Confidence Intervals For Sums And Differences Of Mean Values - HP 50g User Manual

Estimators for the mean and standard deviation of the difference and sum of the
statistics S and S
1
In these expressions, X
samples taken from the two populations, and
of the populations of the statistics S
taken.

Confidence intervals for sums and differences of mean values

If the population variances
the difference and sum of the mean values of the populations, i.e.,
given by:
⎛
⎜
( X X
⎜ 1 2
⎝
For large samples, i.e., n
population variances
sum of the mean values of the populations, i.e.,
⎛
⎜
( X X
⎜
1
⎝
If one of the samples is small, i.e., n
equal, population variances
the variance of
are given by:
2
ˆ
X X
S S 1
1 2
and X
1
2
and
1
2
1
) z
2 /
n
1
> 30 and n
1
2 2
= , the confidence intervals for the difference and
1 2
2
S
1
) z
2 2 /
n
1
2
1
2
, as s = [(n
1 2 p
ˆ
,
2 S S
1 2
are the values of the statistics S
2
S1
and S from which the samples were
1 2
2
are known, the confidence intervals for
2
2
2
( , X X
1
n
2
> 30, and unknown, but equal,
2
2
S
2
( , X X
1
n
2
< 30 or n
1 2
2
= , we can obtain a "pooled" estimate of
2
2
-1) s +(n -1) s
1 1 2
2 2
S 1 S 2
n n
1 2
1
2 2
and are the variances
S2
1
) z
2 2 /
n
1
, are given by:
1 2
2
S
1
) z
2 2 /
n
1
< 30, and with unknown, but
2
]/( n +n -2).
2 1 2
and S from
2
, are
1 2
⎞
2 2
⎟
2
⎟
n
⎠
2
⎞
2
S
⎟
2
.
⎟
n
⎠
2
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