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 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 16 13 11 17 17 13 15 17 After 8 8 12 9 5 10 7 8 Paired T-Test and CI: Study Before, Study After Paired T for Study Before - Study After N Mean StDev SE Mean StudyBefore 8 14.8750 2.2952 .8115 StudyAfter 8 8.3750 2.0659 .7304 Difference 8 6.50000 4.03556 1.42678 95% CI for mean difference: (3.12619, 9.87381) T-Test of mean difference = 0 (vs not = 0): T-Value = 4.56, 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: µd = versus Ha: µd ≠ (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 evidence. (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 against the null hypothesis.

Answer 1

We perform paired t test in minitab to answer the questions

steps : stat, basic statistics, paired t test.

a) null hypothesis is H0 : there is no significant difference among the study time before and after semester

alternative hypothesis is H1 : there is significant difference among the study time before and after semester

minitab output at alpha=0.10, 0.05, 0.01

b) Critical value for T(df=8-1=7) at alpha =0.10, 0.05, 0.01 are respectively 1.860, 2.306 and 3.355

At alpha=0.10 as observed value=4.56>critical value=1.860, we reject the null hypothesis and conclude that there is significant difference among the study time before and after semester. Same thing happens in case of alpha =0.05, 0.01

c) as P-value=0.003<0.01, 0.05, 0.1 we reject the null hypothesis again and draw the same conclusion as above.