A product developer is investigating the tensile strength of a new synthetic fiber that will be used to make cloth for men's shirts. Strength is usually affected by the percentage of cotton used in the blend of materials for the fiber. The engineer conducts a completely randomized experiment with five levels of cotton content and replicates the experiment five times. The data are shown in the following table:
Cotton Weight Percent | Observations
--------------------- | ------------
15 | 7
20 | 12
25 | 14
30 | 19
35 | 7
15 | 12
20 | 17
25 | 19
30 | 25
35 | 10
15 | 11
20 | 18
25 | 18
30 | 23
35 | 11
a) Is there evidence to support the claim that cotton content affects the mean tensile strength? Use a = 0.05. Solve by using the R ANOVA built-in function, provide your code and your output.
b) Use the Fisher LSD method to make comparisons between the pairs of means. What conclusions can you draw?
Hint for the above Problem: Here is a sample CSV file that has part of the data from the problem along with sample R code on how to read it. You will need to put the remaining data into the file as well as additional lines in the R code. Partial contents of the text file "dataMontg-311.txt" (created with a text editor like Notepad on Windows):
MixingTechnique | TensileStrength
--------------- | --------------
MT1 | 3129
MT1 | 3000
MT1 | 2865
MT1 | 2890
MT2 | 3200
MT2 | 3300
MT2 | 2975
MT2 | 3150
Sample R Code to Read the file shown above:
```R
d1 <- read.csv("dataMontg-311.txt")
attach(d1)
level1 <- d1[MixingTechnique == "MT1", "TensileStrength"]
level2 <- d1[MixingTechnique == "MT2", "TensileStrength"]
```