '10
 profgao
 Statistics, Normal Distribution, Standard Deviation, Probability theory

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