Chapter 10

Do students reduce study time in classes where they achieve a higher midterm score? In a Journal of Economic Education article (Winter 2005), Gregory Krohn and Catherine OConnor studied student effort and performance in a class over a semester. In an intermediate macroeconomics course, they found that students respond to higher midterm scores by reducing the number of hours they subsequently allocate to studying for the course. Suppose that a random sample of n = 8 students who performed well on the midterm exam was taken and weekly study times before and after the exam were compared. The resulting data are given in Table 10.6. Assume that the population of all possible paired differences is normally distributed.

Table 10.6

Weekly Study Time Data for Students Who Perform Well on the MidTerm
Students	1	2	3	4	5	6	7	8
Before	13	13	12	16	19	13	18	17
After	8	8	9	12	10	10	18	9

Paired T-Test and CI: Study Before, Study After

Paired T for Study Before - Study After
	N	Mean	StDev	SE Mean
StudyBefore	8	15.1250	2.6959	.9531
StudyAfter	8	10.5000	3.2950	1.1650
Difference	8	4.62500	2.87539	1.01660

95% CI for mean difference: (2.22112, 7.02888)

T-Test of mean difference = 0 (vs not = 0): T-Value = 4.55, P-Value = .0026

(a)Set up the null and alternative hypotheses to test whether there is a difference in the true mean study time before and after the midterm exam.

H₀: _d = versus H_a: _d ?

(b)Above we present the MINITAB output for the paired differences test. Use the output and critical values to test the hypotheses at the .10, .05, and .01 level of significance. Has the true mean study time changed? (Round your answer to 2 decimal places.)

t = We have (Click to select)nostrongvery strongextremely strongevidence.

(c)Use the p-value to test the hypotheses at the .10, .05, and .01 level of significance. How much evidence is there against the null hypothesis?

There is (Click to select)no evidenceextermly strong evidencevery strong evidencestrong evidence against the null hypothesis.