Sampling Distribution, Difference Between Independent Means (1 of 5)
This section applies only when the means are computed from
independent samples. The formulas are more complicated when the two
means are not independent. Let's say that a researcher has come up with
a drug that improves memory. Consider two hypothetical
populations: the performance of people on a memory test if they had
taken the drug and the performance of people if they had not. Assume
that the mean (μ) and the variance (
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) of the distribution of people taking
the drug are 50 and 25 respectively and that the mean (μ)
and the variance (
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) of the distribution of people not taking the drug are 40 and
24 respectively. It follows that the drug, on average, improves performance
on the memory test by 10 points. This 10-point improvement is for the
whole population. Now consider the sampling distribution of the difference
between means. This distribution can be understood by thinking of the
following sampling plan: