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 31.2

2: 26.9 24.0 26.2 20.2 23.7 34.0 17.1 26.8 23.7 25.2

3: 29.8 34.0 27.5 29.4 28.5 26.2 29.9 29.5 30.0 36.4

4: 37.2 44.2 34.1 30.3 31.8 33.1 34.1 32.9 36.3 25.7

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

A) H0: μ1 = μ2 = μ3 = μ4 Ha: all four μi's are unequal

B)H0: μ1 = μ2 = μ3 = μ4 Ha: at least two μi's are unequal

C)H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 Ha: all four μi's are equal

D) H0: μ1 ≠ μ2 ≠ μ3 ≠ μ4 Ha: at least two μi's are equal

2. 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 = ?

3. What can be said about the P-value for the test? Select an answer.

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

4. State the conclusion in the problem context. Select an answer

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 sufficient evidence to conclude that the total Fe differs for at least two of 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 insufficient evidence to conclude that the total Fe differs for the four formations.

Answer 1

applying one way ANOVA:

Source of Variation	SS	df	MS	F	P-value
Between Groups	518.03	3	172.68	11.00	0.0000
Within Groups	565.25	36	15.70
Total	1083.28	39

1)

B)H0: μ1 = μ2 = μ3 = μ4 Ha: at least two μi's are unequal

2)

f = 11.00

3) E)P-value < 0.001

4)

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