In a sample of 1000 people in Texas 540 prefer Coke and the

In a sample of 1000 people in Texas, 540 prefer Coke and the rest Pepsi. We want to test that both Coke and Pepsi are equally popular in the state of Texas.

Solution

Null, both Coke and Pepsi are equally popular Ho: p1 = p2
Alternate, There Is Significance between them H1: p1 != p2
Test Statistic
Sample 1 : X1 =540, n1 =1000, P1= X1/n1=0.54
Sample 2 : X2 =460, n2 =1000, P2= X2/n2=0.46
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.5
Q^ Value For Proportion= 1-P^=0.5
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.54-0.46)/Sqrt((0.5*0.5(1/1000+1/1000))
Zo =3.578
| Zo | =3.578
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =3.578 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != 3.5777 ) = 0.0003
Hence Value of P0.05 > 0.0003,Here we Reject Ho

We don;t have evidence to indicate that both Coke and Pepsi are equally popular