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	28.0	25.2	25.3	27.1	20.5	31.1
2:	26.7	24.0	26.2	20.2	23.7	34.0	17.1	26.8	23.7	24.8
3:	30.1	34.0	27.5	29.4	28.4	26.2	29.9	29.5	30.0	36.1
4:	36.4	44.2	34.1	30.3	31.9	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.

a) H₀: μ₁ = μ₂ = μ₃ = μ₄
H_a: all four μ_i's are unequal

b) H₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄
H_a: all four μ_i's are equal   

c) H₀: μ₁ = μ₂ = μ₃ = μ₄
H_a: at least two μ_i's are unequal

d) H₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄
H_a: at least two μ_i's are equal

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

Source	df	Sum of Squares	Mean Squares	f
Treatments
Error
Total

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

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

a) P-value > 0.100

b) 0.050 < P-value < 0.100

c) 0.010 < P-value < 0.050

d) 0.001 < P-value < 0.010

e) P-value < 0.001

State the conclusion in the problem context.

a) Reject H₀. There is insufficient evidence to conclude that the total Fe differs for the four formations.

b) Fail to reject H₀. There is insufficient evidence to conclude that the total Fe differs for the four formations.

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

d) 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

The statistical software output for this problem is:

Hence,

Hypotheses: Option C is correct.

ANOVA table:

Source	df	Sum of Squares	Mean Squares	f
Treatments	3	515.76	171.92	11.16
Error	36	554.77	15.410
Total	39	1070.54

Test statistic = 11.16

P-value < 0.001

Conclusion: Option C is correct.