And because of the
convergence property of central tendencies, the larger the data set, the better the
estimate we expect our sample average to be of the stable component of the process.
Given the huge sample size in the reading example (about 11,000 eighth graders)
and assuming proper care in composing the sample, we expect that the sample mean
of 264 is very close to this propensity. Assuming that the 1994 mean is of equal
quality, we can be fairly certain that the difference between these two means reflects
a real change in the underlying process that affects reading scores. Note that the