September 3, 1999
This question turns out to have been phrased poorly. It would have been better to ask, "How do we tell that one collection of sample percents is more accurate than another?" This would have made clear that sample size is not the real issue; rather,assessing accuracy is the real issue. As such, one collection of sample percents is more accurate than another if samples in it tend to deviate less from the population percent than does the other collections' percents.
Several of you understood this question to be "what happens to accuracy as we use samples of larger sizes?" That is a good question, but an answer to it does not answer the question of how we determine that one collection is more accurate than another.
Several of you were right on target -- that if we are
in the process of planning to collect a sample to find out something
about a population, the larger the sample we plan the more we
are assured of accurate results. However, at some point, the
increased expense of taking a larger sample does not produce
a proportionate increase in accuracy, and at some point later
point yet the increased expense of taking a yet larger sample
hardly produces any increase in accuracy.
a) What does "285" on the horizontal axis stand for?
It stands for 285 red marbles in a sample
b) What does "100" on the vertical axis stand for?
It stands for 100 samples having a number of red
marbles within some interval
c) What is represented by the highlighted slice of the bar above 300-305?
It stands for a subgroup of all the samples that had 300, 301, 302, or 304 red marbles in them.