Question

I have collected about 200 samples worth of data to determine whether students that are not full time, full time being defined as anyone with 12 or more units, have a higher GPA than students who are full time. For this case our variances are not equal to each other and our samples are independent of each other.

How would you set up the hypothesis test for this case?

I originally have it set up like this but not sure if it is correct.

Students who are not full time are denoted as M₁ and Student who are full time are denoted as M₂

Ho : M₁ - M₂ = 0 *This means that students who not full time have a higher GPA*

H₁ : M₁ - M₂ > 0 *This means that student who are full time have a higher GPA*

Answer 1

Solution :

M1 = mean of Students who are not full time

M2 = mean of Student who are full time

We want to determine whether students that are not full time have a higher GPA than students who are full time

i.e. whether M1 > M2

i.e. whether M1 - M2 > 0

So, hypothesis can be written as

H0 : M1 - M2   0 (It can be considered same as M₁ - M₂ = 0)

H1:  M₁ - M₂   0  

Ho denotes the null hypothesis and H1 denoted the alternative hypothesis.

(valid signs in H0 are   , ,   

valid signs in H1 are   ,   ,   )