Problem - Is it significant? More than 200,000 people worldwide take the Graduate Management Admissions Test (GMAT) each year as they apply for MBA programs. Their scores vary Normally with mean about μ = 525. One hundred students go through a rigorous training program designed to raise their GMAT scores. Test the following hypotheses about the training program

H_o: μ = 525

H_a: μ > 525

in each of the following situations:

(a) The students' average score is x^- = 541.1 and s = 98.0. Is this result significant at the 5% level? Use the 100 degrees of freedom row of Table D in your calculations.

(b) Now suppose that the average score is x^- = 541.3 and s = 98.0. Is this result significant at the 5% level? Use the 100 degrees of freedom row of Table D in your calculations.

(c) Explain how you would reconcile this difference in significance, especially if any increase greater than 15 points is considered a success.