For Exercise 6.93, see page 339; and for 6.94, see page 339.

Question 6.93

6.93 Is it signifcant?

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

in each of the following situations.

  1. The students’ average score is . Is this result signifcant at the 5% level?
  2. Now suppose that the average score is . Is this result signifcant at the 5% level?
  3. Explain how you would reconcile this difference in significance, especially if any increase greater than 15 points is considered a success.

6.93

(a) No. (b) Yes. (c) Even though the first result is not statistically significant, we would still consider it of practical significance because it is more than a 15-point improvement.