Table 1 Grade point averages of male and female students in

Table 1. Grade point averages of male and female students in the combined chemistry and chemical engineering classes.

Solution

Set Up Hypothesis
Null , There Is No-Significance between them Ho: u1 = u2
Alternate , male students have better GPAs than the female students - H1: u1 < u2
Test Statistic
X(Mean)=2.888
Standard Deviation(s.d1)=0.585 ; Number(n1)=11
Y(Mean)=2.975
Standard Deviation(s.d2)=0.46743; Number(n2)=38
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =2.888-2.975/Sqrt((0.34223/11)+(0.21849/38))
to =-0.45
| to | =0.45
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 10 d.f is 1.812
We got |to| = 0.45314 & | t | = 1.812
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value:Left Tail - Ha : ( P < -0.4531 ) = 0.33006
Hence Value of P0.05 < 0.33006,Here We Do not Reject Ho

We don\'t have enough evidence to indicate that male students have better GPAs than the female students