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In this case, the centered confidence intervals for the sum and difference of the
mean values of the populations, i.e., μ
1
±μ
2
, are given by:
where ν = n
1
+n
2
-2 is the number of degrees of freedom in the Student’s t
distribution.
In the last two options we specify that the population variances, although
unknown, must be equal. This will be the case in which the two samples are
taken from the same population, or from two populations about which we
suspect that they have the same population variance. However, if we have
reason to believe that the two unknown population variances are different, we
can use the following confidence interval
where the estimated standard deviation for the sum or difference is
and n, the degrees of freedom of the t variate, are calculated using the integer
value closest to
Determining confidence intervals
The application 6. Conf Interval can be accessed by using ‚Ù—
@@@OK@@@. The application offers the following options:
()
2
2/,21
2
2/,21
)(,)(
pp
stXXstXX ⋅+±⋅−±
αναν
()
2
2/,21
2
2/,21
2121
)(,)(
XXXX
stXXstXX
±±
⋅+±⋅−±
αναν
2
2
2
1
2
1
21
n
s
n
s
s
XX
+=
±
)]1/()/[()]1/()/[(
)]/()/[(
22
2
211
2
1
2
2
2
21
2
1
−+−
+
=
nnSnnS
nSnS
ν