a university is tracking its honors program believes that th

a university is tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. in a sample of 200 graduates, 30 students have a GPA of 3.00 or below .a. In testing the university\'s belief, how does on define the population parameter of interest? b. The value of the test statistics and its associated p-value are? c. In testing the university\'s belief, the appropriate hypothesis are? d. At a 5% significance level, the decision is to?

Solution

Set Up Hypothesis
Null, H0:P=0.2
Alternate, H1: P<0.2
Test Statistic
No. Of Success chances Observed (x)=30
Number of objects in a sample provided(n)=200
No. Of Success Rate ( P )= x/n = 0.15
Success Probability ( Po )=0.2
Failure Probability ( Qo) = 0.8
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.15-0.2/(Sqrt(0.16)/200)
Zo =-1.7678
| Zo | =1.7678
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.768 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Left Tail -Ha : ( P < -1.76777 ) = 0.03855
Hence Value of P0.05 > 0.03855,Here we Reject Ho
we conclude that the proportion of graduates with a GPA of 3.00 or below
is less than 0.20