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  8 
Before  12  16  16  18  18  12  11  16 
After  10  10  6  11  8  6  9  9 
Paired TTest and CI: StudyBefore, StudyAfter
Paired T for StudyBefore  StudyAfter  
N  Mean  StDev  SE Mean  
StudyBefore  8  14.8750  2.7999  .9899 
StudyAfter  8  8.6250  1.8468  .6529 
Difference  8  6.25000  3.05894  1.08150 
95% CI for mean difference: (3.69266, 8.80734)
TTest of mean difference = 0 (vs not = 0): TValue = 5.78, PValue = .0007
(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.

(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=
(A) Hypotheses are already completed in part A
(B) Usig the given data
we get
t statistic = 5.78
t critical = T.INV.2T(alpha,df)
where df = n1 = 81 = 7
and alpha= 0.10,0.05 and 0.01
t critical(0.10,7) = T.INV.2T(0.10,7) = 1.89
t critical(0.05,7) = T.INV.2T(0.05,7) = 2.36
t critical(0.01,7) = T.INV.2T(0.01,7) = 3.50
We can see that the t statistic is greater than all the t critical values
So, we can reject the null hypothesis at 0.10,0.05 and 0.01 significance levels
Therefore, we can conclude that true mean study time changed
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