TESTING SAMPLE DATA There are three commercial tax preparation offices in Benbde
ID: 3254853 • Letter: T
Question
TESTING SAMPLE DATA
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.)
(d) Referring to part (c), if you did conclude that a difference exists, determine which office has the highest mean tax dues. Use a significance level of 0.01. Include all necessary components and show all hand calculations.
Return Office 1 Office 2 Office 3 1 4,376.20 5,100.10 4,988.03 2 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 6 1,324.80 1,450.90 1,356.89 7 2,345.90 2,356.90 2,345.90 8 15,468.75 16,080.78 15,376.70Explanation / Answer
a)
Over here we are having blocks and treatments. Here the three offices are being considered as blocks and the eight returns are considered as treatments. We should consider offices as blocks and find if there is a difference between how they calculate tax returns. Here, we need to have complete data to compare the work of offices and by assigning each office as block, we can compare the output.
b)
c)
H0 : 1 = 2 = . . . = b = 0 versus Ha : at least one of the values differs from the others
p-value=0. p-value is less than alpha, hence reject null hypothesis.
Return Office 1 Office 2 Office 3 Total 1 4,376.20 5,100.10 4,988.03 4,821.44 2 5,678.45 6,234.23 5,489.23 5,800.64 3 2,341.78 2,242.60 2,121.90 2,235.43 4 9,875.33 10,300.30 9,845.60 10,007.08 5 7,650.20 8,002.90 7,590.88 7,747.99 6 1,324.80 1,450.90 1,356.89 1,377.53 7 2,345.90 2,356.90 2,345.90 2,349.57 8 15,468.75 16,080.78 15,376.70 15,642.08 Total 6,132.68 6,471.09 6,139.39 6,247.72 SST 3(4821.44-6247.72)^2……..3(15642.08-6247.72)^2 485653548.8 SSB 8(6132.68-6247.72)^2………8(6139.39-6247.72)^2 598910.2477 Total SS (4376.20-6247.72)^2…….(15376.7-6247.72)^2 486811584 SSE 559124.873 ANOVA Source df SS MS F SST 7 485653548.8 69379078.4 1737.191716 SSB 2 598910.2477 299455.1238 7.498095571 SSE 14 559124.873 39937.49093 Total SS 23 486811584Related Questions
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