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STT 201
UNIT 4
Example Multiple Choice Questions
14.
For each of the following testing situations, give the pvalue of the observed test statistic.
Pick the closest
.
1.
Twosample ttest of H
0
:
μ
1

μ
2
≥
0 versus H
a
:
μ
1

μ
2
< 0, sample sizes n
1
= 12, n
2
= 10,
t
obs
= 1.38.
Adopt the conservative approach to the degrees of freedom.
(a)
.10
(b)
.05
(c)
.20
(d)
.50
(e)
.90
2.
Twosample (large samples) ztest of H
0
:
π
1

π
2
≤
0 v. H
a
:
π
1

π
2
> 0 if p
1
= .47, p
2
= .33 and z
obs
= 1.15.
(a)
.085
(b)
.071
(c)
.054
(d)
.125
(e)
.101
3.
A categorical variable y has five levels.
Two populations are tested for having the same distribution of y
using large samples drawn from each population and
χ
2
obs
= 11.12.
(a)
.085
(b)
.071
(c)
.054
(d)
.025
(e)
.037
4.
A categorical variable y has three levels.
Four populations are tested for having the same distribution of y
using large samples drawn from each population and
χ
2
obs
= 2.20.
(a)
.085
(b)
.001
(c)
.050
(d)
.900
(e)
.100
56.
A researcher administered a reading comprehension test to each of 16 subjects before and after a special
course that each subject took to improve reading comprehension.
The researcher set the hypotheses H
0
:
μ
d
≤
0 and
H
a
:
μ
d
> 0 where d denotes difference (improvement).
The summary of the data is given below.
Descriptive Statistics
N
Mean
Standard deviation
Before
16
52.8
9.3
After
16
56.8
8.1
Difference
16
4.0
7.6
5.
What is the value of t
obs
for testing H
0
?
(a)
2.11
(b)
7.6
(c)
0.45
(d)
2.00
(e)
4.0
6.
What is the pvalue of t
obs
?
(a)
.10
(b)
.05
(c)
.025
(d)
.01
(e)
.005
712.
A veterinarian believes that the rate of hip dysplasia in Boxers (breed of dog) is less than the rate hip
dysplasia in American Bulldogs (breed of dog) and decides to test the hypothesis H
0
:
π
1

π
2
≥
0 v. H
a
:
π
1

π
2
< 0.
A
random sample of 80 Boxers has 8 dogs with hip dysplasia.
A random sample of 140 American Bulldogs has 21
dogs with hip dysplasia.
7.
What is the standard error of the estimate p
1
– p
2
used in calculating the CI for
π
1

π
2
?
(a)
.085
(b)
.071
(c)
.045
(d)
.037
(e)
.101
8.
What is the 99% CI estimate of the difference in population rates
π
1

π
2
?
(a) .05
±
.12
(b) .05
±
.07 (c) .05
±
.09
(d) .05
±
.20 (e) .05
±
.17
9.
What is the standard error of the estimate p
1
– p
2
used in calculating the ztest statistic
? (
Hint: This
is the denominator of ztest statistic.
)
(a)
.085
(b)
.071
(c)
.064
(d)
.047
(e)
.101
10.
Compute the value z
obs
of the ztest statistic.
(a) 0.52
(b)
0.90
(c)
1.96
(d) –1.06
(e)
1.96
11. What is the pvalue of the test statistic z
obs
that is appropriate for this test? Pick the closest.
(a) 0.30
(b)
0.18
(c)
0.14
(d)
0.05
(e)
0.025
12. What decision is reached at 2% level of significance?
(a) reject the null hypothesis
(b) retain the null hypothesis
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View Full Document 1315.
A study is undertaken to compare the distributions
of weights of adult perch in Lake Michigan, Lake Huron
and Lake Erie.
Random samples of sizes 100, 200, 300 respectively are obtained from these lakes and each
sample fish is weighed.
Weight is recorded in four categories. The sample data are shown below.
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This note was uploaded on 09/27/2010 for the course STT STT 201 taught by Professor Sinnott during the Summer '10 term at Michigan State University.
 Summer '10
 SINNOTT

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