Question

a) A study on the amount of dye needed to get the best color for a certain type of fabric was reported. The three amounts of dye, 1/3 %, 1%, and 3% (weight of fabric) were each administered at two different plants. The color density of the fabric was then observed four times for each level of dye at each plant. The data is found in file fabric.txt. (10)

i. Perform an analysis of variance to test the hypothesis, at the 0.05 level of significance, that there is no difference in the color density of the fabric for the three levels of dye and select the appropriate test, and state your conclusion. Report a p-value (5)

ii. Perform a Tukey test at .05 l.o.s. and discuss your findings (5)

b) Corrosion fatigue in metals has been defined as the simultaneous action of cyclic stress and chemical attack on a metal structure. A widely used technique for minimizing corrosion fatigue damage in aluminum involves the application of a protective coating. A study conducted by the Department of Mechanical Engineering at Virginia Tech used 3 different levels of humidity Low: 20–25% relative humidity Medium: 55–60% relative humidity High: 86–91% relative humidity, and 3 types of surface coatings Uncoated: no coating Anodized: sulfuric acid anodic oxide coating Conversion: chromate chemical conversion coating The corrosion fatigue data, expressed in thousands of cycles to failure is stored in file fatigue.txt (15)

i) Perform an analysis of variance with α = 0.05 to test for significant main and interaction effects. (5)

ii) Use Tukey’s test at the 0.05 level of significance to determine which humidity levels result in different corrosion fatigue damage (5)

iii) Use an interaction plot and comment on your findings (5)

Answer 1