Problem 5 – We have done all this work and we have tried to be diligent. Let us see how the study finished. YOU MUST USE STATCRUNCH! (For each of the problems you must state: a) the hypotheses and identify the claim, b) state the test value, c) p-value, d) make a decision and e) summarize the results.)
a) (7 pts) Given the previous information where \mu = 134 and our sample is and s = 2.4 (again with n = 36), is there a significant difference in our sample compared to the population? (Yes, I know there is no given significance level.)
b) (7 pts) We would like to see if there is a linear relationship between heart rates and the number of hours a student studied (0.05 level of significance) and, if so, what is the mathematical relationship. Below is a set of data that was accumulated.
Hours studied, x 11 10 10 10 6 12 9 14
Blood pressure, y 130 129 126 130 133 127 131 131
c) (7 pts) Trying to improve the techniques I use in the classroom and reduce the anxiety of the students, I decided to try an experiment. I decided that I would incorporate more relaxation techniques prior to exams. For a comparison, I subjected the students to twice the exams (evil, I know). [In essence, I did a pre- and post-test.] The scores are below. At \alpha = 0.05, can it be concluded that the relaxation techniques helped improve test scores?
No relax 85 72 91 56 80 94 82 78 68
Relax 88 74 89 67 83 93 85 77 71
d) (7 pts) I took percentages from my last two statistics courses and found that the proportion of students you scored a C-or-better was 87% in class A (n = 30) and 82% in class B (n = 36). At the 0.05 level of significance, can it be concluded whether the proportion of students who scored C-or-better was higher in class A?
e) (7 pts) Looking into teaching evaluations for the statistics courses, we have evaluation scores of male and female professors below. Use a 0.05 significance level to test the claim that female and male professors have evaluation scores with the same variation.
Male 4.4 3.4 4.8 2.9 4.4 4.9 3.5 3.7 3.4 4.8
Female 4.2 3.8 4.3 4.1 3.9 4.2 4.1 4.3 4.5 4.3