T-Score Calculator
t = (x̄ − μ₀) / (s/√n) — for testing a sample mean against a hypothesized population mean.
Result
t-score
2.0000
df = 24.
- Standard error (s/√n)1.0000
- Difference (x̄ − μ)2.0000
- Degrees of freedom24
- |t| > 2 ?No
Step-by-step
- Standard error = s/√n = 5/√25 = 1.0000.
- t = (102 − 100) / 1.0000 = 2.0000.
- Compare to t-table at df = 24 for two-tailed α = 0.05 (~2.06 for df = 25).
How to use this calculator
- Enter sample mean, hypothesized population mean, sample SD, and sample size.
- Read the t-statistic and compare to a t-table at the right df.
About this calculator
t-score is to t-distribution what z-score is to normal — but t accounts for the additional uncertainty when σ is estimated from a small sample. Use t when σ is unknown and sample size is < 30; use z for large samples or known σ.
Frequently asked
Use t when σ is unknown (estimated from sample) and n < 30. For large n, t and z converge — both work.
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