Umbrella Corporation is trying to determine whether a new dr

Umbrella Corporation is trying to determine whether a new drug improves mood in individuals with bipolar disorder. The company gave the drug to 249 individuals (Group 1) and a placebo (or sugar pill) to a separate sample of 238 individuals (Group 2). After one month on the drug, 152 of the patients in Group 1 reported improved mood, while 139 of the patients in Group 2 reported the same.

Calculate the upper bound of a 95% confidence interval for the true difference in the proportion of individuals who experienced improved mood, to two decimal places.

Solution

Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.610441767      
p2 = x2/n2 =    0.584033613      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.044449747      
          
          
For the   90%   confidence level, then  
          
alpha = (1 - confidence level) =    0.05      

z(alpha) =    1.644853627      

Therefore,

upper bound = p1^ - p2^ + z(alpha/2) * sd =    0.09952148 = 0.10   [ANSWER]