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Chapter 11: Confidence Intervals – Large Samples
From
Chapter 10
, we can summarize the properties of the sampling
distribution for the difference between two independent sample means with
the following statements:
As the sample sizes
and
increase, the shape of the distribution of the
differences of the sample means obtained from any population
(distribution) will approach a normal distribution.
The distribution of the differences of the sample means will have a mean
that is equal to
̅
̅
, where
and
are the respective
population means of interest.
The distribution of the differences of the sample means will have a
standard deviation
̅
̅
√
where
and
are the respective
population standard deviations of interest.
These properties can aid us in the construction of a (1 -
)
100 percent
confidence interval for the difference of two population means. The general
equation used in constructing a (1 -
)
100 percent confidence interval for
the difference between two population means for large samples, is given
next.