Question

A clinical trial for hydroxychloroquine was performed and hailed by the leader of a large nation as a huge success. Perhaps the biggest success ever!
In this trial only 292 people who received hydroxychloroquine died, compared to the placebo group, where 837 people died. A total of 3,024 people received hydroxychloroquine, and 11,536 received the placebo.
Plot a graph that best communicates the results of this trial. Do you agree that these results show that hydroxychloroquine is a useful treatment for SARS-CoV-2?

Answer 1

Ho:   p1 - p2 =   0          
Ha:   p1 - p2 >   0          
                  
sample #1   ----->              
first sample size,     n1=   3024          
number of successes, sample 1 =     x1=   292          
proportion success of sample 1 , p̂1=   x1/n1=   0.0965608          
                  
sample #2   ----->              
second sample size,     n2 =    11536          
number of successes, sample 2 =     x2 =    837          
proportion success of sample 1 , p̂ 2=   x2/n2 =    0.072555          
                  
difference in sample proportions, p̂1 - p̂2 =     0.0966   -   0.0726   =   0.0240
                  
pooled proportion , p =   (x1+x2)/(n1+n2)=   0.0775412          
                  
std error ,SE =    =SQRT(p*(1-p)*(1/n1+ 1/n2)=   0.00546          
Z-statistic = (p̂1 - p̂2)/SE = (   0.024   /   0.0055   ) =   4.393
                  
z-critical value , Z* =        1.6449   [excel function =NORMSINV(α)]      
p-value =        0.0000   [excel function =NORMSDIST(-z)]      
decision :    p-value<α,Reject null hypothesis               
                  
NO, we do not agree that these results show that hydroxychloroquine is a useful treatment for SARS-CoV-2