## Related questions with answers

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 $10.5$. Assume that the population of all possible paired differences is normally distributed.

Table $10.5$ Weekly Study Time Data for Students Who Perform Well on the MidTerm

Students | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
---|---|---|---|---|---|---|---|---|

Before | $15$ | $14$ | $17$ | $17$ | $19$ | $14$ | $13$ | $16$ |

After | $9$ | $9$ | $11$ | $10$ | $19$ | $10$ | $14$ | $10$ |

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

Solution

VerifiedThe goal of this task is to set the null and the alternative hypothesis. The hypotheses that will help us try to determine is there a difference between the two population mean study time, the first mean before the midterm exam and the other mean after the same exam, is this a null hypothesis

$H_0: \mu_1-\mu_2 = 0,$

and this alternative hypothesis:

$H_a: \mu_1-\mu_2 \neq 0.$

Here $\mu_1$ represents the population mean of the time that was spent studying before the midterm exam and $\mu_2$ is the population mean of time that was spent studying after that exam.

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