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.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.