with a 
% confidence
interval of length 2B
Here we will derive the sample size needed to obtain an interval of
length 2B, where B indicates the largest possible distance between
any in the confidence interval and the sample mean 
.
Recall that
Solving for n we obtain
Use of the formula above requires 
to be known, which seldom
happens in practice. When is unknown, one either estimate it with
the sample standard deviation from the previous study or just use the
1/4 of the
range (the difference between the largest and the smallest observations)
as a rough guess.
EXAMPLE:\:
A factory claims that the average
working hour of its employees is 40. 49 workers are chosen
randomly and their average working hours is 42 with the standard deviation
equal to 6. For future studies, if we want to construct a 99%
confidence interval with the total length less than two hours, how
large a sample will we need? (Assume 
.)
= 2.58, n = 
.