In a study testing the effects of calcium supplements on blood pressure in men, 12 men were randomly chosen and given a calcium supplement for 12 weeks. The table shows the measurements for each subject's diastolic blood pressure taken before and after the 12-week treatment period. At \(\alpha=0.01\), can you reject the claim that there was no reduction in diastolic blood pressure?

(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 1 23 4 5 6 Before treatment 108 109 120 129 112 111 After treatment 99 115 105 116 115 117 Patient 7 8 9 10 11 12 Before treatment 117 135 124 118 130 115 After treatment 108 122 120 126 128 106