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reason to believe that the two unknown population variances are different, we
can use the following confidence interval
(
)
2
2
/
,
2
1
2
2
/
,
2
1
2
1
2
1
)
(
,
)
(
X
X
X
X
s
t
X
X
s
t
X
X
±
±
⋅
+
±
⋅
−
±
α
ν
α
ν
where the estimated standard deviation for the sum or difference is
2
2
2
1
2
1
2
1
n
s
n
s
s
X
X
+
=
±
and n, the degrees of freedom of the t variate, are calculated using the integer
value closest to
)]
1
/(
)
/
[(
)]
1
/(
)
/
[(
)]
/
(
)
/
[(
2
2
2
2
1
1
2
1
2
2
2
2
1
2
1
−
+
−
+
=
n
n
S
n
n
S
n
S
n
S
ν
Determining confidence intervals
The application
6. Conf Interval
can be accessed by using
‚Ù—
@@@OK@@@
. The application offers the following options:
These options are to be interpreted as follows:
1. Z-INT: 1
µ
.: Single sample confidence interval for the population mean,
µ
, with known population variance, or for large samples with unknown
population variance.
2. Z-INT:
µ1−µ2
.: Confidence interval for the difference of the population
means,
µ
1
-
µ
2
, with either known population variances, or for large
samples with unknown population variances.
