ANOVA

1. What type of experimental design is employed in this problem?
2. Identify the treatments and the dependent variable (Response).
3. Use a multiple boxplot in order to compare responses between different levels.
4. Are there differences between the mean of the responses in at least two of the levels?
5. Do you think this is the result of within-group variation or between-group variation?
6. State clearly the hypothesis that we are testing in this problem.
7. Set up the null and alternative.
8. Run ANOVA on the data and generate the output with plots.
9. Comment on the degree of freedom values for each source of variation. How do you calculate them?
10. Do we reject the hypothesis that we are testing? Why or why not?
11. If you reject, can you tell which level(s) is probably the one(s) that has the different mean? (Hint: use the boxplots from part 1a)
12. If you are suspicious of only one level, repeat the ANOVA without that level and see if you fail to reject the null in the test.
13. Use the histogram of residuals to comment on the normality of error term (residuals) in this ANOVA model.

ANOVA Question 1311 A synthetic ber manufacturer suspect that tensile strength is related to cotton percentage in the ber. An experiment was conducted with ve levels of cotton percentage and with ve replicates in random order. The following tensile strength data was obtained. Does cotton percentage affect the tensile strength? % Cotton Tensile Strength 15 8 9 15 11 10 20 12 17 12 1B 18 25 14 15 18 19 19 30 19 25 20 19 23 35 7 10 11 12 11