On its Web site, the Princeton Review claims that students who have taken its course improve their Graduate Record Examination (GRE) scores, on average, by 210 points (based on the old scoring system). (No other information is provided about this statistic.) Treating this average gain as a population mean, a researcher wonders whether the far cheaper technique of practicing for the GRE on one’s own would lead to a different average gain. She randomly selects five students from the pool of students at her university who plan to take the GRE. The students take a practice test before and after 2 months of self-study. They reported (fictional) gains of 160, 240, 340, 70, and 250 points. (Note that many experts suggest that the results from self-study are similar to those from a structured course for students who have the self-discipline to study on their own. Regardless of the format, preparation has been convincingly demonstrated to lead to increased scores, on average.)

a. Using symbolic notation and formulas (where appropriate), determine the appropriate mean and standard error for the distribution to which we will compare this sample. Show all steps of your calculations.

b. Using symbolic notation and the formula, calculate the t statistic for this sample.

c. As an interested consumer, what critical questions would you want to ask about the statistic reported by the Princeton Review? List at least three questions.