Q7. 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?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Q7. 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?
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