HP 48gII Graphing Calculator Manual do Utilizador descarregar pdf (Página 597)

100

101

Page 18-26

Confidence intervals for sums and differences of mean values

If the population variances σ

and σ

are known, the confidence intervals for

the difference and sum of the mean values of the populations, i.e., µ

±µ

, are

given by:













+⋅+±+⋅−±

2/21

)(,)(

zXX

σσσσ

αα

For large samples, i.e., n

> 30 and n

> 30, and unknown, but equal,

population variances σ

= σ

, the confidence intervals for the difference and

sum of the mean values of the populations, i.e., µ

±µ

, are given by:

.)(,)(

2/21













+⋅+±+⋅−±

zXX

αα

If one of the samples is small, i.e., n

< 30 or n

< 30, and with unknown, but

equal, population variances σ

= σ

, we can obtain a “pooled” estimate of

the variance of µ

±µ

, as s

= [(n

-1)⋅s

+(n

-1)⋅s

]/( n

-2).

In this case, the centered confidence intervals for the sum and difference of

the mean values of the populations, i.e., µ

±µ

, are given by:

(

)

2/,21

)(,)(

stXXstXX ⋅+±⋅−±

αναν

where ν = n

-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

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