An experiment is conducted to investigate the effect of 4 different strengths of
ID: 3438743 • Letter: A
Question
An experiment is conducted to investigate the effect of 4 different strengths of a chemical contained in a liquid cleaner for synthetic leather products. The investigators decide to use leather strips (15 cm long and 1 cm thick) from 3 types (A, B, & C) of synthetic leather. The four strengths of the chemical are taken as levels 0.5, 1, 2, and 4 and the leather bands(strips) are dipped in the chemicals for 30 minutes and the shrinkage amount is measured (in micro meters) for each strip of leather. For a given type of synthetic leather, each strip of leather band was cut out from the same roll of leather (e.g. all leather strips from type A was cut out from one roll of type A synthetic leather). The data is given below.
(a) The investigators are considering the use of an ANOVA model to check whether the mean shrinkage length for each type of chemical is the same. Do you have any objections to the use of an ANOVA model for the data? If any, state clearly.
(b) Now assume that you can carry out an ANOVA model on the data.
i. Determine whether there is a difference in the mean shrinkage lengths for the 4 different strengths of the chemical. If there is a difference, determine where the differences occur. Use a Bonferroni adjustment. (State and check all assumptions of your analysis).
ii. The general public can purchase the above liquid cleaner for synthetic leather with the strength of the chemical in level "1". Determine whether or not the mean shrinkage length for level "1" strength of the chemical is different from level "2" and level "4" strengths. (Appropriate weights for level "2" and level "4" can be obtained by taking the ratio of each level to level "1" as the weight for that level.)
(c) Now consider the fact that there are three different (A, B, & C) types of synthetic leather used in the experiment. The investigators are not interested in studying about the effects of having these 3 different types of leather in the experiment. Their paramount interest is in finding whether the different strengths of the chemical have different mean shrinkage lengths. Do you think it is good idea to ignore the effect of the different types of leather? If not, why? and how would you help them to adjust the design of the study? (Do not perform a statistical analysis for this. A brief (but clear) summary of your thoughts on the issue at hand is sufcient).
(e) Comment how the assumptions for a ANOVA model carry over to the assumptions of a linear regression model?
Type of Leather Concentration Shrunk Length A 0.5 16.5 B 0.5 9 B 0.5 15 B 0.5 13.2 B 0.5 10.3 B 0.5 17 B 0.5 9.8 C 0.5 8 C 0.5 9.8 C 0.5 9.4 A 0.5 7.6 A 0.5 11.5 A 1 12.6 A 1 17.2 A 1 12.8 B 1 15.2 B 1 16.6 B 1 15.2 B 1 14.2 B 1 18 B 1 16 B 1 23.2 B 1 19 B 1 16.2 B 1 15 C 1 17 C 1 13 C 1 18.2 C 1 21.5 C 1 15.4 C 1 19 C 1 22.2 A 1 21 A 2 20.8 A 2 26.8 A 2 27.4 B 2 32 B 2 33.8 B 2 28.8 C 2 25.8 C 2 28.4 C 2 19 C 2 34 A 2 29 A 2 27.4 A 4 22.6 A 4 28.4 B 4 20 B 4 24.2 C 4 30 C 4 32 C 4 19.4 C 0.5 12 A 0.5 9.2 A 0.5 10.4 A 4 23.8 A 4 27 B 4 22 B 4 18 B 4 20 C 4 32.2 C 4 29.6Explanation / Answer
(a) No, I have not any objections to the use of an ANOVA model for the data
(b)
SUMMARY Groups Count Sum Average Variance Row 1 2 17 8.5 128 Row 2 2 8.1 4.05 25.205 Row 3 2 12 6 60.5 Row 4 2 13.6 6.8 67.28 Row 5 2 18.2 9.1 131.22 Row 6 2 13.8 6.9 69.62 Row 7 2 22 11 200 Row 8 2 22.8 11.4 176.72 Row 9 2 28.8 14.4 307.52 Row 10 2 29.4 14.7 322.58 Row 11 2 31 15.5 364.5 Row 12 2 29.4 14.7 322.58 Row 13 2 26.6 13.3 172.98 Row 14 2 32.4 16.2 297.68 Row 15 2 9.7 4.85 37.845 Row 16 2 10.9 5.45 49.005 Row 17 2 27.8 13.9 196.02 Row 18 2 31 15.5 264.5 Row 19 2 9.5 4.75 36.125 Row 20 2 15.5 7.75 105.125 Row 21 2 13.7 6.85 80.645 Row 22 2 10.8 5.4 48.02 Row 23 2 17.5 8.75 136.125 Row 24 2 10.3 5.15 43.245 Row 25 2 16.2 8.1 100.82 Row 26 2 17.6 8.8 121.68 Row 27 2 16.2 8.1 100.82 Row 28 2 15.2 7.6 87.12 Row 29 2 19 9.5 144.5 Row 30 2 17 8.5 112.5 Row 31 2 24.2 12.1 246.42 Row 32 2 20 10 162 Row 33 2 17.2 8.6 115.52 Row 34 2 34 17 450 Row 35 2 35.8 17.9 505.62 Row 36 2 30.8 15.4 359.12 Row 37 2 24 12 128 Row 38 2 28.2 14.1 204.02 Row 39 2 26 13 162 Row 40 2 22 11 98 Row 41 2 24 12 128 Row 42 2 8.5 4.25 28.125 Row 43 2 10.3 5.15 43.245 Row 44 2 9.9 4.95 39.605 Row 45 2 18 9 128 Row 46 2 14 7 72 Row 47 2 19.2 9.6 147.92 Row 48 2 22.5 11.25 210.125 Row 49 2 16.4 8.2 103.68 Row 50 2 20 10 162 Row 51 2 23.2 11.6 224.72 Row 52 2 27.8 13.9 283.22 Row 53 2 30.4 15.2 348.48 Row 54 2 21 10.5 144.5 Row 55 2 36 18 512 Row 56 2 34 17 338 Row 57 2 36 18 392 Row 58 2 23.4 11.7 118.58 Row 59 2 12.5 6.25 66.125 Row 60 2 36.2 18.1 397.62 Row 61 2 33.6 16.8 327.68 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 2041.656 60 34.0276 0.189442 1 1.530912 Within Groups 10956.81 61 179.6198 Total 12998.46 121Related Questions
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