The One-Sample t -Test to compare the mean to a threshold performed by VSP on the selected data values follows the procedure outlined in EPA's Guidance for Data Quality Assessment: Practical Methods for Data Analysis (EPA 2000b, p. 3-7).
$$ t = \frac{ \bar x - AL}{SE} $$
where
\( \bar x \) is the sample mean (See the Summary Data Sub-page for definitions of statistics.)
\( AL \) is the action level or threshold
\( SE \) is the standard error, or \( \large \frac{s}{ \sqrt{n}} \) where \( s \) is the standard deviation of data
This \( t \) is then compared with \( t_{1- \alpha} \), where \( t_{1- \alpha} \) is the value of the t distribution with \( n-1 \) degrees of freedom for which the proportion of the distribution to the left of \( t_{1- \alpha} \) is \( 1 - \alpha \).
For testing the null hypothesis that the population mean is greater than or equal to the threshold (\( H_0 : \mu \geq AL \)), the null hypothesis is rejected if \( t < -t_{1- \alpha} \) , and cannot be rejected if \( t \geq -t_{1- \alpha} \).
For testing the null hypothesis that the population mean is less than or equal to the threshold (\( H_0 : \mu \leq; AL \)), the null hypothesis is rejected if \( t > t_{1- \alpha} \) , and cannot be rejected if \( t \leq t_{1- \alpha } \).