Given two independent random samples with the following resu

Given two independent random samples with the following results: n1 = 130 n2=208 x1 =26 x2=79 Can it be concluded that there is a difference between the two population proportions? Use a significance level of alpha = 0.01 for the test. State the null and alternative hypotheses for the test. H0: p2 Ha: p1 p2

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 =26, n1 =130, P1= X1/n1=0.2
Sample 2 : X2 =79, n2 =208, P2= X2/n2=0.38
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.311
Q^ Value For Proportion= 1-P^=0.689
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.2-0.38)/Sqrt((0.311*0.689(1/130+1/208))
Zo =-3.475
| Zo | =3.475
Critical Value
The Value of |Z | at LOS 0.01% is 2.576
We got |Zo| =3.475 & | Z | =2.576
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho

[ANSWER]

Null, Ho: p1 = p2 . Alternative, Ho: p1 != p2