STA 3024
Homework 2
Section 7459
Form B
Name:
UFID:
This form is only for students whose UFID number begins with 0, 4, 5, or 9.
Answer all problems
neatly
. If you turn in more than one piece of paper, they must be
stapled
. Work
that isn’t neat or stapled may lose points. You don’t need to turn in this problem listing, but you do need
to include your
name
,
UFID number
, and
form code
on your homework.
For each of the following problems, do the following:
•
State the best type of inference method to use (from the ones covered in the Review 2 slides on the
website).
•
State the assumptions and whether or not they are satisfied. Irrespective of whether or not you think
they are satisfied, perform the analysis. The only assumption you may assume true if not stated is
randomization.
•
Perform a hypothesis test, stating the assumptions, teststatistic value, pvalue, and conclusion. Inter
pret the conclusion in the context of the problem.
•
If we went over a confidence interval corresponding to the method you chose, make the 95% confidence
interval. Interpet it in the context of the problem. State whether or not you reach the same conclusion
from the hypothesis test as the confidence interval.
3 problems
×
12 points
2 problems
×
4 points (2 points for right method, 2 points completion)
44 points total
1.
total points: 12
In the first week of January 2012, CBS conducted a poll which asked 1,247 people
if they would vote for President Barack Obama or Governor Rick Perry; 42% responded in favor of
Governor Perry.
In midDecember, CNN/Opinion Research conducted a similar poll asking 1,015
people the same question; 37% responded in favor of Governor Perry. Is there evidence that Governor
Perry’s support has increased from December to January?
Best Inference Method
2 points
Two sample proportions (independent groups)
Assumptions
2 points
•
Data obtained from randomization
•
Two independent groups
•
Categorical response variable for the two groups
•
Large enough sample sizes (at least 10 “successes” and 10 “failures” in each group)
They are all clearly met.
1
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Hypotheses
2 points
H
0
:
p
1

p
2
= 0 vs.
H
A
:
p
1

p
2
>
0
Hypothesis Test
First note the following:
1
= 0
.
42
n
1
= 1247
2
= 0
.
37
n
2
= 1015
=
0
.
42(1247) + 0
.
37(1015)
1247 + 1015
= 0
.
398
2 points
So, we compute
z
=
0
.
42

0
.
37
q
0
.
398(1

0
.
398)
(
1
1247
+
1
1015
)
= 2
.
41
2 points
This gives usa righttailed pvalue of 1.9920=0.008, which is far less than
α
= 0
.
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 Spring '08
 TA
 Normal Distribution, Null hypothesis, Wilcoxon signedrank test, Rick Perry

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