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Chapter 10: Sampling Distributions and the Central Limit Theorem
Definition: Sampling Distribution of a Sample Mean
A sampling distribution of a sample mean is a distribution obtained by using
the means computed from random samples of a specific size obtained from a
population.
In order to investigate properties of the sampling distribution of a sample
mean, simulations of the situation can be done. In this example, 100 samples
of size 50 were generated. Here we will assume that the time spent working
during the week is normally distributed with a mean of 34.6 and a standard
deviation of 1, for the sake of the simulation. You may try your own
simulation if you have access to such statistical software. The descriptive
statistics for a simulation is shown in
Figure 10-14
.
Figure 10-14:
Descriptive Statistics of a Simulation
for Sample Means
Table 10-4
shows some summary information, obtained for the 100
simulated sample means of sample size 50.
Table 10-4:
Some Summary Information for the Simulation on
Sample Means
Observe from the table that the values on the left side are approximately
equal to the corresponding values on the right side. Of course, if we do a