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Simulated observations. Most statistical software
packages have routines for simulating values of variables
having specified distributions. Use your statistical software
to generate 25 observations from the N(30, 5) distribution.
Compute the mean and standard deviation x and s of the
25 values you obtain. How close are x and s to the μ
and σ of the distribution from which the observations were
drawn?
Repeat 19 more times the process of generating 25 observations
from the N(30, 5) distribution and recording x and s. Make
a stemplot of the 20 values of x and another stemplot of the 20
values of s. Make Normal quantile plots of both sets of data.
Briefly describe each of these distributions. Are they symmetric
or skewed? Are they roughly Normal? Where are their centers?
(The distributions of measures like x and s when repeated sets
of observations are made from the same theoretical distribution
will be very important in later chapters.)
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