# 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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