A sample poll of 300 voters from New York City and 200 voter

A sample poll of 300 voters from New York City and 200 voters from Washington D.C. showed that 56% and 48%, respectively, were in favor of a proposed county legislation that would provide universal healthcare services to eligible residents. At the = 0.09 level of significance, test the hypothesis that there is a difference between the two cities in their endorsement of the proposed legislation.

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 =168, n1 =300, P1= X1/n1=0.56
Sample 2 : X2 =96, n2 =200, P2= X2/n2=0.48
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.528
Q^ Value For Proportion= 1-P^=0.472
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.56-0.48)/Sqrt((0.528*0.472(1/300+1/200))
Zo =1.755
| Zo | =1.755
Critical Value
The Value of |Z | at LOS 0.09% is 1.695
We got |Zo| =1.755 & | Z | =1.695
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != 1.7555 ) = 0.0792
Hence Value of P0.09 > 0.0792,Here we Reject Ho

there is a difference between the two cities in their endorsement of the proposed legislation.