Statistics for Environmental Engineers

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Case Study: Mercury in Domestic Wastewater

Extremely low limits now exist for mercury in wastewater effluent limits. It is often thought that whenever the concentration of heavy metals is too high, the problem can be corrected by forcing industries to stop discharging the offending substance. It is possible, however, for target effluent concentrations to be so low that they might be exceeded by the concentration in domestic sewage. Specimens of drinking water were collected from two residential neighborhoods, one served by the city water supply and the other served by private wells. The observed mercury concentrations are listed in Table 18.1. For future studies on mercury concentrations in residential areas, it would be convenient to be able to sample in either neighborhood without having to worry about the water supply affecting the outcome. Is there any difference in the mercury content of the two residential areas?

The sample collection cannot be paired. Even if water specimens were collected on the same day, there will be differences in storage time, distribution time, water use patterns, and other factors. Therefore, the data analysis will be done using the independent t-test.

t-Test to Compare the Averages of Two Samples

Two independently distributed random variables y1 and y2 have, respectively, mean values n and p2 and variances of and o. The usual statement of the problem is in terms of testing the null hypothesis that the difference in the means is zero: n П2 = 0, but we prefer viewing the problem in terms of the confidence interval of the difference.

The expected value of the difference between the averages of the two treatments is:

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