Question

Aspirin prevents blood from clotting and helps prevent strokes. The Second European Stroke Prevention Study asked whether adding another anticlotting drug named dipyridamole would make a difference for patients who had already had a stroke. Here are the data on strokes during the two years of the study: Number of Number of patients strokes Aspirin alone 200 52 Aspirin dipyridamole 200 62 Is there a significant difference in the proportion of strokes in the two groups? Test at a = .01. Round your answers to three decimal places. (a). Select the correct hypotheses where pı denotes the proportion of patients in the aspirin group who suffered a stroke and p2 denotes the proportion of patients in the aspirin + dipyridamole group who suffered a stroke Ho: pi p2, Ha:pı p2 Ho: Pi P2, H:pi > p2 = (b). Without rounding any interim calculations, compute the test statistic: (c). Compute the positive critical value: (d). Using your answer from part (b), compute the p-value: to conclude that there is a significant (d). We Select an answer the null hypothesis and have difference in the proportion of strokes in the two groups Select an answer

Answer 1

a)

b)

sample #1   ----->              
first sample size,     n1=   200          
number of successes, sample 1 =     x1=   52          
proportion success of sample 1 , p̂1=   x1/n1=   0.2600          
                  
sample #2   ----->              
second sample size,     n2 =    200          
number of successes, sample 2 =     x2 =    62          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.3100          
                  
difference in sample proportions, p̂1 - p̂2 =     0.2600   -   0.3100   =   -0.0500
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.2850          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.04514          
Z-statistic = (p̂1 - p̂2)/SE = (   -0.050   /   0.0451   ) =   -1.1076

c)

z-critical value , Z* =        2.5758   [excel formula =NORMSINV(α/2)]  

d)

p-value =        0.2680   [excel formula =2*NORMSDIST(z)]  

e)

do not reject the null hypothesis and have not enough evidence to conclude that there is a significant difference in the proportion of strokes in the two groups