A veterinarian studying suspected causes of enteroliths conc

A veterinarian studying suspected causes of enteroliths, concretelike balls in the colons of horses. She suspects that diet of mostly alfalfa could be a cause. In a study conducted at a veterinary research facility she examines the records of 62 horses with enteroliths (cases) and compares them with the records of 75 horses free of enteroliths (controls). She finds 42 case horses were fed mostly alfalfa compared with 17 control horses. She calculates a 95% confidence interval for (pcase – pcontrol), where pcase is the proportion of horses with enteroliths that are fed mostly alfalfa and pcontrol is the proportion of control horses mostly fed alfalfa as:

A (–0.2841, 0.6173).

B (–0.3007, 0.6008).

C (0.2841, 0.6173).

D (0.3007, 0.6008).

Solution

          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.677419355      
p2 = x2/n2 =    0.226666667      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.076561998      
          
  
          
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 =    0.300693929      
upper bound = p1^ - p2^ + z(alpha/2) * sd =    0.600811447      
          
Thus, the confidence interval is          
          
(   0.300693929   ,   0.600811447 ) [OPTION D, ANSWER]