Frequently Asked Questions
When should I use a z-test instead of a t-test?
Only when the population standard deviation is actually known. This is uncommon. When σ is unknown, use the t-test - even for large samples, it is what software defaults to.
Why does n = 30 matter?
By n ≈ 30, the t and z distributions are essentially indistinguishable. The Central Limit Theorem makes the sampling distribution of the mean roughly normal even when raw data is not, as long as it is not extremely skewed.
What if my data is not normal and n is small?
Use a nonparametric test such as the Wilcoxon signed-rank test, sign test, or Mann-Whitney U. They make weaker assumptions and remain valid for non-normal data.
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This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.