Table 6.29 gives a sample of grades on the first two quizzes in an introductory statistics course. We are interested in testing whether the mean grade on the second quiz is significantly higher than the mean grade on the first quiz.

Table 6.29

(a) Complete the test if we assume that the grades from the first quiz come from a random sample of 10 students in the course and the grades on the second quiz come from a different separate random sample of 10 students in the course. Clearly state the conclusion.
(b) Now conduct the test if we assume that the grades recorded for the first quiz and the second quiz are from the same 10 students in the same order. (So the first student got a 72 on the first quiz and a 78 on the second quiz.)
(c) Why are the results so different? Which is a better way to collect the data to answer the question of whether grades are higher on the second quiz?

Transcribed Image Text:

85 87 72 95 96 First Quiz Second Quiz 56 72 87 80 80 98 95 74 77 82 62 86 78 89 75