t-Test Calculator
Statistics, Inference
Intro: Runs one-sample or two-sample t-tests and reports t-statistic, degrees of freedom, p-value, and a verbal conclusion.
Worked example
- A sample of n=25 has mean x̄=12.4 and s=3.1. Test H₀: μ=10 vs H₁: μ>10 at α=0.05.
- We perform a one-sample right-tailed t-test with $H_0: \mu = 10$ and $H_1: \mu > 10$.
- The test statistic for a one-sample t-test is $t=\dfrac{\bar{x}-\mu_0}{s/\sqrt{n}}$.
- Substitute $\bar{x}=12.4$, $\mu_0=10$, $s=3.1$, and $n=25$.
- Compute the numerator: $\bar{x}-\mu_0 = 12.4-10 = 2.4$.
- Compute the standard error: $s/\sqrt{n} = 3.1/\sqrt{25} = 3.1/5 = 0.62$.
- Now $t = 2.4 / 0.62 \approx 3.871$.
- Degrees of freedom are $df = n-1 = 25-1 = 24$.
- Using the t-distribution with df = 24, the right-tailed p-value for t ≈ 3.871 is about $p \approx 0.0004$ (very small).
- Since $p < 0.05$, we reject $H_0$ and conclude there is significant evidence that $\mu > 10$.
- Answer: $\boxed{t \approx 3.87,\; df=24,\; p \approx 0.0004 \Rightarrow \text{reject }H_0.}$
FAQs
Does this assume equal variances for two-sample tests?
By default we can use the unequal-variances Welch t-test, but an equal-variances option can be added if needed.
Why choose MathGPT?
- Get clear, step-by-step solutions that explain the “why,” not just the answer.
- See the rules used at each step (power, product, quotient, chain, and more).
- Optional animated walk-throughs to make tricky ideas click faster.
- Clean LaTeX rendering for notes, homework, and study guides.
How this calculator works
- Type or paste your function (LaTeX like
\sin,\lnworks too). - Press Generate a practice question button to generate the derivative and the full reasoning.
- Review each step to understand which rule was applied and why.
- Practice with similar problems to lock in the method.