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1.
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To investigate the robustness of the three point estimates, consider the
following data set:
X 12 15 18
Y 16 19 25 28
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(a)
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Obtain the three estimates: median of differences, difference in means,
difference in medians. (Answers: 7, 7, 7).
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(b)
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Next replace the Y observation 28 by 2800. Obtain the three estimates:
median of differences, difference in means, difference in medians. (Answers:
7, 700, 7).
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2.
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We will use the next two problems to investigate the robustness of the
confidence intervals.
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(a)
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Obtain comparison dotplots of the following data:
X:
31 32 33 37 37 44 44 45 45 46 50 50 50
57 57 58 59 59 67 67
Y:
40 45 45 47 50 52 53 53 54 54 55 61 63
66 67 68 73 73 76 83
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(b)
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Using Class code, Two-Sample Hypothesis
and CI (Wilcoxon), obtain the estimate of
and the confidence interval for it using the Wilcoxon.
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(c)
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Using Class code, Two-Sample Hypothesis
and CI (mean), obtain the estimate of
and the confidence interval for it using the difference in means.
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(d)
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Using Class code, Two-Sample Hypothesis
and CI (median), obtain the estimate of
and the confidence interval for it using the difference in medians.
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(e)
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Compare the intervals.
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3.
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Consider the samples (same as last problem but the typo of 67 on the last
data point of the X's was discovered and its true value of 670 has been
put in):
X:
31 32 33 37 37 44 44 45 45 46 50 50 50
57 57 58 59 59 67 670
Y:
40 45 45 47 50 52 53 53 54 54 55 61 63
66 67 68 73 73 76 83
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(a)
-
Using Class code, Two-Sample Hypothesis
and CI (Wilcoxon), obtain the estimate of
and the confidence interval for it using the Wilcoxon.
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(b)
-
Using Class code, Two-Sample Hypothesis
and CI (mean), obtain the estimate of
and the confidence interval for it using the difference in means.
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(c)
-
Using Class code, Two-Sample Hypothesis
and CI (median), obtain the estimate of
and the confidence interval for it using the difference in medians.
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(d)
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Compare the intervals.
