0
$\begingroup$

In a set of N individuals X% have some characteristic.

In a random subset of M individuals of this set, we observe that Y% have the characteristic. Note that M is not necessarily very small compared to N.

1) What is the probability P(N, M, X, Z) that | Y% - X% | <= Z% ?

2) What is the probability P'(N, M, X, Z) that Y% - X% > Z% ?

Example: There are 200 inhabitants in a village. 12% have blue eyes. In a random sample of 20 inhabitants, what is the probability that, among them, the proportion having blue eyes is between 10% and 14% (i.e. 12% +/- 2%)? Strictly greater than 14%?

$\endgroup$
  • $\begingroup$ Hypergeometric distribution. Interpreting 10-14% of 20 to mean 2 or 3, one can use R code sum(dhyper(2:3, 24, 200-24, 20)), which returns 0.5221374. For just 2 with blue eyes it's ${24 \choose 2}{176 \choose 18}/{200 \choose 20}=0.2852916.$ $\endgroup$ – BruceET Jan 7 at 18:46

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.