Sulfur Dioxide (SO₂) is a chemical produced by many natural processes. It is one of the ingredients in acid rain, so it is important to monitor the amount of sulfur dioxide that is released into the atmosphere. In an article published in the journal Atmospheric Environment, several measurements of the maximum hourly concentrations of SO₂ (in milligrams per cubic meter, mg/m³) were reported at each of four different power plants. The data are provided in the table below, along with the sample mean concentration for each plant. Performa complete analysis of this data, at level of significance = 0.05.

Plant	SO2 Concentration				Means
1	925 786 1179 786 859 902				-x1 = 906.17
2	893 891 917 695 675 595				-x2 = 777.67
3	857 1014 1153 883 1053 971				-x3 = 988.50
4	438 619 732 638 677 584				-x4 = 614.67

ANOVA Table:

Source	df	SS	MS	F
Plant	3	478544.830	159514.943	10.187
Error	20	313178.625	15658.931

We reject H₀. The given data does provide significant evidence that the mean hourly sulfur dioxide concentrations differ among these four power plants.

QUESTIONS:

Tukey's Table: Complete the indicated portions of Tukey's table below. Round all calculations to 3 decimal places.

-xi - -xj	q0(i,j)	q	Conclusion
(?)	(?)	(see Q4)	(see Q4)
(?)	(?)	"	(see Q4)
(?)	(?)	"	(see Q4)
(?)	(?)	"	(see Q4)
(?)	(?)	"	(see Q4)
(?)	(?)	"	(see Q4)

First, calculate the standard error used in Tukey's test for this example, given by the formula

_____ (standard error)

Next, calculate the difference in means and the test statistic for each possible pair of groups. Use the rounded standard error reported above when calculating test statistics. Plant 3 vs. Plant 4: ^-x₃ - ^-x₄ = _____ q₀(3,4) = _____ Plant 1 vs. Plant 4: ^-x₁ - ^-x₄ = _____ q₀(1,4) = _____ Plant 3 vs. Plant 2: ^-x₃ - ^-x₂ = _____ q₀(3,2) = _____ Plant 2 vs. Plant 4: ^-x₂ - ^-x₄ = _____ q₀(2,4) = _____ Plant 1 vs. Plant 2: ^-x₁ - ^-x₂ = _____ q₀(1,2) = _____

Plant 3 vs. Plant 1: ^-x₃ - ^-x₁ = _____ q₀(3,1) = _____

2MSE(ni1+nj1)