SECTION 6.4 Confidence Intervals 387
The philosophy behind the confidence intervals whereσis unknown
is pretty much the same as in the previous section. We first choose a
desired level of confidence (1−α)×100% and then choose the appro-
priate leveltα/ 2 which containsα×100% of the population in the two
tails of the distribution. Of course, whicht distribution we choose is
dependent on the size of the sample we take; as mentioned above, the
degrees of freedom is equal ton−1, wherenis the sample size. These
levels are tabulated in any statistics book; as a sample we show how
they are typically displayed (a more complete table is given at the end
of this chapter):
Degrees of
Freedom t. 050 t. 025 t. 005
... ... ... ...
10 1.812 2.228 3.169
11 1.796 2.201 3.106
12 1.782 2.179 3.055
13 1.771 2.160 3.012
... ... ... ...Once we have collected the sample of sizenand have computed the
averagexof the sample, the (1−α)×100% confidence interval becomes
x−tα/ 2 √sx
n,x+tα/ 2
sx
√
n
.