Question

# To determine whether living in an oﬀ-campus residence aﬀects an undergraduate student’s academic achievement at Longwood...

To determine whether living in an oﬀ-campus residence aﬀects an undergraduate student’s academic achievement at Longwood University, samples of 50 on-campus residents and 50 oﬀ-campus residents were drawn randomly and independently from the Longwood undergraduate student body. The GPA for the on-campus residents had mean 2.81 and variance 0.32, while the GPA for the oﬀ-campus students had a mean of 2.72 and variance 0.45. In this problem, you will conduct a two-sample z-test to determine if the data indicates that on-campus residents have higher mean academic achievements than oﬀ-campus residents.

(a) Verify that the conditions are satisﬁed to perform a two-sample z-test for the diﬀerence in mean GPAs of the populations.

(b) Formulate null and alternative hypotheses to test if the mean GPA of on-campus residents is greater than the mean GPA of oﬀ-campus residents.

(c) An academic advisor at Longwood University claims that students who live in on-campus residences tend to have higher academic achievements than students who do not. Do the given data present suﬃcient evidence to justify the advisor’s claim? That is, does the data indicate that the mean GPA of on-campus residents is greater than the mean GPA of oﬀ-campus residents? Test the advisor’s claim using a two-sample hypothesis z-test at the α = 0.05 level. Explain whether your result is signiﬁcant, and what that means regarding the advisor’s claim.