# Predicting future outcomes from samples when sample sizes and distributions are not controlled and vary

I'm very stale in my statistics and am trying to calculate my confidence around a certain mean outcome from an investment firm (I'll use lay person terms so that I am not assuming any particular type of model should be used).

For example, I have two (2) investment firms:

Firm A makes 30 portfolio investments (with 30 outcomes), and the mean return of investments is 5%. Let's say every investment has been 4% or 6% (so 15 investments returned 4% and 15 returned 6%).

Firm B makes 4 portfolio investments (with 4 outcomes), and the mean return is also 5%. They have investment returns of 4%, 4%, 6%, and 6% (so the same min, max, etc as Firm A…just far fewer observations).

Intuitively, if both Firm A and Firm B say to me that "we believe we will generate a 5% return on average for you in your portfolio"…I'm inclined to believe Firm A much more, simply because they have many more observations that I can see.

So, my question is, how do I express my confidence around a 5% estimated portfolio return for each Firm? In my example, the only returns I see are 4% and 6%…but I don't mean to suggest that the future returns can only have a binary distribution. These observations could be -100% up to +1,000% each. I just chose my individual observations of 4% and 6% so that the "curve" looks the same for each Firm.

Can I just use the simple 95% CI = 5% +/- 1.96*StDevSample/(n^.5)? Or, with my unknown distribution, is there a more "all-encompassing" formula?

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