Question

An educational consulting group claims that there is a difference in the mean student loan debt of students who attended private four-year colleges and the mean student loan debt of students who attended out-of-state public four-year colleges. The student loan debt of 18 randomly selected students who attended private four-year colleges and 18 randomly selected students who attended out-of-state public four-year colleges, at the time of graduating college, is recorded. Assume that the population variances of student loan debts are equal for both the private college attendees and the public college attendees and that the distribution of student loan debt is normally distributed for both the private college attendees and the public college attendees. Let the students who attended private four-year colleges be the first sample, and let the students who attended out-of-state public four-year colleges be the second sample. The group conducts a two-mean hypothesis test at the 0.01 level of significance, to test if there is evidence of a difference in student loan debt between the two groups. For this test: H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test. The test results are: t≈6.43 , p-value is approximately 0.000 Which of the following are appropriate conclusions for this hypothesis test? Select all that apply.

Select all that apply:

There is insufficient evidence at the 0.01 level of significance to conclude that there is a difference in commute times between employees who take the bus and employees who take the subway.

Reject H0.

There is sufficient evidence at the 0.01 level of significance to conclude that there is a difference in the mean student loan debt between the two groups of students.

Fail to reject H0.

Answer 1

From the given information above,

the test statistic is 6.43 and P value is 0.0000

Here, P-value is less than 0.01.

We reject the null hypothesis.

There is sufficient evidence to support the claim that at 0.01 level of significance to conclude that there is difference in the mean student loan debt between two groups of student.