A popularly held belief about university professors is that they don’t work very hard and that the higher their rank, the less work they do. A statistics student decided to determine whether the belief is true. She took a random sample of 20 university instructors in the faculties of business, engineering, arts, and sciences. In each sample of 20, 5 were instructors, 5 were assistant professors, 5 were associate professors, and 5 were full professors. Each professor was surveyed and asked to report confidentially the number of weekly hours of work. These data were recorded in the following way:

Column 1: hours of work for business professors (first 5 rows = instructors, next 5 rows = assistant professors, next 5 rows = associate professors, and last 5 rows = full professors)

Column 2: hours of work for engineering professors (same format as column 1)

Column 3: hours of work for arts professors (same format as column 1)

Column 4: hours of work for science professors (same format as column 1)

a. If we conduct the test under the single-factor analysis of variance, how many levels are there?

What are they?

b. Test to determine whether differences exist using a single-factor analysis of variance.

c. If we conduct tests using the two-factor analysis of variance, what are the factors? What are their levels?

d. Is there evidence of interaction?

e. Are there differences between the four ranks of instructor?

f. Are there differences between the four faculties?