It is believed that at least 60 of the residents in a certai

It is believed that at least 60% of the residents in a certain area favor an annexation suit by a neighboring city. What conclusion would you draw if only 110 in a sample of 200 voters favored the suit? Use a 0.05 level of significance.

Solution

Set Up Hypothesis
NULL, at least 60% of the residents are favor H0:P>=0.6
Alternative, below 60% of the residents are favor H1: P<0.6
Test Statistic
No. Of Success chances Observed (x)=110
Number of objects in a sample provided(n)=200
No. Of Success Rate ( P )= x/n = 0.55
Success Probability ( Po )=0.6
Failure Probability ( Qo) = 0.4
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.55-0.6/(Sqrt(0.24)/200)
Zo =-1.44
| Zo | =1.44
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.443 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Left Tail -Ha : ( P < -1.44338 ) = 0.07446
Hence Value of P0.05 < 0.07446,Here We Do not Reject Ho

We conclude at least 60% of the residents are favor