1. A certain statistics instructor, in order to eliminate dishonest behavior on the exam, makes up 3 different exams. Concerned that one of the exams may be more difficult than the others, he randomly selects 6 exams of each version to see if the average scores differ. The means for the three samples are:

X₁= 73X₂=70X₃=67

The teacher also calculates (X_i - GM)²= 380.GM is the notation for the grand mean.

a. What are the hypotheses to see if the average scores differ across tests?

(4 pts)

H_O:H_A:

b. For an alpha = 0.05, draw a picture of the appropriate sampling distribution and identify the CRITICAL value on your picture. (5 pts)

c. Construct the ANOVA table to present the information used to generate the test statistic. (10 pts)

d. What should the statistics instructor decide and conclude about the difficulty level of the test