A recent article reported that a job awaits only one in thre

A recent article reported that a job awaits only one in three new college graduates. A survey of 200 recent graduates revealed that 80 graduates had jobs. At the .02 significance level, can we conclude that a larger proportion of graduates have jobs than reported in the article?

Solution

Set Up Hypothesis
Null, H0:P=0.33
Alternate, H1: P>0.33
Test Statistic
No. Of Success chances Observed (x)=80
Number of objects in a sample provided(n)=200
No. Of Success Rate ( P )= x/n = 0.4
Success Probability ( Po )=0.33
Failure Probability ( Qo) = 0.67
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.4-0.33/(Sqrt(0.2211)/200)
Zo =2.1053
| Zo | =2.1053
Critical Value
The Value of |Z | at LOS 0.02% is 2.05
We got |Zo| =2.105 & | Z | =2.05
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail - Ha : ( P > 2.10532 ) = 0.01763
Hence Value of P0.02 > 0.01763,Here we Reject Ho

We conclude that a larger proportion of graduates have jobs than reported in the article