Because there are no national or regional standards, it is difficult for university admission committees to compare graduates of different high schools. University administrators have noted that an 80% average at a high school with low standards may be equivalent to a 70% average at another school with higher standards of grading. In an effort to more equitably compare applications, a pilot study was initiated. Random samples of students who were admitted the previous year from four local high schools were drawn. All the students entered the business program with averages between 70% and 80%. Their average grades in the first year at the university were computed.

a. Can the university admissions officer conclude that there are differences in grading standards between the four high schools?

b. What are the required conditions for the test conducted in part (a)?

c. Does it appear that the required conditions of the test in part (a) are satisfied?