I have a batch with a number of items, and I would like to prove that
it is likely that _all_ items in the batch are within a certain limit
by taking some random tests.
The example below follows a procedure I think might be correct, but I
am far from certain since I am still on a steep learning curve. Could
someone please tell me how wrong it is and/or the assumptions that
must be met?
----------------------------
No. items in batch: 25
Salt content must be: > 1.5
X: salt content in a randomly chosen item in the batch
Assuming X is normally distributed
Tested values: { 1.9, 2.2, 1.7, 2.1, 1.9 }
Sample size n = 5
Sample avg = 1.96
Sample's std.dev.= 0.1949
Diff between test limit and average: 1.96 - 1.5 = 0.46
Finding nor. dist's Z value: 0.46 / 0.1949 = 2.35975
For the given dist, the likelihood for selecting an item above the
limit is: Pr(X>1.5) = 0.99085
Pr(all items in batch > 1.5) = Pr(X>1.5)^25 = 0.79481
Thus, there is a 20.5% chance that one or more items in the batch is
below the given limit.
Is this procedure correct?
If this procedure is correct, am I right in assuming that it is not
the sample size that has greatest influence, but the variance of the
test data?
Thanks for any feedback,
Vegard Bakke
.
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