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2.6 Reverse Null Hypothesis Testina <br />The Guideline Regarding Selected Coal We 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 met this obligation, but reverse null hypothesis testing was <br />also employed as a means to verify the successful passage of all success criteria at Snowcap Mine. The <br />following formula exhibits the procedure utilized to determine the calculated "t- statistic" for reverse null <br />two- sample hypothesis testing: <br />For two - sample testing (with a reference area) for assumed eeaual variances (usual case), the <br />following test would be performed (ry = revegetated unit, ra = reference area): <br />x — 0.9x <br />tc = ry 'a Where the pooled variance sv — <br />fSP2( 1 + 1 <br />nry nra <br />S2 _ [(n. - 1)0.81s ra - l�srr„� <br />P (nra +n,)— 2 <br />Then if t, >_ t for t (a =0.1, nra +nry -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 />Y, —0.9x 0.81sz s2 <br />tc = ry ra Where wra = ra and w, = ry <br />VW, — wra nra nry <br />and the degrees of freedom are approximated by: <br />(wra + wry ) 2 <br />W'2 <br />ra + wry <br />nra —1 nr„ —1 <br />Then if t, >_ tfor t(a =o.1, appmx. d.f.) the test is successful. <br />CEDAR CREEK ASSOCIATES, Inc. Page 15 Snowcap - Phase III Bond Release <br />Evaluation - 2012 <br />