Test weather P1 P2 given the sample data x1 28 n1 254 x2

Test weather P_1 P_2 given the sample data: x_1 = 28, n_1 = 254, x_2 = 36, n_2 = 301 at significance level alpha = 0.05.

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 =28, n1 =254, P1= X1/n1=0.11
Sample 2 : X2 =36, n2 =301, P2= X2/n2=0.12
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.115
Q^ Value For Proportion= 1-P^=0.885
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.11-0.12)/Sqrt((0.115*0.885(1/254+1/301))
Zo =-0.344
| Zo | =0.344
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =0.344 & | 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 != -0.3441 ) = 0.7307
Hence Value of P0.05 < 0.7307,Here We Do not Reject Ho