Question

The following data was reported on total Fe for four types of iron formation (1 = carbonate, 2 = silicate, 3 = magnetite, 4 = hematite).

1:	21.0	28.1	27.8	27.0	27.5	25.2	25.3	27.1	20.5	31.3
2:	26.7	24.0	26.2	20.2	23.8	34.0	17.1	26.8	23.7	24.6
3:	30.1	34.0	27.5	29.4	28.0	26.2	29.9	29.5	30.0	35.6
4:	36.3	44.2	34.1	30.3	32.1	33.1	34.1	32.9	36.3	25.7

Carry out an analysis of variance F test at significance level 0.01. State the appropriate hypotheses.

H₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄
H_a: all four μ_i's are equal H₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄
H_a: at least two μ_i's are equal     H₀: μ₁ = μ₂ = μ₃ = μ₄
H_a: at least two μ_i's are unequal H₀: μ₁ = μ₂ = μ₃ = μ₄
H_a: all four μ_i's are unequal

Summarize the results in an ANOVA table. (Round your answers two decimal places.)

Source	df	Sum of Squares	Mean Squares	f
Treatments	2	3	4	5
Error	6	7	8
Total	9	10

Give the test statistic. (Round your answer to two decimal places.)
f = 11

What can be said about the P-value for the test?

P-value > 0.100 0.050 < P-value < 0.100     0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001

State the conclusion in the problem context.

Reject H₀. There is sufficient evidence to conclude that the total Fe differs for at least two of the four formations. Reject H₀. There is insufficient evidence to conclude that the total Fe differs for the four formations.     Fail to reject H₀. There is insufficient evidence to conclude that the total Fe differs for the four formations. Fail to reject H₀. There is sufficient evidence to conclude that the total Fe differs for at least two of the four formations.

Answer 1