When would you use a t-test instead of a z-test for a mean?
PICTURE THIS: 1, 2, 2, 8
Simple meaning
Use a t-test when the variance is estimated from the sample, especially with modest n, because the t distribution has heavier tails.
WHY — Hypothesis Testing instead of guessing?
Why interviewers care about Hypothesis Testing:
on Hypothesis Testing.
the situation, the default choice, and one exception - that reads as experience.
Name the idea, why it exists, then one short example.
End with when you use it and one common pitfall.
STEPS — What happens step by step?
Before you speak the answer, walk the interviewer through these steps:
- 1Use a t-test when
the variance is estimated from the sample, especially with modest n, because the t distribution has heavier tails.
- 2A z-test assumes a
known standard deviation or a sample large enough that the estimate is treated as known.
- 3For binary conversion rates,
a proportion test or bootstrap is often more natural than a raw-mean z-test.
- 4Give an example
One tiny concrete case you can say aloud.
- 5Common mistake
What juniors usually get wrong.
- 6Close
When you pick this over the alternative.
EXAMPLE — See it in action
Here's a short line you can speak, broken into clear beats:
Note: Adapt this scaffold to your own project — keep it under 60–90 seconds.
Key takeaway
Use a t-test when the variance is estimated from the sample, especially with modest n, because the t distribution has heavier tails. A z-test assumes a known standard deviation or a sample large enough that the estimate is treated as known.