Six hundred and five survivors of a heart attack were random

Six hundred and five survivors of a heart attack, were randomly assigned to follow either (1) a diet close to the \"prudent diet step 1\" of the American Heart Association or (2) a Mediterranean-type diet consisting of more bread and cereals, more fresh fruit and vegetables, more grains, more fish, fewer delicatessen food, less meat. Over four years, researchers collected information on number of deaths from cardiovascular causes e.g., heart attack and strokes. Of the 303 survivors who followed the AHA diet 24 died of cardiovascular disease. Of the 302 survivors who followed the Mediterranean diet, 14 died of cardiovascular disease. Is there a significant difference in the proportion of patients who die of cardiovascular disease across the two diet plans? Run the test at a 5% level of significance. 1) Write out the appropriate null hypothesis and the alternative hypothesis; 2) Calculate the test statistic (show your work); 3) Give your conclusion including a comparison to alpha or the critical value.

Solution

1.

Let p1 = the proportion of those who died in AHA diet

p2 = the proportion of those who died in Mediterranean diet

Formulating the hypotheses          
Ho: p1 - p2   =   0  
Ha: p1 - p2   =/=   0   [ANSWER, HYPOTHESES]

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2.

Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.079207921      
p2 = x2/n2 =    0.046357616      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.019674664      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    1.669675514   [ANSWER, TEST STATISTIC]

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3.  
          
          
Thus, the p value is, for a two tailed test,
          
P =    0.094983581  

As P > 0.05, we FAIL TO REJECT HO.

Thus, there is no significant difference in the proportion of patients who die of cardiovascular disease across the two diet plans. [CONCLUSION]