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If the initial samples do not provide a suitable estimate of the mean (i.e., the inequality is false), <br />additional samples would be collected until the inequality (n <_ n) becomes true. <br />2.6 Reverse Null Hypothesis Testing <br />The Guideline Regarding Selected Coal Mine Bond Release Issues (CDMG, 1995) states in Part 4 <br />that, "Other than a demonstration of adequate sample size, no statistical calculations are required in this <br />case to document success." All sampled units in 2011 met this obligation, but reverse null hypothesis <br />testing was also employed as a means to validate the successful passage of all success comparisons at <br />Snowcap Mine. In this regard, the following formula exhibits the procedure utilized to determine the <br />calculated "t- statistic" for reverse null two- sample hypothesis testing: <br />For two- sample testing (with a reference area) for assumed equal variances (usual case), the <br />following test would be performed (ry = revegetated unit, ra = reference area): <br />t = <br />A <br />x —0.9x <br />ra \ Where the pooled variance s p 2 = <br />s 2 1 + 1 <br />fl" nra / <br />2 _ [(nra - 1�0.81s, + (n -1)sr <br />S p <br />(n„ +n")-2 <br />Then if t >_ t for t (a =0.1, nra +nrv-2 d.f.) the test is successful. <br />For two- sample testing (with a reference area) for unequal variances (infrequent case), the <br />following test would be performed <br />x —0.9x 0.81s` s <br />t = , ra Where w = ra and w, = ry <br />'Jwry — wra nra nry <br />and the degrees of freedom are approximated by : <br />( + w ry ) <br />Wm + w ry <br />n — 1 n,,, —1 <br />Then if & >_ tfor t (a =o.1, approx. d.f.) the test is successful. <br />Cedar Creek Associates, Inc. 13 Snowcap Mine - 2011 <br />Phase III Bond Release Evaluation - Year 1 <br />