Paired t-test Exercise
Exercise objective: Utilize what you have learned to conduct
and analyze a paired t-test using MINITABTM.
1. A corrugated packaging company produces material which has
creases to make boxes easier to fold. It is a critical to quality
characteristic to have a predictable Relative Crease Strength. The
quality manager is having her lab test some samples labeled 1-11.
Then those same samples are being sent to her colleague at
another facility who will report their measurements on those same
1-11 samples.
2. The US quality manager wants to know with 95% confidence what
the average difference is between the lab located in Texas and the
lab located in Mexico when measuring Relative Crease Strength.
3. Use the data in columns “Texas” & “Mexico” in “RM Suppliers.mtw”
to determine the answer to the quality manager’s question.
OSSS LSS Green Belt v10.0 - Analyze Phase
1
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Paired t-test Exercise: Solution
Because the two labs
ensured to exactly report
measurement results for
the same parts and the
results were put in the
correct corresponding row,
we are able to do a paired ttest.
The first thing we must do
is create a new column with
the difference between the
two test results.
Calc>Calculator
OSSS LSS Green Belt v10.0 - Analyze Phase
2
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Paired t-test Exercise: Solution
We must confirm the differences (now in a new calculated column) are
from a Normal Distribution. This was confirmed with the AndersonDarling Normality Test by doing a graphical summary under Basic
Statistics.
Summary for TX_MX-Diff
A nderson-Darling N ormality Test
-0.50
-0.25
0.00
0.25
0.50
A -S quared
P -V alue
0.45
0.222
M ean
S tDev
V ariance
S kew ness
Kurtosis
N
0.22727
0.37971
0.14418
-0.833133
-0.233638
11
M inimum
1st Q uartile
M edian
3rd Q uartile
M aximum
0.75
-0.50000
-0.10000
0.40000
0.50000
0.70000
95% C onfidence Interv al for M ean
-0.02782
0.48237
95% C onfidence Interv al for M edian
-0.11644
0.50822
95% C onfidence Interv al for S tD ev
95% Confidence Intervals
0.26531
0.66637
Mean
Median
0.0
OSSS LSS Green Belt v10.0 - Analyze Phase
0.2
0.4
3
0.6
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Paired t-test Exercise: Solution
As we’ve seen before, this 1 Sample T analysis is found with:
Stat>Basic Stat>1-sample T
OSSS LSS Green Belt v10.0 - Analyze Phase
4
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Paired t-test Exercise: Solution
Even though the Mean difference is 0.23, we have a 95% confidence interval that
includes zero so we know the 1-sample t-test’s null hypothesis was “failed to be
rejected”. We cannot conclude the two labs have a difference in lab results.
Histogram of TX_MX-Diff
(with Ho and 95% t-confidence interval for the mean)
5
The P-value is greater than
0.05 so we do not have the
95% confidence we wanted
to confirm a difference in the
lab Means. This confidence
interval could be reduced
with more samples taken
next time and analyzed by
both labs.
OSSS LSS Green Belt v10.0 - Analyze Phase
Frequency
4
3
2
1
0
_
X
Ho
-0.50
5
-0.25
0.25
0.00
TX_MX-Diff
0.50
0.75
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