Epa 402-R-98-008 - Statistical Procedures For Certifying Phosphogypsum For Entry Into Commerce - U.s. Environmental Protection Agency - 1998 Page 16
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17there, the increased sample size reduces the standard deviation of the sampling distribution
x
sufficiently that the new critical value,
*
, is less than 10 pCi/g.
2
This is the basis for the provision in Section 61.207(c), which requires further testing by
increasing the sample size, as discussed in Procedure 1, steps (6) through (11), on p. 6.
In one sense, Figure 5 is an over simplification because it shows the two distributions
with the same mean. This is unlikely to occur in practice because any change in the individual
members of a sample (here an increase in sample size), would be expected to cause changes in
both the sample mean, and the standard deviation, due to random variations in the observations
included in the sample., Therefore, the mean of the new sampling distribution would not be
expected to be exactly the same as the mean of the original sampling distribution, nor would the
standard deviation of the new sampling distribution be expected to be exactly one half the
standard deviation of the original to be exactly one half the standard deviation of the original
sampling distribution.
The result is that the increased sample size required in Section 61.207(c), and described
x
in Procedure 1, steps (6) through (11), does not guarantee that the recalculated value for
* will
be below 10 pCi/g. /The recalculated sample mean may be larger than the mean previously
calculated, or the recalculated sample standard deviation may not be as small as expected. If the
x
recalculated
* is not less than or equal 10 pCi/g the sample size can again be increased and the
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