This free hypothesis test calculator works out the test statistic, p-value, critical value and a plain-English reject or fail-to-reject decision for a one-sample z test, one-sample t test (summary stats or raw data), one-proportion z test, two-sample t test (Welch or pooled), two-proportion z test and paired t test. Choose a two-tailed, left-tailed or right-tailed alternative and any significance level α, then read the shaded rejection region, full step-by-step working and the exact TI-84 keystrokes for Z-Test, T-Test, 1-PropZTest, 2-SampTTest and 2-PropZTest. Already have a z or t score? The P-value from z / t tab works as a quick p-value calculator.
Contents
How to Use the Hypothesis Test Calculator
- Pick the test. 1-sample t, 1-sample z, 1 proportion, 2-sample t, 2 proportions, paired t, or p-value from a statistic you already have.
- Enter your numbers. Type summary statistics (mean, standard deviation, n) or paste raw data, plus the null value such as μ₀ or p₀.
- Choose H₁ and α. Two-tailed (≠), left-tailed (<) or right-tailed (>), and a significance level such as 0.05.
- Read the result. You get the p-value, test statistic, degrees of freedom, critical value, the decision and a sentence you can put in a report. Use Copy share link to save or send your exact inputs.
Which Hypothesis Test Should I Use?
| Situation | Test | TI-84 menu |
|---|---|---|
| One mean, σ unknown (usual case) | One-sample t test | 2:T-Test |
| One mean, population σ given | One-sample z test | 1:Z-Test |
| One proportion vs a claimed p₀ | One-proportion z test | 5:1-PropZTest |
| Two independent means | Two-sample t test (Welch or pooled) | 4:2-SampTTest |
| Two independent proportions | Two-proportion z test | 6:2-PropZTest |
| Same subjects measured twice (before/after) | Paired t test | 2:T-Test on L1 − L2 |
Hypothesis Test Formulas
- One-sample z: z = (x̄ − μ₀) / (σ/√n)
- One-sample t: t = (x̄ − μ₀) / (s/√n), df = n − 1
- One proportion: z = (p̂ − p₀) / √(p₀(1 − p₀)/n)
- Two-sample t (Welch): t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂), Welch–Satterthwaite df. Pooled: uses sₚ and df = n₁ + n₂ − 2
- Two proportions: z = (p̂₁ − p̂₂) / √(p̂(1 − p̂)(1/n₁ + 1/n₂)) with pooled p̂ = (x₁ + x₂)/(n₁ + n₂)
- Paired t: t = d̄ / (s_d/√n) on the differences d = before − after, df = n − 1
Worked example: a sample of n = 30 has mean 52.3 and s = 6.1. Test H₀: μ = 50 against H₁: μ ≠ 50 at α = 0.05. SE = 6.1/√30 = 1.1137, so t = 2.3/1.1137 = 2.0652 with df = 29. The two-tailed p-value is 0.0479, which is below 0.05, so we reject H₀. The critical values are ±2.0452 and 2.0652 is just beyond them, which agrees.
How to Find a P-Value from z or t
The p-value is the area under the curve beyond your test statistic, assuming H₀ is true.
- Right-tailed: p = P(Z ≥ z) or P(T ≥ t)
- Left-tailed: p = P(Z ≤ z) or P(T ≤ t)
- Two-tailed: p = 2 × P(Z ≥ |z|) or 2 × P(T ≥ |t|)
For example, z = 2.1 gives a two-tailed p-value of 0.0357, and t = 2.1 with df = 24 gives 0.0464. On a TI-84 use normalcdf(2.1, 1E99, 0, 1) or tcdf(2.1, 1E99, 24) and double it for a two-tailed test. For more on normal-curve areas, see our normal distribution calculator and z-score calculator.
Critical Values for Common Significance Levels
| α | z (one-tailed) | z (two-tailed) | t, df = 10 (two-tailed) | t, df = 30 (two-tailed) |
|---|---|---|---|---|
| 0.10 | 1.2816 | ±1.6449 | ±1.8125 | ±1.6973 |
| 0.05 | 1.6449 | ±1.9600 | ±2.2281 | ±2.0423 |
| 0.01 | 2.3263 | ±2.5758 | ±3.1693 | ±2.7500 |
| 0.001 | 3.0902 | ±3.2905 | ±4.5869 | ±3.6460 |
How to Do a Hypothesis Test on a TI-84
- Press STAT, then the right arrow twice to open TESTS.
- Choose 1:Z-Test, 2:T-Test, 4:2-SampTTest, 5:1-PropZTest or 6:2-PropZTest.
- Set Inpt to Stats to type x̄, Sx and n, or Data if your values are in L1 (and L2).
- Enter μ₀ or p₀, pick ≠, < or > for the alternative, highlight Calculate and press ENTER. Draw shows the shaded curve.
For a paired test, store L1 − L2 in L3 and run T-Test on L3 with μ₀ = 0. The calculator above writes these steps out with your own numbers and shows the expected screen. Practise on our TI-84 Plus CE calculator online.
Reject or Fail to Reject the Null Hypothesis
If the p-value ≤ α, reject H₀: the data would be unusual if H₀ were true, so there is evidence for H₁. If the p-value > α, fail to reject H₀: the data are consistent with H₀. Failing to reject is not proof that H₀ is true, only that the sample was not strong enough evidence against it. The critical-value method always gives the same answer: reject when the statistic falls in the shaded rejection region.
Hypothesis Tests and Confidence Intervals
A two-tailed test at α = 0.05 matches a 95% confidence interval: you reject H₀: μ = μ₀ exactly when μ₀ is outside the interval. Use our confidence interval calculator to see how big the effect might be, not just whether it is significant. To get s from raw data first, use the standard deviation calculator.
Why This Hypothesis Test Calculator Is Different
- Seven tools in one: z, t (summary or raw data), one proportion, two-sample t (Welch or pooled, summary or raw data), two proportions, paired t, and p-value from a z or t score.
- Exact p-values and critical values for any degrees of freedom, including decimal Welch df, checked against statistical software on thousands of cases.
- TI-84 keystrokes for Z-Test, T-Test, 1-PropZTest, 2-SampTTest and 2-PropZTest with your own numbers, plus the expected screen.
- A shaded curve showing the rejection region and the p-value area, step-by-step working and a plain-English conclusion.
- Share links, dark mode and a layout that works on phones. See all our tools on the math and statistics calculators page.
Hypothesis Test Calculator FAQ
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