Statistics for Environmental Engineers

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23.5    Difference of Two Means. We wish to be able to distinguish between true mean concentrations of mercury that differ by at least 0.05 [ig/L for a = 0.05 (the probability of falsely rejecting that the two means are equal) and в = 0.20 (the probability of failing to reject they are equal) if A = |n — nl = 0.02. From the case study in Chapter 18, we use sp = 0.0857 ^g/L as an estimate of a. Determine the required sample size, assuming np = nc.


23.6    Equivalence of Two Means. We wish to determine whether the mercury concentrations in wastewater from areas served by the city water supply and by private wells are equivalent. We wish to distinguish true mean concentrations that differ by at least A = 0.02 ^g/L, but are willing to establish, on a practical basis, an equivalence interval of в = ±0.05 ^g/L for the difference. Assuming np = nc, use a = 0.05, в = 0.20, and sp = 0.0857 ^g/L to determine the required sample size.


23.7    Phosphorus Inventory. To estimate the average and the total amount of phosphorus in a reservoir, the reservoir was divided into three strata (surface layer, bottom layer, and intermediate layer). Portions of reservoir water were collected at random (with respect to vertical and horizontal location) within each strata. The data are:


Strata


Volume


wh


nh


Measurements (^g / L)


1


4,000,000


0.40


10


21


12

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