Page 184 - Statistics for Environmental Engineers

L1592_frame_C21 Page 183 Tuesday, December 18, 2001 2:43 PM

Exercises
21.1 Phosphorus in Biosolids. A random sample of n = 5 observations yields the values y = 39.0 µg/L
and s = 2.2 µg/L for total phosphorus in biosolids from a municipal wastewater treatment plant.

1. Calculate the two-sided 95% confidence interval for the mean and the two-sided 95%
tolerance interval to contain at least 99% of the population.
2. Calculate the two-sided 95% prediction interval to contain all of the next five observations.
3. Calculate the two-sided 95% confidence interval for the standard deviation of the population.

21.2 TOC in Groundwater. Two years of quarterly measurements of TOC from a monitoring well
are 10.0, 11.5, 11.0, 10.6, 10.9, 12.0, 11.3, and 10.7.
1. Calculate the two-sided 95% confidence interval for the mean and the two-sided 95%
tolerance interval to contain at least 95% of the population.
2. Calculate the two-sided 95% confidence interval for the standard deviation of the population.
3. Determine the upper 95% prediction limit for the next quarterly TOC measurement.

21.3 Spare Parts. An international agency offers to fund a warehouse for spare parts needed in
small water supply projects in South Asian countries. They will provide funds to create an
inventory that should last for 5 years. A particular kind of pump impeller needs frequent
replacement. The number of impellers purchased in each of the past 5 years is 2770, 3710,
3570, 3080, and 3270. How many impellers should be stocked if the spare parts inventory is
created? How long will this inventory be expected to last?

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