ii Determine the Pvalue for the test b In a study on the eff

ii. Determine the P-value for the test b. In a study on the effects of sodium restricted diets on hypertension, 24 out of 55 hypertensive patients were on sodium restricted diets, and 36 out of 149 non-hypertensive patients were on sodium restricted diets. i.) Test the hypothesis that the proportion of patients on sodium restricted diets is higher for hypertensive patients at significant level = 0.05. What is your decision? ii. What is the P-value for this test? Find the 95% two sided confident interval of this test. What is your conclusion? iii.

Solution

i)

Let p1 = proportion of hypertensive

Let p2 = proportion of non-hypertensive

Formulating the hypotheses          
Ho: p1 - p2   <=   0  
Ha: p1 - p2   >   0  
Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.436363636      
p2 = x2/n2 =    0.241610738      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.075508878      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    2.579205282      
          
As significance level =    0.05   , then the critical z is  
          
zcrit =    1.644853627      

As |z| > 1.645, we REJECT HO.

Thus, there is significant evidence that the proportion of patients on sodium restricted diets is higher for hypertensive patients. [CONCLUSION]

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ii)
          
Also, the p value is, as this is one tailed,          
          
P =    0.004951396   [ANSWER]

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iii)

For the   95%   confidence level, then  
          
alpha/2 = (1 - confidence level)/2 =    0.025      
z(alpha/2) =    1.959963985      
          
lower bound = p1^ - p2^ - z(alpha/2) * sd =    0.046758216      
upper bound = p1^ - p2^ + z(alpha/2) * sd =    0.34274758      
          
Thus, the confidence interval is          
          
(   0.046758216   ,   0.34274758 ) [ANSWER]

As this interval is totally greater than 0, then we have significant evidence that the proportion of patients on sodium restricted diets is higher for hypertensive patients. [CONCLUSION]