12. You wish to see whether students perform differently on essay tests and on multiplechoice tests. You select a sample of eight students enrolled in an introductory biology course and have each student take an essay test and a multiple-choice test. Both tests cover the same unit of instruction and are designed to assess mastery of factual knowledge.

(Half the students take the essay test first; the remaining half take the multiplechoice test first.) The results are as follows:

Student A B C D E F G H Essay: 43 39 44 47 30 46 34 41 Multiple choice: 45 33 46 49 28 43 36 37 Using the direct-difference method:

(a) Set up the statistical hypotheses.

(b) Compute D, SSD, and sD.

(c) Perform the test (a ¼ :05).

(d) Draw final conclusions.