Page 119 - Standard Handbook Of Petroleum & Natural Gas Engineering

104 Mathematics

where K,,, = estimated value of the K statistic
F = distribution factor
D = measure of dispersion
(For one-sided confidence intervals, the * is replaced by + or by -.)
If (3 is known, the confidence interval on the mean is
1. Two sided

- (3 - (3
x-z,,--pIx++,,-
&- &

2. One sided, lower limit
- (3
<
x - z, - p I CQ
&-
3. One sided, upper limit

-
--m I p I X +z, -
(3
J;;
where = sample mean = Kes,
n = sample size
Z,,Z~,~ = values of random variables, with standard normal distribution,
cutting off (1 - y) and (1 - y/2) respectively in the tail of the
distribution, and a = 1 - y (the level of significance) = F
o/& = measure of dispersion

If (3 is unknown, the equations are
1. Two sided

2. One sided, lower limit

- S
x- t, - p I
<
&-
3. One sided, upper limit

-
--m I I x+ t, -
S
VL