A recent report criticizes SAT-test-preparation providers for promising big score gains without any hard data to back up such claims (The Wall Street Journal, May 20, 2009). Suppose eight college-bound students take a mock SAT, complete a three-month test-prep course, and then take the real SAT. The data set, labeled Mock_SAT, can also be found on the text website.

a. Specify the competing hypotheses that determine whether completion of the test-prep course increases a student’s score on the real SAT.
b. Assuming that the SAT scores difference is normally distributed, calculate the value of the test statistic and its associated p-value.
c. At the 5% significance level, do the sample data support the test-prep providers’claims?

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Student Score on Mock SAT 1830 1760 2000 2150 1630 1840 1930 1710 Score on Real SAT 1840 1800 2010 2190 1620 1960 1890 1780