Tax Assessors In response to a complaintthat a particular tax assessor (A) wasbiased, an

Chapter 10, Problem 46

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Tax Assessors In response to a complaintthat a particular tax assessor (A) wasbiased, an experiment was conducted to compare theassessor named in the complaint with another taxassessor (B) from the same office. Eight propertieswere selected, and each was assessed by both assessors.The assessments (in thousands of dollars) areshown in the table.Property Assessor 1 Assessor 21 276.3 275.12 288.4 286.83 280.2 277.34 294.7 290.65 268.7 269.16 282.8 281.07 276.1 275.38 279.0 279.1Use the MINITAB printout to answer the questions thatfollow.MINITAB output for Exercise 10.46Paired T-Test and CI: Assessor A, Assessor BPaired T for Assessor A - Assessor BN Mean StDev SE MeanAssessor A 8 280.78 7.99 2.83Assessor B 8 279.29 6.85 2.42Difference 8 1.487 1.491 0.52795% lower bound for mean difference: 0.489T-Test of mean difference = 0 (vs > 0):T-Value = 2.82 P-value = 0.013a. Do the data provide sufficient evidence to indicatethat assessor A tends to give higher assessmentsthan assessor B?b. Estimate the difference in mean assessments for thetwo assessors.c. What assumptions must you make in order for theinferences in parts a and b to be valid?d. Suppose that assessor A had been compared with amore stable standardsay, the average x of theassessments given by four assessors selected fromthe tax office. Thus, each property would be assessedby A and also by each of the four other assessors and(xA x) would be calculated. If the test in part a isvalid, can you use the paired-difference t-test to testthe hypothesis that the bias, the mean differencebetween As assessments and the mean of the assessmentsof the four assessors, is equal to 0? Explain