Confidence Intervals For Sums And Differences Of Mean Values, - HP 49g+ User Manual

Confidence intervals for sums and differences of mean values
If the population variances σ
the difference and sum of the mean values of the populations, i.e., µ
given by:
( X X ) z
1 2 α 2 /
For large samples, i.e., n
population variances σ
1
sum of the mean values of the populations, i.e., µ
( X X ) z
1 2 α 2 /
If one of the samples is small, i.e., n
equal, population variances σ
the variance of µ ±µ
, as s
1 2
In this case, the centered confidence intervals for the sum and difference of
the mean values of the populations, i.e., µ
( X X
1
where ν = n
+n -2 is the number of degrees of freedom in the Student's t
1 2
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
2 and σ 2
are known, the confidence intervals for
1 2
2 2
σ σ
1 2 ( , X X
1
n n
1 2
> 30 and n > 30, and unknown, but equal,
1 2
2 = σ 2
, the confidence intervals for the difference and
2
2 2
S S
1 2 ( , X X
1
n n
1 2
< 30 or n
1 2
2 = σ 2
, we can obtain a "pooled" estimate of
1 2
2 2
= [(n -1)⋅s +(n -1)⋅s
p 1 1 2
±µ
, are given by:
1 2
2
) t s ( , X X
2 ν , α 2 / p 1
±µ
1
2 2
σ σ
) z 1 2
2 α 2 /
n n
1 2
±µ
, are given by:
1 2
2 2
S S
) z 1 2
2 α 2 /
n n
1 2
< 30, and with unknown, but
2
]/( n +n -2).
2 1 2
2
) t s
2 ν , α 2 / p
Page 18-26
, are
2
.