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# 13.30

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## Elena Marten

on 25 April 2011

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#### Transcript of 13.30

13.30 Preventing Strokes Aspirin prevents blood from clotting and so helps prevent strokes. The second European Stroke Prevention Study asked whether adding another anticlogging drug, named dipyridamole, would be more effective for patients who had already had a stroke. Here are the data for on strokes and deaths during the two years of the study. Aspirin Alone
Aspirin + dipyridamole # of patients
1649
1650 # of strokes
206
157 # of deaths
182
185 (a) The study was a randmomized experiment. Outline the design of the experiment. SRS of patients who have already had a stroke 1649 patients 1650 patients Aspirin alone Aspirin + dipyridamole Compare results (b) Is there a significant difference in the proportion of strokes between these two treatments? Carry out an appropriate test to help answer this question. Step 1: Hypotheses We want to use this comparative randomized experiment to draw conclusions about p , the proportion of patients who had a stroke after taking aspirin alone, and p , the proportion of patients who have after taking aspirin and dipyridamole. We hope to show that dipyridamole reduces strokes, so we have a one-sided alternative: H : p = p
H : p < p 0 1 2 a 1 2 Step 2: Conditions SRS Normality Independence The two samples can be viewed as SRSs from their respective populations n p = (1649)(.11) = 181.39
n p = (1650)(.11) = 181.50
n (1-p ) = (1649)(.89) = 1467.61
n (1-p ) = (1650)(.89) = 1468.50 1 1 2 2 c ^ c c c ^ ^ ^ Since all four of these values are larger than 5, we are safe using a Normal approximation. We must assume that the population is at least 10 times as large as both samples of stroke patients. Step 3: Calculations z = __________________ p - p ^ ^ 1 2 / - _________________ p (1- p )(1/n + 1/n ) c c ^ ^ z = 2.726 Step 4: Interpretation The p-value, .9968, tells us that we have strong evidence that fails to reject the null hypothesis. Aspirin alone and aspirin + dipyridamole have similar effects. P-value = .9968 (c) Construct and interpret a 95% confidence interval for the difference in the proportion of deaths for these two treatments. (p - p ) + z* p (1- p ) p (1- p ) __________________ __________________ n n + / _____ _ 1 1 1 2 2 2 1 2 ^ ^ ^ ^ ^ ^ - (.00767, .05033) It is 95% confident that the percent of people who had strokes is somewhere between 0.77% and 5.0% lower among the people who were given aspirin + dipyridamole. (d) Describe a Type I and a Type II error in this setting. Which is more serious? Explain. Type I Error: We determine that the dipyridamole is effective when it actually is not.
Type II Error: We determine that the dipyridamole does not reduce the risk of strokes when it actually does.
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