Question

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) (2 points) Verify that the conditions are satisfied to perform a two-sample z-test for the difference in mean GPAs of the populations. (b) (4 points) 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) (12 points) An academic advisor at Longwood University claims that students who live in oncampus 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.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) (2 points) Verify that the conditions are satisfied to perform a two-sample z-test for the difference in mean GPAs of the populations. (b) (4 points) 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) (12 points) An academic advisor at Longwood University claims that students who live in oncampus 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.

Answer 1

a.

Conditions to perform a two-sample z-test for the difference in mean:

1. Populations are normally distributed.

2. Samples are independent

3. Population standard deviations are known.

All conditions are satisfied.

b.

Hypothesis:

c.

Test statistic,

Critical value at 5% level of significance = 1.645

Since calculated z is less than critical value we accept null hypothesis and conclude that the mean GPA of on-campus residents is same as the mean GPA of off-campus residents..

Hence there is sufficient evidence that the advisor’s claim was wrong (not true).