Question

The following data was reported on total Fe for four types of iron formation (1 = carbonate, 2 = silicate, 3 = magnetite, 4 = hematite). 1: 20.7 28.1 27.8 27.0 28.1 25.2 25.3 27.1 20.5 31.8 2: 26.4 24.0 26.2 20.2 24.2 34.0 17.1 26.8 23.7 24.5 3: 29.9 34.0 27.5 29.4 27.9 26.2 29.9 29.5 30.0 35.7 4: 37.1 44.2 34.1 30.3 31.8 33.1 34.1 32.9 36.3 25.8 Carry out an analysis of variance F test at significance level 0.01. State the appropriate hypotheses. H0: μ1 = μ2 = μ3 = μ4 Ha: all four μi's are unequal H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 Ha: at least two μi's are equal H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 Ha: all four μi's are equal H0: μ1 = μ2 = μ3 = μ4 Ha: at least two μi'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 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? 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. You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

Answer:

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

1: 20.7 28.1 27.8 27.0 28.1 25.2 25.3 27.1 20.5 31.8

2: 26.4 24.0 26.2 20.2 24.2 34.0 17.1 26.8 23.7 24.5

3: 29.9 34.0 27.5 29.4 27.9 26.2 29.9 29.5 30.0 35.7

4: 37.1 44.2 34.1 30.3 31.8 33.1 34.1 32.9 36.3 25.8

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

H0: μ1 = μ2 = μ3 = μ4 Ha: at least two μi'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 Error Total Give the test statistic. (Round your answer to two decimal places.)

ANOVA table
Source	SS	df	MS	F	p-value
Treatment	518.34	3	172.78	11.03	0.0000
Error	563.91	36	15.66
Total	1,082.26	39

f = 11.03

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

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.

Excel Addon Megastat used.

One factor ANOVA
	Mean	n	Std. Dev
	26.16	10	3.450	Type1
	24.71	10	4.420	Type2
	30.00	10	2.872	Type3
	33.97	10	4.793	Type4
	28.71	40	5.268	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	518.342	3	172.7807	11.03	0.0000
Error	563.914	36	15.6643
Total	1,082.256	39