More than 200,000 people worldwide take the GMAT examination each year as they apply for MBA programs. Their scores vary Normally with mean about 525 and standard deviation about 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: u=525
Ha: u>525

a) If the students’ average score is xbar = 541.4 . Is this result significance at the 5% level?
b) The average score is xbar= 541.5. Is this result significance at the 5% level?
c) Explain how you would reconcile this difference in significance, especially if any increase greater than 15 points is considered a success.