Students applying to graduate school may be asked to take an admissions test. To study how well these tests predict performance in grad school, one study hypothesized a positive relationship between scores on the Graduate Management Admissions Test (GMAT) and performance in an MBA (Masters of Business Administration) program such that higher GMAT scores are associated with higher levels of academic performance (Ahmadi, Raiszadeh, & Helms, 1997). The researchers obtained the GMAT score (range: 200 to 800) and grade point average (GPA) (range: 0.00 to 4.00) from students in an MBA program. The findings from the study are reproduced using the following sample of 26 students:

a. State the null and alternative hypotheses (H₀ and H₁).

b. Make a decision about the null hypothesis.
(1) Calculate the degrees of freedom (df).
(2) Set alpha (α), identify the critical values, and state a decision rule.
(3) Calculate the Pearson correlation (r).
(4) Make a decision whether to reject the null hypothesis.
(5) Determine the level of significance.
(6) Calculate a measure of effect size (r²).

c. Draw a conclusion from the analysis.

d. Relate the result of the analysis to the research hypothesis.

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Student GMAT GPA Student GMAT GPA 1 710 3.65 7 330 2.80 2 570 3.40 8 590 3.60 3 460 3.25 9 460 2.50 4 450 3.70 10 430 2.70 5 320 3.15 11 680 3.00 6 530 3.55 12 530 3.05 13 360 2.50 20 600 3.15 14 590 3.80 21 470 3.50