Exhibit 7-4: A group of researchers has developed a method that they hypothesize will improve physics test scores.They randomly selected nine students to participate in their study.The nine students were administered an ACT test, trained in the new method, and then administered an alternate form of the ACT test.The following data are their scores:
$ \begin{array}{lll}\text {Subject } & {\text {Test 1 }}{} & \text {Test 2 } \ 1 & 20 & 19 \ 2 & 20 & 20 \ 3 & 24 & 21 \ 4 & 24 & 24 \ 5 & 24 & 22 \ 6 & 17 & 15 \ 7 & 18 & 15 \ 8 & 18 & 16 \ 9 & 20& 18\end{array} $
-Refer to Exhibit 7-4.The degrees of freedom for the test are the
A) number of rows -1 time the number of columns -1.
B) number of pairs of numbers -1.
C) total number of cases -2.
D) none of these are true.

Question

Exhibit 7-4: A group of researchers has developed a method that they hypothesize will improve physics test scores.They randomly selected nine students to participate in their study.The nine students were administered an ACT test, trained in the new method, and then administered an alternate form of the ACT test.The following data are their scores:
 $ \begin{array}{lll}\text {Subject } & {\text {Test 1 }}{} & \text {Test 2 } \ 1 & 20 & 19 \ 2 & 20 & 20 \ 3 & 24 & 21 \ 4 & 24 & 24 \ 5 & 24 & 22 \ 6 & 17 & 15 \ 7 & 18 & 15 \ 8 & 18 & 16 \ 9 & 20&  18\end{array} $
-Refer to Exhibit 7-4.The degrees of freedom for the test are the
A) number of rows -1 time the number of columns -1.
B) number of pairs of numbers -1.
C) total number of cases -2.
D) none of these are true.

Quizplus · Accepted Answer

The degrees of freedom for a paired samples t-test, which is appropriate for this scenario where the same subjects are measured before and after an intervention, is calculated as the number of pairs (subjects) minus one. Here, there are 9 pairs (subjects), so the degrees of freedom are 9 - 1 = 8.

Exhibit 7-4: a Group of Researchers Has Developed a Method