Question

4. The drug ancrod was tested in a double-blind clinical trial in which stroke patients were randomly assigned to receive either ancrod or a placebo. One of the response variables in the study was whether or not the subjects experienced intracranial hemorrhaging. Of the 84 patients who received ancrod, 13 hemorthaged. Of the 77 patients who received the placebo, only three hemorrhaged. a. Is there a significant difference in hemorrhaging rates between treatments? Shovw your work and include all steps for full credit.(6pt) Quantify the difference in hemorrhaging rates with the appropriate measure and interpret it in the context of the problem. (2pt) b.

Answer 1

Test for p_1 = p_2 We want to test whether hypothesis: H_0: p_1 - p_2 = 0 H_a: p_1 p_2 notequalto 0 This is two tailed test. (Null Hypothesis Alternative Hypothesis, also called H_1) x_1 = 13, n_1 = 84, x_2 = 3, n_2 = 77 p_1 = 13/84 almostequalto 0.154762 almostequalto 0.155, p_2 = 3/77 almostequalto 0.038961 almostequalto 0.039 Significance level, alpha = 0.05 The test for difference in proportion is done by pooled sample proportion: p = x_1 + x_2/n_1 + n_2 pr p_1 n_1 + p_2 n_2/n_1 + n_2 and q = 1 - p (notations may differ) p = 13 + 3/84 + 77 almostequalto 0.099379 = q almostequalto 0.900621 Pooled Standard Error: Se = squareroot pq/n_1 + pp/n_2 = squareroot (0.099379) (0.900621)/84 + (0.099379) (0.900621)/77 almostequalto 0.0472 Test statistic, z-observed = p_1 - p_2/SE = p_1 - p_2/squareroot pq/n_1 + pp/n_2 (0.154762) - (0.038961)/0.0472 almostequalto 2.483385