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1.
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Finish the example for the twin data. Recall the paired differences were:
pair N H D
1 74 63 11
2 43 33 10
3 61 41 20
4 79 67 12
5 80 65 15
6 73 80 -7
7 56 43 13
8 98 84 14
9 84 74 10
10 52 48 4
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(a)
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Obtain the value of the Wilcoxon test statistic. (Actually determine the
number of negative averages (2) and subtract it for 10(11)/2.
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(b)
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Obtain the p-value for a two sided-test. Use class code of course, Wilcoxon
for paired designs. Conclude in terms of the problem.
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(c)
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Obtain (from class code) the estimated effect and the associated confidence
interval. Conclude in terms of the problem.
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2.
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From Cushney and Peebles (1905)a, J. of Phisiology: Ten patients
were selected for a study. The average number of hours that they slept
was deterimed. There were two parts to the study. In Part 1, they were
given by a flip of the coin one of two drugs, Laevo and Dextro, and the
average (over a week) number of excess hours (over their usual average)
was recorded. In Part 2 (after a wash out period), they were given the
other drug, and the average (over a week) number of excess hours (over
their usual average) was recorded. The data are:
Patient Dextro Laevo
1 0.7 1.9
2 -1.6 0.8
3 -0.2 1.1
4 -1.2 0.1
5 -0.1 -0.1
6 3.4 4.4
7 3.7 5.5
8 0.8 1.6
9 0.0 4.6
10 2.0 3.4
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(a)
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Obtain the value of the Wilcoxon test statistic, (diff = D - L).
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(b)
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Compare it what you would expect under H0.
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(c)
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Obtain the p-value for a two sided-test. Use class code of course, Wilcoxon
for paired designs. Conclude in terms of the problem.
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(d)
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Obtain (from class code) the estimated effect and the associated confidence
interval. Conclude in terms of the problem.
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3.
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The data below are some measurements recorded by Charles Darwin in 1878.
They consist of 15 pairs of heights in inches of cross-fertilized plants
and self-fertilized plants, Zea mays, each pair grown in the same pot.
POT CROSS SELF
1 23.500 17.375
2 12.000 20.375
3 21.000 20.000
4 22.000 20.000
5 19.125 18.375
6 21.550 18.625
7 22.125 18.625
8 20.375 15.250
9 18.250 16.500
10 21.625 18.000
11 23.250 16.250
12 21.000 18.000
13 22.125 12.750
14 23.000 15.500
15 12.000 18.000
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(a)
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Obtain the value of the Wilcoxon test statistic, (diff = C - S).
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(b)
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Compare it what you would expect under H0.
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(c)
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Obtain the p-value for a two sided-test. Use class code of course, Wilcoxon
for paired designs. Conclude in terms of the problem.
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(d)
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Obtain (from class code) the estimated effect and the associated confidence
interval. Conclude in terms of the problem.
