Quality Quiz from Professor Cleary
Congratulations:
"Yes" is correct.
Click here for a more complete video explanation
Walker Runn was actually right this time with his
guess about Type I error. Of course he will be expecting a promotion.
Walker actually did a twoway analysis of variance. The two factors he considered were plant and shift. This type of analysis answers three questions:
1. Is there a significant difference among outputs in the three plants?
2. Is there a significant difference between outputs of the day and night shifts?
3. Are there combinations of shift and plant that are significantly different from other combinations?
Walker was looking at the second question above,
whether significance differences emerged in the two shifts. The
data below demonstrates that the day shift average is 8.9 and the
night shift average is 13.7.
Of course, these numbers are different from one
another, but hypothesis testing will indicate whether that difference
is statistically significant and make a statement about one's confidence
in the conclusion. The steps in hypothesis testing are:
Step 1:
Interpretation for H0: The
day shift and the night shift produce the same amount of output.
This is a null hypothesis.
Step 2:
Interpretation : An alpha value of .01 suggests
a willingness to accept a 1 percent chance of rejecting the null
when it is actually true. This is known as a Type I error.
(Note: Walker continues to confuse
the alpha value with a famous Italian car, such as the one that
is garaged in the PQ Systems basement. See the photo below of my
other Alfa.)
Step 3:
Calculate the statistical F
value to test this hypothesis:
Walker uses DOEpack
EZ, so he does not require a calculator. As indicated,
the F value for shift is 38.52.
Step 4:
Compare the calculated F value
to the tabular F value, found in any statistics textbook.
For this case, the tabular F
value is 9.33. Since the calculated F is greater than the
tabular F value, the null that the output of the day and
night shifts is the same can be rejected. The figure below illustrates
this:
A second way to answer this question
is to explain what the Pvalue of <0.001 means. Walker correctly
saw this as a probability of a Type I error. In that this is smaller
than the alpha value of .01 chosen in Step 2, you would conclude
that the null that the day and night shifts produce the same outputs
can be rejected.
Stay tuned to see what guesses Walker Runn makes next month.
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