a) A statistics professor would like to determine whether students in the class showed improved performance on the final exam as compared to the midterm examination. A random sample of 7 students selected from a large class revealed the following scores: midterm 70, 62, 57, 68, 89, 63, 82 and on the final 80, 79, 87, 88, 85, 79, 91. We will test to determine if there evidence of an improvement on the final examination, at the 1% significance level. What is the alternate hypothesis?

(Uf does nto equal Um, where f+final and M=midterm, UfUf, Uf>Um)

b)A statistics professor would like to determine whether students in the class showed improved performance on the final exam as compared to the midterm examination. A random sample of 7 students selected from a large class revealed the following scores: midterm 70, 62, 57, 68, 89, 63, 82 and on the final 80, 79, 87, 88, 85, 79, 91. We will test to determine if there evidence of an improvement on the final examination, at the 1% significance level. What is the critical value?

c)A statistics professor would like to determine whether students in the class showed improved performance on the final exam as compared to the midterm examination. A random sample of 7 students selected from a large class revealed the following scores: midterm 70, 62, 57, 68, 89, 63, 82 and on the final 80, 79, 87, 88, 85, 79, 91. We will test to determine if there evidence of an improvement on the final examination, at the 1% significance level. What is your test statistic?

d)A statistics professor would like to determine whether students in the class showed improved performance on the final exam as compared to the midterm examination. A random sample of 7 students selected from a large class revealed the following scores: midterm 70, 62, 57, 68, 89, 63, 82 and on the final 80, 79, 87, 88, 85, 79, 91. We will test to determine if there evidence of an improvement on the final examination, at the 1% significance level. What is your decision?

(do not reject Ho, reject Ho, reject H1, inconclusive)

e)A statistics professor would like to determine whether students in the class showed improved performance on the final exam as compared to the midterm examination. A random sample of 7 students selected from a large class revealed the following scores: midterm 70, 62, 57, 68, 89, 63, 82 and on the final 80, 79, 87, 88, 85, 79, 91. We will test to determine if there evidence of an improvement on the final examination, at the 1% significance level. What is your conclusion?

(there is no difference between the scores, there is no evidence of a significant improvement on the final, there is evicence of a significant improvement on the final, students scored better on the midterm).