Question

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 O'Connor 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 11.5. Assume that the population of all possible paired differences is normally distributed. Table 11.5 Weekly Study Time Data for Students Who Perform Well on the Midterm Students 1 2 3 4 5 6 7 Before 17 14 17 17 16 16 19 After 9 11 16 10 9 16 10 8 19 11 Paired T-Test and Cl: StudyBefore, Study After Paired T for StudyBefore - StudyAfter N Mean StDev StudyBefore 8 16.8750 1.6421 StudyAfter 8 11.5000 2.8785 Difference 8 5.37500 3.50255 SE Mean .5806 1.0177 1.23834 95% Cl for mean difference: (2.44679, 8.30321) T-Test of mean difference = 0 (vs not = 0): T-Value = 4.34, P-Value = .0034 (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. HO: pd = versus Ha: ud #

Answer 1

Solution The nutt and alternative hypotheus are to ed=0 Hud 70 b) test statistic t = 4.34 when « : 0.10, de 7 Curtical value of tcout = tol to.cole : to toit 1.894 when -0-01 critical value of twittel -tool = 3.499 to tait when R 0.05 Critical value of tweit tala to.osle - 2.365 totcut Ho yes value SD علي mean p-value * for at the cares test statistic t is greater than cortical have enough endence to suject towe study time has changed c) 0.0034 p-value Lou p-value p-value 20.05 so, there a enough Evidence against hypothesis, true mean study time has changed ¿ 010) neti