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Chapter 10: Sampling Distributions and the Central Limit Theorem
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Table 10-12:
Properties of the Sampling Distribution for the
Difference Between two Independent Sample Means
Next we can investigate the shape of the distribution for these differences of
the sample means.
Figure 10-31
shows a histogram for the simulation for
this situation. Observe that the shape of the distribution of the simulated
differences of sample means is approximately bell-shaped or normal. This
normality approximation will get better and better as the sample sizes from
the two populations increase.
We can investigate with other sample sizes, population means, and
variances. However, we will generally observe the same properties.
We can generalize the observations in a very important theorem called the
Central Limit Theoremfor the Difference betweenTwo Sample Means
.
This theorem is stated in
Table 10-13
.