Populaton Percent (Percent of Yes in Population) | Number of Samples Drawn | % of Sample Percents within 1 Percentage Point of Population % | % of Sample Percents within 2 Percentage Points of Population % | % of Sample Percents within 3 Percentage Points of Population % | % of Sample Percents within 4 Percentage Points of Population % |

57% | 2000 |
36% |
64% |
82% |
93% |

60% | 2000 |
36% |
65% |
85% |
93% |

65% | 2000 |
37% |
65% |
85% |
95% |

32% | 3000 |
37% |
66% |
85% |
94% |

We notice that for every group of samples in our collection, a little more than 1/3 (36%) of the percents calculated from them lie within one percentage point of their population percents, roughly 2/3 of them (65%) lie within two percentage points of their population percents, roughly 85% of them lie within three percentage points, and roughly 94% of the samples lie within four percentage points of their respect population percents.

This table suggests that percents calculated from random samples of size 500 are a;pproximately equally variable regardless of what the population percent is. So, one generalization is:

Underlying population percents have very little influence on the variability of 500-item samples taken from them.

Will these patterns hold for:

a) Large collections of small samples (e.g., samples of size 15)?

b) Small collections of large samples (e.g., 15 samples of size 500)?

How would we investigate these questions?