Statistics for Environmental Engineers

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3.36


3.56


0.78


20


2.14


2.48


2.90


3.21


3.50


0.66


30


2.08


2.39


2.78


3.06


3.48


0.53


40


2.05


2.35


2.73


2.99


3.49


0.45


60


2.02


2.31


2.67


2.93


3.53


0.37


1.96


2.24


2.57


2.80


<x>


0.00

Source: Hahn, G. J. (1970). J. Qual. Tech., 3, 18-22.


A random sample of n = 5 observations yields the values y = 28.4 [lg/L and s = 1.18 ^g/L. An additional m = 10 specimens are to be taken at random from the same population.


1.    Construct a two-sided (simultaneous) 95% prediction interval to contain the concentrations of all 10 additional specimens. For n = 5, m = 10, and a = 0.05, the factor is 5.23 from the second row of Table 21.2. The prediction interval is:


28.4    ± 5.23(1.18) = [22.2, 34.6]


We are 95% confident that the concentration of all 10 specimens will be contained within the interval 22.2 to 34.6 ^g/L.


2.    Construct a two-sided prediction interval to contain the mean of the concentration readings of five additional specimens randomly selected from the same population. For n = 5, m = 5, and 1 — a = 0.95, the factor is 1.76 and the interval is:


28.4    ± 1.76(1.18) = [26.3, 30.5]


We are 95% confident that the mean of the readings of five additional concentrations will be in the interval 26.3 to 30.5 ^g/L.

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