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Chapter 10: Sampling Distributions and the Central Limit Theorem
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populations and compute the differences for the sample means for these
repeated samples.
Definition: Sampling Distribution of the Difference Between Two
Independent Sample Means
A sampling distribution of the difference between two independent sample
means is a distribution obtained by using the difference of the sample means
computed from random samples obtained from the two populations.
Again, we can use statistical software to help with the investigation of the
properties of the sampling distribution of the difference between two sample
means through simulations. The statistical software was used to simulate
10,000 samples of size of 36 were simulated from normal distributions
with
means
= 5 and
= 9, and standard deviations
= 3 and
= 5. The
descriptive statistics for the differences of the sample means for a simulation
is given in
Figure 10-31
.
Figure 10-31:
Descriptive Statistics of Simulation for
DifferencebetweenTwo Sample Means
Let
̅
̅
represent the mean of the differences of the sample means, and
̅
̅
represent the standard deviation of the differences of the sample