1. (Chapter 10, Section 10.1, Exercise 6. “Origin of Precambrian Iron Formations”) Carry out the ANOVA to investigate if the average Fe percentage for any of the four iron formations is different.
a. How many treatments are there? How many replications for each treatment?
b. State the null and alternative hypothesis for the average Fe percentage for any of the four iron formations.
c. Construct the ANOVA table using the summary statistics provided below. (You can also use R software. The dataset “iron” is on blackboard.)
∑∑ 2 = 33882.24
Treatment
Mean
Carbonate
̅ = 26.08
1.
Hematite
̅ = 33.84
2.
Magnetite
̅ = 29.95
3.
Silicate
̅ = 24.69
3.
d. Make a decision about the test and interpret.
e. Do the following diagnostic plots suggest that the model assumptions are inappropriate? Justify each assumption separately.
2. An experiment was run to compare = types of boxes (treatment) with respect to
compression strength. Each treatment is replicated 7 times.
a. Complete the ANOVA table by filling in the blanks with the correct values.
Source
Df
SS
MS
F
P-Value
Treatment
0.0668
Error
0.0151
Total
b. Let i be the true average compression strength for box type = 1, 2, 3. Construct the
Tukey’s interval for each pair of the i- j. Use the
Treatment
Mean
sample mean from the table.
1
̅ = 21.714
1.
2
̅ = 21.525
2.
3
̅ = 21.750
3.
Total
̅= 21.682
..
c. Apply the T Method and draw the underscore plot for comparing the treatments. Briefly explain your results.
