Question

1. A double blind, randomly allocated medical experiment is comparing two possible treatments for an immune-system disorder. Patients are randomly assigned treatments.

	Response	No Response
Treatment A	45	120
Treatment B	95	70

1. Show that Treatment B has the better response rate.

Answer 1

Ho:   p1 - p2 =   0          
Ha:   p1 - p2 <   0          
                  
sample #1   ----->              
first sample size,     n1=   165          
number of successes, sample 1 =     x1=   45          
proportion success of sample 1 , p̂1=   x1/n1=   0.2727          
                  
sample #2   ----->              
second sample size,     n2 =    165          
number of successes, sample 2 =     x2 =    95          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.5758          
                  
difference in sample proportions, p̂1 - p̂2 =     0.2727   -   0.5758   =   -0.3030
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.4242          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.05441          
Z-statistic = (p̂1 - p̂2)/SE = (   -0.303   /   0.0544   ) =   -5.5691
                  
z-critical value , Z* =        -1.6449   [Excel function =NORMSINV(α)      
p-value =        0.000   [Excel function =NORMSDIST(z)      
decision :    p-value<α,Reject null hypothesis               

there is enough evidence that  Treatment B has the better response rate