A politician claims that he is supported by a clear majority

A politician claims that he is supported by a clear majority of voters. In a recent survey, 33 out of 63 randomly selected voters indicated that they would vote for the politician. Use a 5% significance level for the test.

Calculate the sample proportion. (Round your answer to 3 decimal places.)

Calculate the value of test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

Calculate the p-value of the test statistic.

Solution

Set Up Hypothesis
Null, H0:P<=0.5
Alternate,is supported by a clear majority of voters H1: P>0.5
Test Statistic
No. Of Success chances Observed (x)=33
Number of objects in a sample provided(n)=63
No. Of Success Rate ( P )= x/n = 0.5238
Success Probability ( Po )=0.5
Failure Probability ( Qo) = 0.5
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.52381-0.5/(Sqrt(0.25)/63)
Zo =0.378
| Zo | =0.378
Critical Value
The Value of |Z | at LOS 0.1% is 1.28
We got |Zo| =0.378 & | Z | =1.28
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Right Tail - Ha : ( P > 0.37796 ) = 0.35273
Hence Value of P0.1 < 0.35273,Here We Do not Reject Ho

We don\'t have evidence that he is supported by a clear majority of voters