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# The article “Effect of Varying Solids Concentration and

ISBN: 9780073401331 38

## Solution for problem 12SE Chapter 3

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

Step 3 of 3

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