A claim states that the proportion of the U S household that

A claim states that the proportion of the U S household that watched the super Bowl on TV is Not 40% in a random sample 74 of 140 households had watched the most recent super bowl. Text the claim at the a= 0.05 signification level by comparing the calculated x-scpre to the critical z-score

Solution

Set Up Hypothesis
Null, H0:P=0.4
Alternate, H1: P!=0.4
Test Statistic
No. Of Success chances Observed (x)=74
Number of objects in a sample provided(n)=140
No. Of Success Rate ( P )= x/n = 0.5286
Success Probability ( Po )=0.4
Failure Probability ( Qo) = 0.6
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.52857-0.4/(Sqrt(0.24)/140)
Zo =3.1053
| Zo | =3.1053
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =3.105 & | Z | =1.96
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != 3.1053 ) = 0.0019
Hence Value of P0.05 > 0.0019,Here we Reject Ho

We have enough evidence to indicate that that the proportion of the U S household
that watched the super Bowl on TV is Not 40%