There are three commercial tax preparation offices in Benbde, Minnesota. The local Better Business Bureau (BBB) has been receiving some complaints that one of the offices does not understand tax law well enough to provide expert advice. The complaints state that to safeguard itself, the preparing office overstates the tax due by the payer and thus avoids later problems with the IRS.

The BBB has decided to invest several thousand dollars in grant money to test the claim. It has selected eight people at random and has asked that they allow each of the three offices to prepare their taxes using the same information.

(a) Discuss why the BBB set this test up as a randomized block design. Why did it think it was important to have all three offices do the returns for each of the eight people?
(b) Test to determine whether the blocking was necessary in this situation. Use a significance level of 0.01. Include all necessary components and show all hand calculations. (It is not necessary to show details of any summary statistics used.)
(c) Based on the sample data, can the BBB conclude that there is a difference in the mean taxes due on tax returns. Use a significance level of 0.01. Include all necessary components and show all hand calculations. (It is not necessary to show details of any summary statistics used.)

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Return Office 1 Office 2 Office 3 4,376.20 5,100.10 4,988.03 5,678.45 6,234.23 5,489.23 3 2,341.78 2,242.60 2,121.90 4 9,875.33 10,300.30 9,845.60 5 7,650.20 8,002.90 7,590.88 1,450.90 1,356.89 1,324.80 2,345.90 2,356.90 2,345.90 15,468.75 16,080.78 15,376.70 7,