Question

These problems may be solved using Minitab. Copy and paste the appropriate Minitab output into a word-processed file. Add your explanations of the output near the Minitab output. DO NOT SIMPLY ATTACH PAGES OF OUTPUT AS AN APPENDIX.

Each problem should be able to fit on one or two pages, and each problem should include the following:

• Minitab output for the ANOVA.
• Written statement interpreting the ANOVA.
• Four-in-one plot of the residuals.
• Written interpretation as to whether the three assumptions of the ANOVA were met.
• Tukey comparisons if necessary.
• A written summary of your interpretation of the analysis in terms of the problem. This may involve more than one statement. In other words, state which group is “best” in terms of the problem.

1. Consider the following ANOV output for an experiment.

Source	DF	SS	MS	F	P-Value
Factor	5	?	?	?	?
Error	?	27.28	?
Total	29	66.44

1. Complete the ANOVA table (show calculations).
2. How many levels (treatments) are being examined.
3. Assuming the sample size for each treatment was consistent, how many replicates did the experimenter use?
4. What is the critical value of F for the test being conducted?

Answer 1

a)

from above:

df error =29-5 =24

SS(Factor) =66.44-27.28 =39.16

MS(factor) =39.16/5 =7.832

MS(error) =27.28/24 =1.137

F =MS(Factor)/.MS(error ) =7.832/1.137 =6.89

p value for (5,24) df and above tst statistic =0.0004

Source	df	SS	MS	F
factor	5	39.160	7.832	6.89
error	24	27.280	1.137
total	29	66.440

b)

number of levels =df(factor)+! =5+1 =6

c)replicates =(df error)/levels+1 =24/6+1 =5

d)critical value of F for 0.05 level and 5,24 degree of freedom =2.621