Exercise 2: "We Computed the Mean, So We Already Know the Real Answer" — Possible Solution
====================================================================================

WHAT'S WRONG WITH THIS REASONING
------------------------------
The colleague is conflating two genuinely different things this
chapter's own descriptive-vs-inferential distinction keeps separate:
computing a mean FROM the data actually collected (a descriptive
statistic, Fundamentals' own Chapter 9 territory) versus knowing the
TRUE value across the entire population the data was only a sample
of (an inferential claim, this course's own territory).

A computed mean is exact and correct - but only as a description of
the specific data points that happened to be collected. It says
nothing on its own about how close that number is likely to be to the
true population value, or how much it might have differed if a
different sample had been collected instead. Two different samples
drawn from the exact same underlying reality will almost always
produce two different means - the "real answer" the colleague
believes they already have is really just one specific sample's own
result, not a guaranteed match to the truth.

WHAT'S MISSING: A MEASURE OF UNCERTAINTY
------------------------------
Confidence intervals exist specifically to communicate how much
uncertainty remains even after a mean has been correctly computed -
they don't replace the computed mean, they add the honest range of
values the true population mean could plausibly be, given how much
(or how little) data was actually collected. A small sample can
produce a perfectly correctly computed mean that is still quite far
from the true population value purely by chance - something the raw
mean alone gives no way to detect.

WHY THIS WORKS AS AN ANSWER
------------------------------
The explanation identifies the specific conflation the colleague is
making (a description of the sample vs. a claim about the true
population) using this chapter's own core distinction, and explains
concretely what a confidence interval adds that the mean alone cannot
provide, rather than simply asserting the colleague is wrong.