Statistics for Environmental Engineers

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The form of a two-sided tolerance interval is the same as a confidence interval:


У ± K 1-a,p,ns


where the factor K1-apn has a 100(1 — a)% confidence level and depends on n, the number of observations in the given sample. Table 21.1 gives the factors (tn-1a/2 hjn) for two-sided 95% confidence intervals


Factors for Two-Sided 95% Confidence Intervals and Tolerance Intervals for the Mean of a Normal Distribution


n


Confidence Intervals


(?n-1, a/2/Vn)


K1-a, p, n


for Tolerance Intervals


p = 0.90


p = 0.95


p = 0.99


4


1.59


5.37


6.34


8.22


5


1.24


4.29


5.08


6.60


6


1.05


3.73


4.42


5.76


7


0.92


3.39


4.02


5.24


8


0.84


3.16


3.75


4.89


9


0.77


2.99


3.55


4.63


10


0.72


2.86


3.39


4.44


12


0.64


2.67


3.17


4.16


15


0.50


2.49


2.96


3.89


20


0.47


2.32


2.76


3.62


25


0.41


2.22


2.64


3.46


30


0.37


2.15


2.55


3.35


40


0.32


2.06


2.45


3.22


60


0.26


1.96


2.34


3.07


0.00


1.64


1.96


2.58

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