A medical researcher claims that a new drug affects the number of headache hours experienced by headache sufferers. The numbers of headache hours (per day) experienced by eight randomly selected patients before and after taking the drug are shown in the table. At \(\alpha=0.05\), can you support the researcher's claim?

Use a Wilcoxon test to test the claim by doing the following.

(a) Identify the claim and state \(H_{0}\) and \(H_{a}\).

(b) Decide whether to use a Wilcoxon signed-rank test or a Wilcoxon rank sum test.

(c) Find the critical value(s).

(d) Find the test statistic.

(e) Decide whether to reject or fail to reject the null hypothesis.

(f) Interpret the decision in the context of the original claim.

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Patient Headache hours (before) 0.9 2.3 2.7 1 2 3 4 5 10 2.4 2.9 67 1.9 1.2 3.1 8 Headache hours (after) 1.4 1.5 1.4 1.8 1.3 0.6 0.7 1.9