Hypothesis Testing
Problem for Senate Polls
Question: The table below has data on the margin in
percentages Republican Candidate minus Democratic candidate for all polls up to
August 29, 2016 in the major Senate battles for 2016. Test the hypothesis that the mean difference
in the Republican minus Democratic margin percentage is zero versus the null
hypothesis that this margin is not zero.
Do we reject the null hypothesis? Would we have rejected the null hypothesis
if we had employed a onetailed test rather than a twotailed test?
Recent Senate Poll
Results


State

Republican minus Democrat
Senate Candidate Margin

Ohio

15

Ohio

8

Ohio

7

Ohio

9

Ohio

5

Ohio

5

Ohio

4

Penn

7

Penn

3

Penn

4

Penn

2

Penn

1

Penn

1

Penn

7

Florida

5

Florida

5

Florida

6

Florida

2

Florida

13

Florida

3

Wisc

11

Wisc

13

Wisc

10

NC

5

NC

2

NC

2

NC

4

Iowa

7

Iowa

9

Iowa

10

Iowa

10

Iowa

10

Iowa

1

Iowa

7

Nevada

0

Nevada

1

Nevada

2

Nevada

2

Arizona

13

Arizona

2

Arizona

9

Colorado

16

Colorado

15

Colorado

15

Colorado

13

Colorado

6

Analysis: I conducted the test in Excel. See calculations in the table below.
Hypothesis Test Results


Count

46

STD

7.996

Average

1.457

Zscore

1.235

pvalue Z score

0.217

The twotailed pvalue for the twotailed test is 2 x
(1NORMSDIST(ZSCORE))
At 0.217 this pvalue suggests we cannot reject the null
hypothesis at any conventional critical value.
The onetailed test that Republicans are outpacing Democrats
would have a pvalue greater than 0.10.
Again we would end up accepting the null hypothesis of no difference.
Comments: it is
somewhat remarkable that the Republican Average Senate vote is larger than the
Democratic Average Senate vote in this sample because most of the states in the
sample are blue states that Obama won twice and many of the Republican
incumbents are still in their first term and only got elected in 2010, a very
good year for Republicans. The
Democrats might manage to take back the Senate because the Republicans must
defend a lot of seats in blue states but Democratic Senate candidates are
running worse than expected in Ohio, Florida, and Nevada, all states where
Hillary Clinton has a big lead.
A discussion of polling data on a statebystate level and
some of my political insights can be found in the following post.
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