One University moved from semester system to quarter system

One University moved from semester system to quarter system this Spring. The dean of Engineering School believes that the GPA of student has declined in the quarter system. To test his hypothesis, he randomly selected 10 students and found the grades given in table below.

Can the dean conclude at 0.05 significance level that the grades of the students declined after the conversion?

Solution

Set Up Hypothesis
Null , Ho: u1 = u2
Alternate, the grades of the students declined after the conversion- H1: u1 > u2
Test Statistic
X(Mean)=2.977
Standard Deviation(s.d1)=0.596 ; Number(n1)=10
Y(Mean)=2.95
Standard Deviation(s.d2)=0.62; Number(n2)=10
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =2.977-2.95/Sqrt((0.35522/10)+(0.3844/10))
to =0.1
| to | =0.1
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 9 d.f is 1.833
We got |to| = 0.09928 & | t | = 1.833
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value:Right Tail -Ha : ( P > 0.0993 ) = 0.46155
Hence Value of P0.05 < 0.46155,Here We Do not Reject Ho

We don\'t have evidence to support the grades of the students declined after the conversion