10.44 Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart att
ID: 2959203 • Letter: 1
Question
10.44 Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study,researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people (average age
58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for the
inactive pill.
(a) State the appropriate hypotheses.
(b) Obtain a test statistic and p-value. Interpret the results at a = .01.
(c) Is normality assured?
(d) Is the difference large enough to be important?
(e) What else would medical researchers need to know before prescribing this drug widely? (Data
are from Science News 153 [May 30, 1998], p. 343.)
Explanation / Answer
a) I used a z-test for two proportions to compare whether the proportion of patients with a heart attack on lovastatin was significantly different from the proportion of patients with a heart attach on the placebo. H0: p1 = p2 HA: p1 ? p2 b) p^ = (X1 + X2)/(n1 + n2) = (57 + 97)/(2325 + 2081) = 0.035 SE = sqrt [ (p^)(1-p^)(1/n1 + 1/n2) ] SE = sqrt [ (0.035)(0.965)(1/2325 + 1/2081) ] SE = sqrt[(0.035)(0.965) (0.0009] SE = 0.005546 z = (p^1 - p^2 ) / SE z = (57/2325 – 97/2081) / 0.005546 z = (0.0245 - 0.0466) / 0.005546 z = -3.98 By table lookup, p < 0.001, so we have sufficient evidence to reject the null hypothesis and state that patients on lovastatin are significantly less likely to have heart attacks. c) The sample sizes are large enough to assure normality d) Yes. The difference is significant and also substantial. e) Researchers should check for side effects, drug interactions, and other possible negative effects. They should also check to see if it is equally effective for major subgroups in the sample (e.g. males and females)Related Questions
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