BHS Statistics

September 7, 1999

The key to this assignment was to GO SLOW in reading the column labels. "% of Sample Percents" refers to a fraction of the collection of samples that were drawn repeatedly from some population.

The phrase "... within x percentage points of the population percent" refers to a range surrounding the population percent. In the first example, the population percent was .57 (57%). Therefore, for a sample to be within 1 percentage point of the population percent, it would have to have a percent saying yes that is between 56% and 58%.

For example, with regard to the first histogram:

2000 Samples of 500 each taken from a population having .57 of it believing "yes".

Analysis: There are 2000 samples. The population percent is .57 (i.e., 57% of the population believes "yes"). Any sample having a percent saying yes between .56 and .58 will be within 1 percentage point of the population percent. 362 of the samples had percentages between .56 and .57; 355 of them had percentages between .57 and .58. Therefore, 717 of these 2000 samples, or approximately 36%, were within 1 percentage point of the population percent.

And so on for the rest of the tables.

 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%