Census Data shows that 364 of Women Ages 1834 resided with F

Census Data shows that 36.4% of Women Ages 18-34 resided with Family in 2014. If you take a random sample of 50 young women and find that 20 of them live with family. Is this enough evidence to say that even more young women are living with family in 2015 than 2014? use .05 significance

Solution

Set Up Hypothesis
Null, H0:P<=0.364
Alternate,even more young women are living with family in 2015 H1: P>0.364
Test Statistic
No. Of Success chances Observed (x)=20
Number of objects in a sample provided(n)=50
No. Of Success Rate ( P )= x/n = 0.4
Success Probability ( Po )=0.364
Failure Probability ( Qo) = 0.636
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.4-0.364/(Sqrt(0.231504)/50)
Zo =0.5291
| Zo | =0.5291
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =0.529 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Right Tail - Ha : ( P > 0.52906 ) = 0.29838
Hence Value of P0.05 < 0.29838,Here We Do not Reject Ho

we have enough evidence to indicate that even more young women are living with family in 2015