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The article “Effect of Varying Solids Concentration and

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 12SE Chapter 3

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 12SE

The article “Effect of Varying Solids Concentration and Organic Loading on the Performance of Temperature Phased Anaerobic Digestion Process” (S. Vandenburgh and T. Ellis, Water Environment Research, 2002:142-148) discusses experiments to determine the effect of the solids concentration on the performance of treatment methods for wastewater sludge. In the first experiment, the concentration of solids (in g/L) was 43.94 ± 1.18. In the second experiment, which was independent of the first, the concentration was 48.66 ± 1.76. Estimate the difference in the concentration between the two experiments, and find the uncertainty in the estimate.

Step-by-Step Solution:
Step 1 of 3

Solution 12SE

Step1 of 3:

Let us consider X be the concentration of solid in the first Experiment and Y be the concentration of solid in the second Experiment.

We have

X = 43.94,   and Y = 48.66,

We need to estimate the difference in the concentration between the two experiments, and find the uncertainty in the estimate.

Step2 of 3:

The difference in the concentration between the two experiments is given by

                  =

                                                             = 4.72

Hence, T = 4.72.

1).Differentiate  with respect X then we get

Let u = X - Y

     du = 1

Apply chain rule then we get

                      =

                                                       =

Substitute “u” value in above equation we get

                                              =

                                           =

                                                                =

                                                        = -1

Hence, = -1.

Step3 of 3:

2).Differentiate  with respect Y then we get

Let...

Step 2 of 3

Chapter 3, Problem 12SE is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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The article “Effect of Varying Solids Concentration and

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