You have already seen a few examples of tests using nonparametric statistics suc

Question

You have already seen a few examples of tests using nonparametric statistics such as the rank-sum test. This assignment will detail a test used to compare data from matched pairs, like before and after tests, called the sign test for matched pairs. Remember that as with all nonparametric tests, this is the test you would need to use when the data don’t follow a normal distribution. For this assignment, you will answer questions and solve problems involving paired data. Instructions 1.Answer the following questions in a Word document: •Review the following data where patients with high blood pressure are given a drug that is thought to lower their blood pressure. The “before” amounts represent their blood pressure before taking the medicine. The “after” amounts represent their blood pressure after taking the medicine for three months: Subject Before After 1 140 140 2 148 140 3 146 138 4 154 152 5 142 144 6 151 148 7 140 138 8 148 146 9 146 148 10 154 150 11 142 140 12 151 148 13 153 150 •State why a sign test for matched pairs would be appropriate for this example. •Set up the hypotheses to determine if the claim is that the medicine helps to reduce blood pressure. •Calculate the test statistic and p-value for this example. •What would your conclusion be at the 0.05 level of significance?

Explanation / Answer

W-value: 7
Mean Difference: 7.92
Sum of pos. ranks: 71
Sum of neg. ranks: 7

Z-value: -2.5103
Mean (W): 39
Standard Deviation (W): 12.75

Sample Size (N): 12 (because the first diff is 0)

The W-value is 7. The critical value of W for N = 12 at p 0.05 is 13. Therefore, the result is significant at p 0.05.

Before After Diff Abs Rank Signed Rank 140 140 0 0 n/a n/a 148 140 8 8 11.5 11.5 146 138 8 8 11.5 11.5 154 152 2 2 3.5 3.5 142 144 -2 2 3.5 -3.5 151 148 3 3 8 8 140 138 2 2 3.5 3.5 148 146 2 2 3.5 3.5 146 148 -2 2 3.5 -3.5 154 150 4 4 10 10 142 140 2 2 3.5 3.5 151 148 3 3 8 8 153 150 3 3 8 8

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