1)You are interested in the final exam scores of one MAT 113 sections compared to another. The instructors cannot release the scores, but you are able to sample scores from each sections and find:
Section A: 87, 99, 86, 68, 95, 78, 69, 64, 65, 77, 90, 100, 81, 65, 58, 56, 65, 66, 89, 85, 66, 97, 54, 82, 99, 90, 72, 90, 76, 81, 71
Section C: 97, 68, 67, 58, 81, 96, 56, 73, 74, 76, 72, 89, 88, 65, 51, 59, 53, 83, 100, 93, 53, 50, 66, 66, 53, 99, 69, 61, 58, 97, 69, 40, 70, 66
You are in section A and hear the other section’s test was harder. Do these samples provide evidence at the 5% level that the exam in section C was harder?
2)A college has a new tutoring center, to test its effectiveness 20 random clases with multiple sections and a common final are selected. In some of the sections attending a tutoring session at the new center is required, in other sections it is optional. Below we have the average scores for each type of section for each of the 20 classes (all are different, bio, chem, history, stats, etc). Is there evidence at the 1% significance level that requiring attendance at the tutoring center results in improved test grades?
ClassRequiredOptional
18470
28172
39071
47677
57895
69588
77775
88884
98670
109389
117884
127770
137783
148885
157884
168087
177658
188877
197971
207171
3)We believe that people who enjoy math more are less likely to miss class. To test this, we divide our class data into 2 groups, a group of students who missed 1 or fewer classes and a group of students who miss 2 or more classes. Do we have sufficient evidence at the 5% level to conclude those who attend class more regularly have a higher average math enjoyment rating?
4)Form a hypothesis about a difference of means of two populations. Make sure that these populations are such that you need to subset the data (so do not just compare your math ratings to a different rating). State your hypothesis and then provide your findings.
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