STA 2023
Practice Questions
Final Exam
STATISTICAL INFERENCE TABLE:
(GIVEN on the test)
Case
parameter
estimator
standard error
Sampling
Distribution
one mean
x
n
s
t (n-1)
Mean of
matched pairs
difference
d
d
x
d
s
n
t (n-1)
difference
of two
independent
means
2
1
2
1
x
x
2
2
2
1
2
1
n
s
n
s
t with conservative
df
= smallest of
(n
1
-1) and (n
2
-1)
one
proportion
p
p
ˆ
CI:
ˆ
ˆ
(1
)
p
p
n
ST:
n
p
p
)
1
(
0
0
z
difference
of two
independent
proportions
2
1
p
p
2
1
ˆ
ˆ
p
p
CI:
1
1
2
2
1
2
ˆ
ˆ
ˆ
ˆ
(1
)
(1
)
p
p
p
p
n
n
ST:
2
1
1
1
)
ˆ
1
(
ˆ
n
n
p
p
z
McNemar
YN
NY
TS
YN
NY
OR
NY
YN
TS
YN
NY
NEED TO KNOW:
Confidence Interval
: estimator +/- (t or z) est. standard error
Test Statistic:
#
(
)
o
estimator
from
H
t
or
z
estimate
of
stderr

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Questions 1 – 4
An education researcher has developed a new technique to teach Spanish to
high school students. To prove this new method is better, she will teach two groups of students
for an entire semester, one with the new method and one with the standard method used today in
high schools. She wishes to obtain 12 sets of identical twins, 24 people total, and split the twins
up so that one of each twin is in Class 1, which will receive the new technique, and one is in
Class 2, which will receive the old technique. At the end of the semester both classes will take a
standardized exam and the results will be compared.
1. What method should be used to analyze this data?
a) one mean
b) two independent means
c) matched pairs
d) two independent proportions
2. What should our hypotheses be to test if your new method is better than the old method?
a) H
0
:
2
= 0 vs. H
A
:
2
< 0
b) H
0
:
D
= 0 vs. H
A
:
D
< 0
c) H
0
:
2
= 0 vs. H
A
:
2
0
d) H
0
:
D
= 0 vs. H
A
:
D
0
3. What distribution would you use to look up the p-value for this test of hypothesis?
4. Suppose we collect the data from this experiment and we find a p-value of 0.009. Which of the
following is our conclusion at any reasonable alpha level?