Can you estimate a 90% CI of candyfloss sold over a month based on that information?
Not without additional assumptions, some of which are “obviously” incorrect. In particular:
If the estimates are correlated, combining estimates does not improve the CI as much as otherwise.
(In the worst case, combining estimates may not improve the CI at all!)
Consider, for instance, if your estimate of the number of candyfloss purchases over the month was based on a sample including the same shop as your other estimate.
You need to make assumptions (or have information about) the distribution, not just the extremes.
A common (and bad) assumption is that everything is a Normal distribution (or some simple transformation of a normal distribution, like log-normal).
Unfortunately, in most cases the product of two distributions is a mess. (If you want a pointer, look here.)
One notable set of exceptions is log-transformations of various distributions. (This is because in logspace the multiplication turns into a convolution, which is often a whole lot easier to calculate.)
For instance: the product of two log-normal distributions is “easy”. (Of course, then you need to with with the distributions not straight CIs). Beware correlations however.
Not without additional assumptions, some of which are “obviously” incorrect. In particular:
If the estimates are correlated, combining estimates does not improve the CI as much as otherwise.
(In the worst case, combining estimates may not improve the CI at all!)
Consider, for instance, if your estimate of the number of candyfloss purchases over the month was based on a sample including the same shop as your other estimate.
You need to make assumptions (or have information about) the distribution, not just the extremes.
A common (and bad) assumption is that everything is a Normal distribution (or some simple transformation of a normal distribution, like log-normal).
Unfortunately, in most cases the product of two distributions is a mess. (If you want a pointer, look here.)
One notable set of exceptions is log-transformations of various distributions. (This is because in logspace the multiplication turns into a convolution, which is often a whole lot easier to calculate.)
For instance: the product of two log-normal distributions is “easy”. (Of course, then you need to with with the distributions not straight CIs). Beware correlations however.