Question 2 A researcher wishes to learn whether the GPA of i

Question 2.
A researcher wishes to learn whether the GPA of incoming flight students may be a factor in the

number of flight hours the student completes in the first semester of college. The researcher has collected the flight hours of a random sample of students in a group of high GPA students and low GPA students.

Low GPA

42 45 40 37

High GPA

43 51 56 40

41 32 41 54 48 51 50 55

45.

46.

The researcher is testing whether GPA may be a factor in differences in flight time accumulated in the first semester at college.
Their hypothesis is: The mean flight time of students with a low GPA is different than those incoming students with a high GPA.

A t-test can be used to test the probability that the two means do not differ. The alternative is that the means differ; one of them is greater than the other.
This is a two-tailed test because the researcher is interested in if GPA changes flight time.

Solution

Low GPA: n1=4, xbar1=41, s1=3.366502

High GPA: n2=14, xbar2=46.64286 , s2=6.800533

Let mu1 be the mean for low gpa

Let mu2 be the mean for high gpa

Ho: mu1=mu2(i.e. null hypothesis)

Ha: mu1 not equal to mu2 (i.e. alternative hypothesis)

The test statistic is

t=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(41-46.64286)/sqrt(3.366502^2/4+6.800533^2/14)

=-2.28

The degree of freedom =n1+n2-2=4+14-2=16

It is a two-tailed test.

Assume that the significant level a=0.05

The critical values are t(0.025, df=16) = -2.12 or 2.12 (from student t table)

Since t=-2.28 is less than -2.12, we reject Ho.

So we can conclude that the mean flight time of students with a low GPA is different than those incoming students with a high GPA.