My statistics class at high school level taught the following:

The number of samples you need is very difficult to calculate correctly, requiring deep analysis of standard deviations and variances.

But surprisingly, you can simply know you've reached large number status when over 10 items exist in each category.

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Ex: when doing a heads vs tails coin flip experiment, you likely have a large number once you have over 10 heads and over 10 tails. No matter how biased the coin is.

Or in this 'Lotto ticket' example, you have a large number of samples after gathering enough data to find over 10 Jackpot winners.

The right way to do a carbon tax is to refund 100% of the money to the population. Everyone gets a check every month for the entire amount collected, divided by the number of citizens. This way it costs you nothing unless you emit more carbon than the average person, and you can even come out ahead if you emit less. On top of that, it ends up being a net transfer from corporations to individuals, because corporations still pay the tax but only individuals get the checks.

It would also be a very informative trial run for a UBI (though in this case the amount would be smaller).

The "problem" with this is strictly politics: a) It would actually work, so the fossil fuel energy companies hate it; b) There is no opportunity for graft because the money is distributed to everyone and not just the politically connected, so there is no special interest lobby trying to make it happen.