7 An experiment was conducted to test the effect of a new dr

7. An experiment was conducted to test the effect of a new drug on a viral infection. The infection was induced in 100 mice, and the mice were randomly split into two groups of 50. The first group, the control group, received no treatment for the infection. The second group received the drug. After a 30-day period, the proportions of survivors, pˆ1 and pˆ2, in the two groups were found to be 0.34 and 0.64 respectively.

a.[6] Use a 95% confidence interval to estimate the actual difference in the cure rates, i.e. p1 p2, for the treatment versus the control groups.

b.[4] Based on this confidence interval can you conclude that the drug is effective? Why?

Solution

a)

Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.34      
p2 = x2/n2 =    0.64      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.095372952      
          
          
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   -0.486927551      
upper bound = p1^ - p2^ + z(alpha/2) * sd   -0.113072449      
          
Thus, the confidence interval is          
          
(   -0.486927551   ,   -0.113072449 ) [ANSWER]

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b)

YES, because the whole interval is less than 0, which means p2 is convincingly greater than p1. [ANSWER]