# Statistics for Environmental Engineers

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 1 day 2 days 3 days 5 days 7 days 12 days 20 days 0.40 0.99 0.95 1.53 1.25 2.12 2.42 0.55 0.95 1.00 1.77 1.35 2.21 2.28 0.61 0.98 1.05 1.75 1.90 2.34 1.96 0.66 0.95 1.20 1.95 1.95 1.95 1.92

35.2    BOD Experimental Design I. (a) Fit the BOD model у = 6Щ — exp (-02t)] to the data for days 1, 2, 3, and 5 in Exercise 35.1. (b) Plot the data and the fitted model. (c) Plot the approximate 95% joint confidence region. (d) Select three pairs of parameter values from within the joint confidence region and plot the curves obtained by using them in the model.

35.3    BOD Experimental Design II. Fit the BOD model to the first two rows of data (two replicates) for days 3, 5, 7, 12, and 20, plot the joint confidence region, and compare the result with the confidence region obtained in Exercise 35.1 or 35.2. Discuss how changing the experimental design has affected the size and shape of the confidence region.

35.4    Monod Model. Fit the Monod model yt = 01xil(02 + xi) + ei to the following data and plot the joint confidence region of the parameters.

Substrate    5.1    20.3    37    74.5    96.5    112    266    386

Growth Rate    0.059    0.177    0.302    0.485    0.546    0.610    0.792    0.852

35.5 Haldane Model. Fit the Monod model у = 01xi/(02 + xi) + ei and the Haldane model yi = —0 1-t2 + et to the following data. у is the growth rate; x is substrate (phenol) concen-

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