Quiz 5
EMA 4714  Materials Selection and Failure Analysis
KEY
Wednesday, March 30, 2005
1. [10 points] Two batches [10,000 pieces each] of
selftapping steel fasteners were received from a heat
treating facility who claimed that one batch had been
tempered for twice the time as the other. The paperwork
had been misplaced and there was no way of knowing
which batch was which. A series of hardness
measurements performed on pieces selected at random
from each batch resulted in data contained within the table
to the right. For your convenience [provision of same
being a prime driving force for my existence], I have
calculated means and standard deviations for the two sets
of sample data. Based on your statistical analysis, and
using a level of significance [
α
] of 0.05, does the data
allow a determination that the two batches were subjected
to different tempering times?
***************************************************************************
First, determine which test statistic to use: s
2
2
/s
1
2
= 6.95; from F tables, critical region for
ν
= 9 = 2.44 [
α
= 0.05]: use Statistical Test 7,
σ
unknown and s
1
not equal to s
2
k = [s
1
2
/n
1
]/[s
1
2
/n
1
+ s
2
2
/n
2
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 Spring '08
 Staff
 Statistics, Normal Distribution, Standard Deviation, α, 0.5%

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