An approximate t-test is used to test the null hypothesis (\(H_0\)) of whether the site is dirty or clean. For either case, the t-statistic is given by
$$t=\frac{\hat\mu-AL}{SE},$$
where \(\hat\mu\) is the estimate of the sample mean from the Product Limit Estimator (Kaplan-Meier), \(AL\) is the action level, and \(SE\) is the standard error of \(\hat\mu\).
For \(H_0:\mu\geq AL\) (site is dirty) versus the alternative hypothesis \(H_A : \mu < AL\), the p-value for the test is given by \(P(T_{{n}_d-1} \leq t)\) , where \(T_{{n}_d-1}\) is a \(t\) random variate with \(n_d-1\) degrees of freedom and \(n_d\) is the number of detects in the data.
For \(H_0:\mu\leq AL\) (site is clean) versus \(H_A:\mu> AL\), the p-value for the test is given by \(P(T_{n_d-1}>t)=1-P(T_{n_d-1}\leq t)\).
The interpretation of the p-value is the same for both types of null hypothesis. In a formal test of hypothesis with significance level \(\alpha\), \(H_0\) is rejected if the p-value is less than \(\alpha\). The p-value is a measure of the evidence against \(H_0\). That is, the smaller the p-value, the stronger the evidence against \(H_0\) (and the stronger the evidence in favor of \(H_A\)).