Question

Proffesor. R wants to know if the GPA of foreign students is higher than the GPA of American students. He collects data on a random sample of 500 students and finds that the GPA of foreign students is 0.13 points higher than the GPA of American students (standard error 0.08). What is the null hypothesis? What is the alternative hypothesis? Can we reject the null hypothesis at the 5% level? Explain how you arrive at your answer. If your answer to b) was that we can reject the null hypothesis, answer the following: Does this show that the GPA of foreign students is higher than the GPA of American students in the population? Why or why not? If your answer to b) was that we cannot reject the null hypothesis, answer the following: Does this show that there is no difference between the GPA of foreign students and the GPA of American students in the population? Why or why not?

Answer 1

Let D= GPA of foreign students-GPA of American students

We are testing,

H0: Ud=0 vs H1: Ud>0

Test statistic: 0.13/0.08= 1.625

p-value of this one sided test is: (z test since n>120)

P(z>1.625) = 0.0521 (from standard normal distribution tables)

Since the p-value of this test>significance level of 0.05, we have insufficient evidence to Reject H0 at the 5% significance level.

So, since we fail to Reject H0, we conclude:

b) There is no difference between the GPA scores of foreign and American students.