before endorsing a candidate for political office a newspape

before endorsing a candidate for political office, a newspaper editor surveys 200 randomly selected readers and finds that 120 favor the candidate in question. at the .05 level of significance, test the editor\'s claim the candidate is favored by at least 2/3 of the readers

Solution

Set Up Hypothesis
Null,candidate is favored by at least 2/3 of the readers H0:P>=0.667
Alternate, H1: P<0.667
Test Statistic
No. Of Success chances Observed (x)=120
Number of objects in a sample provided(n)=200
No. Of Success Rate ( P )= x/n = 0.6
Success Probability ( Po )=0.667
Failure Probability ( Qo) = 0.333
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.6-0.667/(Sqrt(0.222111)/200)
Zo =-2.0105
| Zo | =2.0105
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =2.011 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Left Tail -Ha : ( P < -2.0105 ) = 0.02219
Hence Value of P0.05 > 0.02219,Here we Reject Ho

We don\'t have evidence to support that the candidate is favored by at least 2/3 of the readers