Statistics › Section J · Hypothesis testing with two samples › Topic J.3
Two means with known standard deviations
When both populations' spreads are known from specifications or long calibration - rare, but real - the two-mean comparison runs on the standard normal instead of t. The structure is the two-sample t test's, with every estimated s replaced by a known σ.
In this topic
- The rare clean case
- The known-sigma z statistic
- Worked example: two laboratories
- Worked example: the companion interval
- Conditions: the same, plus honesty about σ
- Why this case matters less every year
- Choosing the comparison test
- Common mistakes to avoid
- Key takeaways
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