Question

You would like to compare the mean GPA between sociology majors and math majors at BYU-I. In order to do that, you select a random sample of 40 students who are Math majors and 40 who are sociology majors.

In the above question suppose your confidence interval was [0.32, 0.74], what does that tell you about the mean GPA of sociology majors as compared to math majors?

  

There is insufficient evidence to show that they are different.

   

There is a significant difference between them.

   

The true mean for sociology majors is 0.32 and the true mean for the math majors is 0.74.

   

The true mean for sociology majors is 0.74 and the true mean for the math majors is 0.32.

   

The sociology majors have a much higher GPA than the math majors.

Answer 1

Here, we are testing

We see the confidence interval for the difference in means is .

Since the confidence interval does not include 0, i.e. , one mean is clearly above the other mean .

We can conclude that

There is a significant difference between them

Here it is not clear whether each stands for sociology majors and math majors or vice versa.

If stands for sociology majors, then

The sociology majors have a much higher GPA than the math majors.

is also correct.