In a certain industrial process, an automatic grinding machine that produces the
ID: 2746907 • Letter: I
Question
In a certain industrial process, an automatic grinding machine that produces the least surface roughness is to be selected. Four repeat test were run, using machines submitted by three different suppliers and the following data were obtained. Determine with 90% confidence whether there is any significant difference between machines, and if so which one should be selected. What type of experimental design is employed in this problem? Identify the treatments and the dependent variable (Response). Use a multiple box plot in order to compare responses between different levels. a. Are there differences between the mean of the responses in at least two of the levels? Do you think this is the result of within-group variation or between-group variation? State clearly the hypothesis that we are testing in this problem: set up the null and alternative. Run ANOVA on the data and generate the output with plots a. Comment on the degree of freedom values for each source of variation. How do you calculate them? b. Do we reject the hypothesis that we are testing? Why or why not? c. If you reject, can you tell which level(s) is probably the one(s) that has the different mean? i. 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. d. Use the histogram of residuals to comment on the normality of error term in this ANOVA model.Explanation / Answer
Answer:
The ANOVA test is:
Anova: Two-Factor Without Replication SUMMARY Count Sum Average Variance B 4 64 16 4.666666667 C 4 57 14.25 2.916666667 20 2 28 14 8 18 2 32 16 8 15 2 33 16.5 0.5 17 2 28 14 2 ANOVA Source of Variation SS df MS F P-value F crit Rows 6.125 1 6.125 1.484848485 0.310101 10.12796448 Columns 10.375 3 3.458333 0.838383838 0.555894 9.276628154 Error 12.375 3 4.125 Total 28.875 7