Suppose the Acme Drug Company develops a new drug designed t

Suppose the Acme Drug Company develops a new drug, designed to prevent colds, The company states that the drug is equally effective for men and women. To test this claim, they choose a simple random sample of 150 women and 300 men from two male and female populations. At the end of the study, 38% of the women caught a cold; and 45% of the men caught a cold. Based on these findings, can we reject the company\'s claim that the drug is equally effective for men and women Use a 0.05 level of significance.

Solution

Null , There Is No Significance between them Ho: p1 = p2
Alternate , There Is Significance between them H1: p1 != p2
Test Statistic
Sample 1 : X1 =57, n1 =150, P1= X1/n1=0.38
Sample 2 : X2 =135, n2 =300, P2= X2/n2=0.45
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.427
Q^ Value For Proportion= 1-P^=0.573
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.38-0.45)/Sqrt((0.427*0.573(1/150+1/300))
Zo =-1.415
| Zo | =1.415
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =1.415 & | Z | =1.96
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != -1.4153 ) = 0.157
Hence Value of P0.05 < 0.157,Here We Do not Reject Ho

[ANSWER]
We have evidence to cliam that the drug is equally effective for men and women