10.47 Tax Assessors In response to a complaint that a particular tax assessor (A) was biased, an experiment was conducted to compare the assessor named in the complaint with another tax assessor (B) from the same office. Eight properties were selected, and each was assessed by both asses- sors. The assessments (in thousands of dollars) are shown in the table:

a. Do the data provide sufficient evidence to indicate that assessor A tends to give higher assessments than assessor B?

b. Estimate the difference in mean assessments for the two assessors.

c. What assumptions must you make in order for the inferences in parts a and b to be valid?

d. Suppose that assessor A had been compared with a more stable standard-say, the average of the assessments given by four assessors selected from the tax office. Thus, each property would be assessed by A and also by each of the four other assessors and (XA-) would be calculated. If the test in part a is valid, can you use the paired- difference / test to test the hypothesis that the bias, the mean difference between A's assessments and the mean of the assessments of the four assessors, is equal to 0? Explain.

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Property Assessor A Assessor B 1 76.3 75.1 2345678 2 88.4 86.8 80.2 77.3 4 94.7 90.6 5 68.7 69.1 6 82.8 81.0 7 76.1 75.3 8 79.0 79.1 Use the MINITAB printout to answer the questions. MINITAB output for Exercise 10.47 Paired T-Test and Cl: Assessor A, Assessor B Paired T for Assessor A Assessor B N Mean StDev SE Mean Assessor A 80.7750 7.9939 2.8263 Assessor B 8 79.2875 6.8510 2.4222 Difference 8 1.48750 1.49134 0.52727 95% lower bound for mean difference: 0.48855 T-Test of mean difference = 0 (vs > 0): T-Value = 2.82 P-value = 0.013