Suppose eight college-bound students take a mock SAT, complete a three-month testprep course, and then take the real SAT. A portion of the data is shown in the accompanying table.

Student..................... Score on Mock SAT............... Score on Real SAT

1................................................. 1830.................................. 1840

2................................................. 1760.................................. 1800

⋮......................................................⋮........................................⋮

8................................................ 1710.................................. 1780

a. Specify the competing hypotheses to determine whether the median score on the real SAT is greater than the median score on the mock SAT.

b. At the 5% significance level, what is the decision rule?

c. Calculate the value of the test statistic T.

d. Is there sufficient evidence to conclude that the median score on the real SAT is greater than the median score on the mock SAT?