An Ohio university wishes to demonstrate that car ownership is detrimental to academic achievement. A random sample of 100 students who do not own cars had a mean grade point average (GPA) of 2.681 while a random sample of 100 students who own cars had a mean GPA of 2.55.
a. Assuming that the independence assumption holds, and letting µ1 = the mean GPA for all students who do not own cars, and µ2 = the mean GPA for all students who own cars, use the above data to commute a 95 percent confidence interval for µ1 - µ2. Assume here that σ1 = .7 and σ2 = .6.
b. On the basis of the interval calculated in part a, can the university claim that car ownership is associated with decreased academic achievement? That is, can the university justify that µ1 is greater than µ2? Explain.
c. Set up the null and alternative hypotheses that should be used to attempt to justify that the mean GPA for non-car owners is higher than the mean GPA for car owners.
d. Test the hypotheses that you set up in part c with a = .05. Again assume that σ1 = .7 and σ2 = 6. Interpret the results of this test. That is, what do your results say about whether car ownership is associated with decreased academic achievement?