Use the results of Exercises 1 and 2 to create a plot that illustrates the interaction evident from the data. Use the plot in Figure 1.3 in Example 1.3 as a guide. Could the type of information found in Exercises 1 and 2 have been found in an observational study in which there was no control on injection velocity and mold temperature by the analyst? Explain why or why not.
Exercise 1
Many manufacturing companies in the United States and abroad use molded parts as components of a process. Shrinkage is often a major problem. Thus, a molded die for a part is built larger than nominal size to allow for part shrinkage. In an injection molding study it is known that the shrinkage is influenced by many factors, among which are the injection velocity in ft/sec and mold temperature in ?C. The following two data sets show the results of a designed experiment in which injection velocity was held at two levels (low and high) and mold temperature was held constant at a low level. The shrinkage is measured in cm × 104.
Shrinkage values at low injection velocity:
72.68
|
72.62
|
72.58
|
72.48
|
73.07
|
72.55
|
72.42
|
72.84
|
72.58
|
72.92
|
Shrinkage values at high injection velocity:
71.62
|
71.68
|
71.74
|
71.48
|
71.55
|
71.52
|
71.71
|
71.56
|
71.70
|
71.50
|
(a) Construct a dot plot of both data sets on the same graph. Indicate on the plot both shrinkage means, that for low injection velocity and high injection velocity.
(b) Based on the graphical results in (a), using the location of the two means and your sense of variability, what do you conclude regarding the effect of injection velocity on shrinkage at low mold temperature?
Exercise 2
Consider the situation of Exercise 1.28. But now use the following data set, in which shrinkage is measured once again at low injection velocity and high injection velocity. However, this time the mold temperature is raised to a high level and held constant.
Shrinkage values at low injection velocity:
76.20
|
76.09
|
75.98
|
76.15
|
76.17
|
75.94
|
76.12
|
76.18
|
76.25
|
75.82
|
Shrinkage values at high injection velocity:
93.25
|
93.19
|
92.87
|
93.29
|
93.37
|
92.98
|
93.47
|
93.75
|
93.89
|
91.62
|
(a) Construct a dot plot with both data sets on the same graph and identify both means (i.e., mean shrinkage for low injection velocity and for high injection velocity).
(b) Comment on the influence of injection velocity on shrinkage for high mold temperature. Take into account the position of the two means and the variability around each mean.
(c) Compare your conclusion in (b) with that in (b) In which mold temperature was held at a low level. Would you say that there is an interaction between injection velocity and mold temperature? Explain.