Given the same values for p and z, why are there 4 different values of n that produce the 4% MoE?
If I solve for n with p=.5, z=1.96, and MoE=.04, I get 600.25 which is more or less what you listed for the final chart. Where are 86, 486, and 588 coming from?
The formula for the margin of error is GENERALLY taught to ignore population size (because above a certain number, as low as the tens of thousands, the difference becomes negligible)
But when your random sample is “deleterious” to the population size (like 86 out of 100 or 500 out of 2500) it becomes significant.
Technically, it matters from 25,000 to 500,000 but it's tenths or hundredths.
The formula, in school, is (in my opinion) taught as more of a concept than a fact. People plug the numbers in without understanding what the output means. And because (as you saw in the article) populations of interest are generally uncountable, no one bothers testing it.
So in my book, and briefly in the article, I offer examples of COUNTABLE population sizes to show that the MOE is not a mere concept, but a testable, provable, and even tangible one.
Ok, I'll bite.
Given the same values for p and z, why are there 4 different values of n that produce the 4% MoE?
If I solve for n with p=.5, z=1.96, and MoE=.04, I get 600.25 which is more or less what you listed for the final chart. Where are 86, 486, and 588 coming from?
Great question.
The formula for the margin of error is GENERALLY taught to ignore population size (because above a certain number, as low as the tens of thousands, the difference becomes negligible)
But when your random sample is “deleterious” to the population size (like 86 out of 100 or 500 out of 2500) it becomes significant.
Technically, it matters from 25,000 to 500,000 but it's tenths or hundredths.
The formula, in school, is (in my opinion) taught as more of a concept than a fact. People plug the numbers in without understanding what the output means. And because (as you saw in the article) populations of interest are generally uncountable, no one bothers testing it.
So in my book, and briefly in the article, I offer examples of COUNTABLE population sizes to show that the MOE is not a mere concept, but a testable, provable, and even tangible one.