a reasearcher wishes to test the effect of a particular blood pressure drug. A r

Question

a reasearcher wishes to test the effect of a particular blood pressure drug. A random sample of 11 patients were enrolled into the study and given the medication. blood pressure data was collected prior to receiving the drug and again after administration. unfortunately, the actual data was lost and all that remains are records of direction of the change(that is if the difference was <0, =0, >0) suppose 2 patient experienced no change, 2patiens'blood pressures went up, and the rest 7 went down. at the 10% level, is there enough evidence to conclude the drug is effective at lowering blood pressure, that is , is the median change less than 0?

Explanation / Answer

Hypotheses: The null and alternative hypotheses are as follows:

H0: the distributions of blood pressure before and after the medication are identical.

H1: the distribution of blood pressure after medication is shifted to the left of other distribution (blood pressure has reduced after the medication)

Test statistic: the test is left tailed test, therefore, the test statistic is T_, the rank sum of the negative differences. From given data, T_+T+=n(n+1)/2, where, n is the number of non-zero differences that are ranked.

Substituting n=2, T_+T+=3. Thus, T_ is either 1 or 2.

The rejection region is T_<=T0, where T0 is critical T for n=11 pairs. The critical T is 14 (from critical T value Wilcoxon signed rank test)

The test statistic is less than critical T. Therefore, reject null hypothesis and conclude that drug is effective at lowering blodd pressure.

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