The state real estate commission is mandated to provide an examination that ensures a person passing the exam will have a minimum level of competence. This provides protection for the members of the public in their dealing with real estate firms. The state regulatory agency is responsible for establishing the acceptable level of safe practice and for determining whether an individual meets that standard. The real estate board has received several complaints about the grading of the essay questions on the exams. The board’s staff designs a study to evaluate their current testing procedure by evaluating the differences in the grading of the essay questions on the real estate exam. The study included 25 real estate exam graders and a random sample of 30 exams taken during the past year. Because the grading of the exams is very time consuming, each grader was assigned 6 exams to score, with the scores given in the following table. The number in parenthesis is the identifer for the grader.
a. Describe by name the type of design used. Verify that the structural conditions of your selected design are satisfied in this study.
b. Is there a difference in the average scores of the graders? Justify your answer at the .05 level.
c. Was it necessary to include the exam factor in the design and subsequent analysis of the data?
d. Using the residuals, do there appear to be any violations in the conditions needed to run tests of hypotheses in the analysis of variances?
e. Do you think that the board should be concerned with the differences in the graders’ evaluations of the exams if a difference of four units in their scores is deemed to be an important difference?
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