Walker Runn was flat-out wrong. He had confused the sum of X-bars with a Type I
error. To learn about alpha values and hypothesis testing, keep reading.
Data from the production lines was as follows:
The production on Line 2 is clearly less than that of Line 1. The
question remains whether the difference is due to natural variation or it
can be ascribed to the two lines actually operating differently. Using
traditional hypothesis testing, one can apply the 't test ':
Step 1:
Interpretation: The null hypothesis (Ho) is that Line 1 and Line 2 are not significantly
different.
Step 2:
Interpretation: An alpha value of 5 percent suggests a willingness to accept
a 5 percent chance of rejecting the null when it is actually true. Known as
a Type I
error.
Step 3:
Calculate statistical t value:
Step 4: Make decision:
a) Look up tabular t value in a statistics textbook. In this case, it is
equal to 2.71.
b) Compare the value from Step 3 to 2.71. If it is greater, reject; if not,
accept.
Interpretation: In this case, the mean values are different enough from each
other that one would conclude that Lines 1 and 2 are indeed different from
one another.
How would X-MR charts created for each line compare?
If this exercise brings back dark memories of a statistics course and its
innumerable calculations, welcome to the new technology. Your DOEpack
program will do the work for you.
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