A sample of 50 freshmen had a mean GPA of 28 GPA is the weig

A sample of 50 freshmen had a mean GPA of 2.8 (GPA is the weighted mean), with a standard deviation of 0.5, over all their courses taken in their first semester. Test the claim, at the 0.05 level to determine if the first semester GPA is less than a B (3.0). show work. Use the p-value method.
A) Null hypothesis: ?
B) Alternative hypothesis: ?
C) test statistic: ?
D) p-value: ?
E) initial conclusion: ?
F) conlsuion: ?

Solution

A & B)
Set Up Hypothesis
Null, H0: U=3
Alternate, H1: U<3
C)
Test Statistic
Population Mean(U)=3
Sample X(Mean)=2.8
Standard Deviation(S.D)=0.5
Number (n)=50
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =2.8-3/(0.5/Sqrt(49))
to =-2.828
D)
P-Value :Left Tail -Ha : ( P < -2.8284 ) = 0.00338
Hence Value of P0.05 > 0.00338,Here we Reject Ho

E)
the first semester GPA is less than a B (3.0)

F)
We have evidence to to determine if the first semester GPA is less than a B (3.0)