The number of allergic people in a population of size N can be modeled as a Binomial(N, p) distribution, where p is the probability that any individual person is allergic.
The maximum likelihood estimate for p when we observe 1 allergic person out of 12 is just 1/12, or 8.33%. This is our best guess if we had to name an exact number.
We can get a 95% confidence interval on the value of p using the Clopper-Pearson method with the following R code:
The number of allergic people in a population of size N can be modeled as a Binomial(N, p) distribution, where p is the probability that any individual person is allergic.
The maximum likelihood estimate for p when we observe 1 allergic person out of 12 is just 1/12, or 8.33%. This is our best guess if we had to name an exact number.
We can get a 95% confidence interval on the value of p using the Clopper-Pearson method with the following R code:
> binom.test(x=1, n=12, p=1/12) … 95 percent confidence interval: 0.002107593 0.384796165 …So we know with 95% confidence that the probability that any individual person is allergic to moon dust is with the range 0.21% and 39%.
Yeah, okay, that’s pretty useless. I agree with them…