A medical research team conducted a study to test the effect

A medical research team conducted a study to test the effect of a migraine drug. In the study, 400 objects took the drug and 407 subjects took a placebo. The results after two hours are shown below. At a=0.03, can you reject the claim that the proportion of subjects who are pain free is the same for the two groups? Round your answers to three decimal places.

Solution

Null Hypothesis, There Is No Significance between them Ho: p1 = p2
Alternate Hypothesis, There Is Significance between them H1: p1 != p2
Test Statistic
Sample 1 : X1 =100, n1 =400, P1= X1/n1=0.25
Sample 2 : X2 =41, n2 =407, P2= X2/n2=0.101
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.175
Q^ Value For Proportion= 1-P^=0.825
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.25-0.101)/Sqrt((0.175*0.825(1/400+1/407))
Zo =5.583
| Zo | =5.583
Critical Value
The Value of |Z | at LOS 0.03% is 2.17
We got |Zo| =5.583 & | Z | =2.17
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != 5.583 ) = 0
Hence Value of P0.03 > 0,Here we Reject Ho

We don\'t have evidence to support the proportion of subjects who are pain
free is the same for the two groups