6.90 Is it significant? More than 200,000 people worldwide take the GMAT examination each year when they apply for MBA programs. Their scores vary Normally with mean μ = 540 and standard deviation σ = 100. One hundred students go through a rigorous training program designed to raise their GMAT scores. Test the following hypotheses about the training program

H₀: μ = 540

H_a: μ > 540

in each of the following situations.

1. (a) The students’ average score is . Is this result significant at the 5% level?

2. (b) Now suppose that the average score is . Is this result significant at the 5% level?

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