Do students reduce study time in classes where they achieve ahigher midterm score? In a Journal of Economic Educationarticle (Winter 2005), Gregory Krohn and Catherine O’Connor studiedstudent effort and performance in a class over a semester. In anintermediate macroeconomics course, they found that “studentsrespond to higher midterm scores by reducing the number of hoursthey subsequently allocate to studying for the course.” Supposethat a random sample of n = 8 students who performed wellon the midterm exam was taken and weekly study times before andafter the exam were compared. The resulting data are given in Table10.6. Assume that the population of all possible paired differencesis normally distributed.

Table 10.6

Weekly Study Time Data for Students Who Perform Well on theMidTerm
Students	1	2	3	4	5	6	7	8
Before	15	19	12	17	16	15	11	16
After	11	18	9	10	8	9	11	10

Paired T-Test and CI: Study Before, StudyAfter

   

Paired T for Study Before - Study After
	N	Mean	StDev	SE Mean
StudyBefore	8	15.1250	2.5877	.9149
StudyAfter	8	10.7500	3.1053	1.0979
Difference	8	4.37500	2.87539	1.01660

95% CI for mean difference: (1.97112, 6.77888)

T-Test of mean difference = 0 (vs not = 0): T-Value = 4.30,P-Value = .0036

(a) Set up the null and alternative hypothesesto test whether there is a difference in the true mean study timebefore and after the midterm exam.

H₀: µ_d=  versus H_a: µ_d?

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

t =   We have (Click to select)noverystrongextremely strongstrong evidence.

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

There is (Click to select)very strong evidenceextermly strongevidencestrong evidenceno evidence against the null hypothesis.