A study reported the results of a randomized trial of wholeb

A study reported the results of a randomized trial of whole-body hypothermia (cooling) for neonatal hypoxicdash–ischemic encephalopathy (brain problems in babies due to lack of oxygen). 27 of the100 infants randomly assigned to hypothermia died and 43 of the 90 infants in the control group died. What is the test statistic? (z)

Solution

Test Statistic
Sample 1 : X1 =27, n1 =100, P1= X1/n1=0.27
Sample 2 : X2 =43, n2 =90, P2= X2/n2=0.478
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.368
Q^ Value For Proportion= 1-P^=0.632
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.27-0.478)/Sqrt((0.368*0.632(1/100+1/90))
Zo =-2.965