Students who wish to go to graduate school are often required to take a graduate record exam. It has been suggested that students who prepare using a paper prep book do better, on average, than...

Students who wish to go to graduate school are often required to take a graduate record exam. It has been suggested that students who prepare using a paper prep book do better, on average, than students who use the online prep materials provided by the exam's administrators. In order to investigate this claim, the mean score, x̅_1, for a random sample of students how use a paper pre book will be compared to the mean score, x̅_2, for a random sample of students who use the online materials. Let the mean score for all students who use paper prep books be μ1μ1 and the mean score for all students who use the online materials be μ2μ2 . Which of the following are appropriate null and alternative hypotheses for this study?

a) Null hypothesis: μ1 = μ2 Alternative hypothesis: μ1 > μ2
b) Null hypothesis: x̅_1 = x̅_2 Alternative hypothesis: x̅_1 > x̅_2

c) Null hypothesis: x̅_1 > x̅_2 Alternative hypothesis: x̅_1 = x̅_2

d) Null hypothesis: x̅_1 = x̅_2 Alternative hypothesis: x̅_1 >= x̅_2

e) Null hypothesis: μ1 > μ2 Alternative hypothesis: μ1 = μ2