1. On its website, the Kaplan Prep claims that students who have taken its course improve their GRE scores, on average, by 210 points. (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 using books and CDs will lead to a different average gain. She randomly selects nine 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 study. They report gains of 260, 240, 340, 170, 250, 230, 250, 220, and 250 points. Are gains in GRE scores from taking the Kaplan Prep course different from GRE gains when studying using books and CDs? Assume an alpha level of .05. (5 points)
2. What type of t-test will you use to answer this question? Why did you choose this test?
3. Use the five steps of hypothesis testing to answer the question.
4. Write up your conclusion as if it were for a publication.

These are the five steps of hypothesisthat you will need to use for part B

STEP 1: RESTATE QUESTION AS RESEARCH AND NULL HYPOTHESES

For this step, we determine the two populations that are being compared. Then, we generate our hypotheses. We need to determine if we are making a directional (e.g., more or less) hypothesis or non-directional (e.g., different) hypothesis for the research hypothesis (H₁).

STEP 2: COMPARISON DISTRIBUTION CHARACTERISTICS

This step tells us about what the comparison distribution looks like (i.e., spread in relation to mean). It starts out as a distribution of scores, but we need to convert it to a distribution of means.

STEP 3: CUTOFF SCORES ON THE COMPARISON DISTRIBUTION AT WHICH TO REJECT H₀

This step tells us where the critical region(s) on the comparison distribution start. For this step, we need to figure if we have a one or two tailed test and what our significance or p level are. We use our knowledge of the normal curve for this step.

STEP 4: DETERMINE YOUR SAMPLE'S SCORE ON THE COMPARISON DISTRIBUTION

For this step, we calculate a z test to determine where our sample mean falls on the comparison distribution.

STEP 5: Decision

Based on where our sample mean fall on the comparison distribution (determine by the z test) we either reject H₀or fail to reject H₀.