please guys I need help with this problem Thank you all Over

please guys I need help with this problem.

Thank you all.

Over the last decade, many Americans have been able to stop smoking. However, a recent survey suggests that asthmatic children are more likely to be exposed to second-hand smoke than children without asthma.^19 In a random sample of 300 children without asthma, 132 were regularly exposed to second-hand smoke, and in a random sample of 325 children with asthma, 177 were regularl exposed to second-hand smoke. Is there any evidence to suggest that the proportion of children with asthma who are exposed to second-hand smoke is greater than the proportion for children without asthma? Use alpha = 0.01.

Solution

Null, There Is No Significance between them Ho: p1 > p2
Alternate, children with asthama exposed to second hand smoke is greater H1: p1 < p2
Test Statistic
Sample 1 : X1 =132, n1 =300, P1= X1/n1=0.44
Sample 2 : X2 =177, n2 =325, P2= X2/n2=0.545
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.494
Q^ Value For Proportion= 1-P^=0.506
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.44-0.545)/Sqrt((0.494*0.506(1/300+1/325))
Zo =-2.613
| Zo | =2.613
Critical Value
The Value of |Z | at LOS 0.01% is 2.326
We got |Zo| =2.613 & | Z | =2.326
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Left Tail - Ha : ( P < -2.6135 ) = 0.00448
Hence Value of P0.01 > 0.00448,Here we Reject Ho

we have evidence to suggest that the proportion of children with asthma who are
exposed to second-hand smoke is greater than the proportion for children without asthma