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Sample Adeauacv Calculations for Reclaimed Area Parameter Estimation with Hypothesis <br />Testing <br />When hypothesis testing is employed, the Colorado Mined Land Reclamation Board (CMLRB) <br />(1995) prescribes the following formula for calculation of sample size: <br />(ta + fp)z s2 <br />Nmin= <br />~d Q`2 <br />t° =one-tailed t-value with (n-1) degrees of freedom, a=0.10 <br />t~ =one-tailed t-value with (n-1) degrees of freedom, p=0.25 <br />sZ =sample variance <br />d = 0.1 (level of precision or desired detectable reduction) <br />O = 90% of the reference area sample mean or 90% or the technical standard <br />Sample Variance for Sample Adeauacv Calculations <br />For one-stage sampling, variance was calculated as the square of the standard deviation. For <br />the two-stage sampling of total annual production and shrub density, calculation of sample <br />variance for use in the sample adequacy formulas was as follows (Expression 10.10 of Cochran <br />1963): <br />1-ft <br />z <br />Vy = S, <br />1-f2 <br />+ Sp2 <br />mn <br />where: <br />Vy =Overall variance of the total annual production or shrub density data <br />f, = n/N <br />f2 = m/M <br />S,Z =variance among primary unit means <br />S22 =variance among elements within primary units relative to the orimary unit means <br />N =total number of primary units that exist within the study area and are to be potentially <br />sampled as <br />n = number of primary units actually sampled / a.. <br />M =total number of sample elements (secondary units) that exist within each primary unit and are <br />potentially to be sampled ~~ ~~ /~ <br />f i <br />