Two production lines in a factory are producing the same cast iron component. You are inspecting the absolute surface ro

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Two production lines in a factory are producing the same cast
iron component. You are inspecting the
absolute surface roughness of cast iron component produced by the
two production lines. Following are the
absolute surface roughness (unit: mm) for the samples taken from
two production lines.
Line-A: 0.8406, 0.8104, 0.8234, 0.8198, 0.8235, 0.8462, 0.8123,
0.7976, 0.8184, 0.8265, 0.7873, 0.7971
Line-B: 0.8305, 0.7905, 0.8352, 0.8380, 0.8145, 0.8465, 0.8244,
0.8014, 0.8309, 0.8405, 0.8256, 0.8476
(a) Construct box plots of surface roughness of components from
two production lines using the data
above. Add labels of medians in the plot. Show graph with two
samples’ plots combined in a single graph.
Hint: Not grouped plots.
(b) Test if roughness of the component is approximately normally
distributed for both production lines?
You may test each data set individually or test both data sets at
the same time. Report results with plots
used.
(c) Is the variance of product’ surface roughness same for
Line-A and Line-B?
(d) Test the hypothesis that both lines produce components with
equal surface roughness. Use α =
0.05. What is the P-value of the test? Hint: solution for (c) is
needed to set up the hypothesis test.
(e) Report the 95% two-sided CI on the mean difference in
roughness for the components from two
lines.