Environmental scientists are investigating the efficacy of a new industrial filtration plant designed to reduce lead concentrations in a local river system. They measured lead levels (in parts per billion, ppb) at 8 different sampling sites both before and after the plant became operational. The recorded concentrations are presented in the following table:
Site12345678Before (ppb)45.250.148.439.852.547.044.649.3After (ppb)43.848.548.638.050.245.144.947.5 \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text{Site} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text{Before (ppb)} & 45.2 & 50.1 & 48.4 & 39.8 & 52.5 & 47.0 & 44.6 & 49.3 \\ \hline \text{After (ppb)} & 43.8 & 48.5 & 48.6 & 38.0 & 50.2 & 45.1 & 44.9 & 47.5 \\ \hline \end{array} SiteBefore (ppb)After (ppb)145.243.8250.148.5348.448.6439.838.0552.550.2647.045.1744.644.9849.347.5By stating your hypotheses clearly, test at the 2.5% level of significance whether the filtration plant has successfully reduced the mean lead concentration in the river. You should assume that the differences in lead levels follow a normal distribution.
