A presidential candidate has decided to enter primaries in t

A presidential candidate has decided to enter primaries in those states in which at least 20% of voters support her. Random samples of 200 voters were taken in each of a number of states. In New Hampshire, 33 voters supported the candidate. Test at a 5%(0.05) level of significance to determine whether the candidate should enter the New Hampshire primary. What is the p-value for this test? What is your conclusion?

Solution

Set Up Hypothesis
Null, at least 20% of voters support her H0:P>=0.2
Alternate, H1: P<0.2
Test Statistic
No. Of Success chances Observed (x)=33
Number of objects in a sample provided(n)=200
No. Of Success Rate ( P )= x/n = 0.165
Success Probability ( Po )=0.2
Failure Probability ( Qo) = 0.8
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.165-0.2/(Sqrt(0.16)/200)
Zo =-1.2374
| Zo | =1.2374
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.237 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Left Tail -Ha : ( P < -1.23744 ) = 0.10796
Hence Value of P0.05 < 0.10796,Here We Do not Reject Ho

[ANSWER]
1. P-value = 0.10796
2. We have evidence to support at least 20% of voters support her