According to a recent poll 53 of Americans would vote for th

According to a recent poll 53% of Americans would vote for the incumbent president. If a random sample of 100 people results in 45% who would vote for the incumbent, test the claim that the actual percentage is 53%. Use a 0.10 significance level.

Solution

Set Up Hypothesis
Null, H0:P=0.53
Alternate, H1: P!=0.53
Test Statistic
No. Of Success chances Observed (x)=45
Number of objects in a sample provided(n)=100
No. Of Success Rate ( P )= x/n = 0.45
Success Probability ( Po )=0.53
Failure Probability ( Qo) = 0.47
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.45-0.53/(Sqrt(0.2491)/100)
Zo =-1.6029
| Zo | =1.6029
Critical Value
The Value of |Z | at LOS 0.1% is 1.64
We got |Zo| =1.603 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -1.60289 ) = 0.10896
Hence Value of P0.1 < 0.109,Here We Do not Reject Ho
We have evidence that actual percentage is 53%