The quality control department of a fabric finishing plant is studying the effects of several factors on dyeing for a bl

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The quality control department of a fabric finishing plant is
studying the effects of several factors on dyeing for a blended
cotton/synthetic cloth used to manufacture shirts. Two cycle times
and two temperatures were selected. Twelve small specimens of cloth
were dyed under each set of conditions. The finished cloth was
compared to a standard, and a numerical score of the quality was
assigned. The results are shown in the following table:
Temperature
Cycle Time
300°
330°
40
22
28
31
23
38
33
25
28
32
24
37
38
27
36
24
24
34
27
26
24
30
27
36
38
60
35
36
34
38
35
34
36
38
32
37
38
34
33
35
31
41
36
29
35
40
36
35
35
32
2-1 (a)
What statistical technique allows us to estimate the effects of
cycle time and temperature on dyeing quality simultaneously by
testing a single statistical model?
(b) State one of the assumptions of this statistical technique and
comment briefly how to check whether this assumption is met. (8
marks)
2-2
State the null hypotheses that the statistical technique identified
in 2-1 will test. Three hypotheses are expected. (6 marks)
2-3 Run
the statistical test identified in 2-1 with R and a package of your
choice.
(a) Copy and paste the code and the output, and write brief
statements to report the test statistics results.
(b) Briefly interpret the results. (12 marks)
2-4 (a)
Based on the statistical test output, identify one quantity that
estimates unexplained random variation, and state its value.
(b) Write one sentence to interpret the quantity. (4 marks)