Discrete variable 95% confidence intervals

Question

For a discrete variable with values ranging from 0 to 100, what are the 95% confidence intervals if

I sample 100 items? If I sample 200 items. Each sample measurement could be in limited categories, 3-6. Specifically, my sample space is ordinal numbers from 0 to 100. I either will observe 100 items or 200 items.

If I find e.g. 4 in one category after 100 or 200 observations, could the 95% confidence interval be from 0-8 or?

How much better are 200 'samples' than 100 samples?

 

Is there a way to calculate this interval? Are there tables for this?

 

thank you

Answer 1

Yes there are ways to calculate this. Your set up is basically a histogram where the probability density function of each category is f(x) = (number of points in category)/(total number of points in sample * width of category).

 

E(X) = sum [all x] x f(x)

V(X) = ( sum [all x] x² ) - E(X)2

95% confidence interval = E(X) +/- 1.96 sqrt(V(X)/n)

 

Increasing the number of samples helps increasing the accuracy of the confidence interval.