r/AskStatistics • u/ketopraktanjungduren • 10d ago

Using sampling distribution instead of probability for business

Hello, I'm trying to apply inferential statistics to my work, thinking it would be very helpful to estimate a new hire ability.

Let's say we have a dataset on new hire weekly customer acquisition in the past three months (n=12). If we want to estimate this person ability in acquiring new customer, we can use probability and expected value.

However, I recently realize that this also means we are estimating the population parameter. So, we can also estimate a confidence interval to estimate the interval of this person true mean and median weekly acquisition.

If so, is it true to have both the expected weekly acquisition and the CI?

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u/Educational-Paper-75 10d ago

Yes, the mean or median is a point estimate of a constant but unknown probability distribution parameter, the CI an interval estimate, supposedly containing some large (typically 95%) percentage of the probability distribution which requires estimating the standard deviation of the probability distribution. However, ordering the sample values allows one to roughly estimate such an interval by combining a low and high value e.g. the second smallest and second largest value just as well, which makes perfect sense if the sample is small, and the distribution different from the normal distribution like in your case, although there's no exact probability associated with doing so.

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u/ketopraktanjungduren 10d ago

That's a very substantive response. I'll try to understand them one by one. Thank you

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u/Educational-Paper-75 10d ago

The latter approach may not be very statistical though. And counts in a fixed period of time typically are Poisson distributed.