Epa 402-R-98-008 - Statistical Procedures For Certifying Phosphogypsum For Entry Into Commerce - U.s. Environmental Protection Agency - 1998 Page 13
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17being considered for entry into commerce for agricultural purposes is greater than 7.5 pCi/g, and
is rejected if the sample mean is less than or equal 7.5 pCi/g. The region of rejection is the
shaded area to the left of 7.5 pCi/g in Figure 2.
Therefore, if a sample drawn from an area of a stack with an unknown concentration has
a mean less than or equal 7.5 and a standard deviation of 8.2, the null hypothesis would be
rejected, which means that the phosphogypsum is judged to be acceptable for use for agricultural
purposes.
Although this illustration is a straightforward application of a test of an hypothesis, the
test can be structured somewhat more conveniently with some recalculation. This is done by
*
x
determining a different critical value,
, based on the sampling distribution for sample drawn
from the area of the stack being tested. The new critical value is calculated using the following
equation:
s
,
* =
+
x
x
z
n
th
x
where
*
is the 95
percentile, which determines the upper 5% tail area,
x
is the mean of the measured radium concentration (in pCi/g) measured from the
n samples,
s
is the standard deviation of the measured radium concentration (in pCi/g)
measured from the n samples,
and
z =
1.64, based on an upper tail area equal 5%.
The critical value has been redefined, and has changed numerical value. Nevertheless,
the new decision rule has the same outcome as the previously formulated decision rule. This is
shown in the following equations:
s
,
x #
if
10 - z
n
s
#
x
then
+ z
10,
n
#
*
x
or
10.
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