Estimating from Small samples

 A common example we touched often on in consulting within the enterprise.  Though the new methods have made this ever more crucial.

Estimating from small random samples— Understanding the underlying probabilities at play!
By Vinodh Kumar Ravindranath in TowardDataScience

Suppose you are asked to prove how useful a feature could be. Lets say you have to estimate the number of users on your platform that would benefit from a certain feature or change on your product.

Sampling from a population

You pick a “random uniform sample” of 1% of the users. They are now exposed to the feature. In a week’s time, you have figured that 1000 users are actively using the feature.

Now the time comes for you to get the feature to be rolled out to the entire traffic. You now have to answer the question from the management on how many users could potentially benefit from this feature.

And you are going to say 100,000 because on a 1% random uniform sample, 1000 liked it. Sounds reasonable?

I am going to stop right here and ask this flip question.

Suppose there were really 100,000 people who would like this feature and benefit from it. What is the chance (or probability) that you would get this number of 1000 from this 1% sample?

I think this is where people tend to get a lot confused. I have heard answers saying that they are 100% sure. And the reasoning would be that this was a perfectly random sample, or random uniform sample, to be precise! ....  '