AI Statistics Solver›Hypothesis Testing Solver

Free Hypothesis Testing Solver

Hypothesis Testing Solver
with Full Step-by-Step Output

Enter your sample data, choose a test type, and get a complete worked solution — null hypothesis, test statistic, p-value, and conclusion — all explained in plain English.

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Hypothesis Testing Solver

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Select Test Type

Sample Mean (x̄)

Hypothesized Mean (μ₀)

Std Deviation (s)

Sample Size (n)

Significance Level (α)

Tail

Or paste the full problem (optional)

Setting up null and alternative hypotheses…
Calculating test statistic…
Finding p-value and critical value…
Writing conclusion…

Test Output

H₀: μ = 75 | H₁: μ ≠ 75 (two-tailed)
Test statistic: t = (78 − 75) / (10 / √25) = 1.500
Degrees of freedom: df = 25 − 1 = 24

Critical value: t* = ±2.064 (α=0.05, two-tailed, df=24) p-value: p = 0.1473 Decision: |t| = 1.500 < t* = 2.064 and p = 0.1473 > α = 0.05 → FAIL TO REJECT the null hypothesis Conclusion: Insufficient evidence at the 5% level to conclude the population mean differs from 75. Effect size (Cohen’s d): d = 3/10 = 0.30 (small-to-medium)

Full test result is ready

See the p-value, critical value, decision, and plain-English conclusion

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How It Works

Three steps to a complete test

The solver handles every stage — from stating hypotheses to writing the conclusion.

Enter your data

Fill in sample statistics or paste the full problem. Choose test type and significance level.

Solver runs the test

Calculates test statistic, degrees of freedom, critical value, and p-value using the correct formula.

Read the conclusion

Get a plain-English decision — reject or fail to reject H₀ — plus an effect size and interpretation.

What’s Included

More than just a t-test calculator

Every output includes the full reasoning — not just the final number.

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6 test types

One-sample t, two-sample t, paired t, z-test for proportions, chi-square, and F-test all supported.

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Full hypothesis setup

H₀ and H₁ stated clearly before every calculation, so you see the test logic from the start.

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p-value + critical value

Both approaches shown — reject based on p-value or critical region, whichever your course requires.

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Plain-English conclusion

The final decision is written out as a sentence you can use directly in a report or assignment.

What Is a Hypothesis Testing Solver?

A hypothesis testing solver automates the mechanical steps of a statistical hypothesis test — setting up the null and alternative hypotheses, computing the test statistic, finding the p-value, and writing a conclusion. For students and researchers, this means seeing the full logic of the test without having to look up t-tables or memorize formulas.

Hypothesis testing appears in psychology research methods, biology lab reports, economics papers, and business analytics courses. The challenge for most students isn’t understanding what a test is for — it’s executing all the steps correctly without making arithmetic errors or choosing the wrong formula.

Types of Hypothesis Tests Supported

One-Sample t-Test

Used when comparing a sample mean to a known or hypothesized population mean. Requires sample mean, standard deviation, sample size, and the hypothesized value. This is the most common test in introductory statistics courses.

Two-Sample t-Test

Compares the means of two independent groups — for example, test scores between two classes, or blood pressure between a treatment and control group.

Paired t-Test

Used when the two sets of observations are related, such as before-and-after measurements on the same subjects. The test operates on the differences between paired values.

z-Test for Proportions

Tests whether a sample proportion differs from a hypothesized population proportion. Common in survey analysis, quality control, and election polling contexts.

Chi-Square Test

Tests whether observed frequencies differ from expected (goodness-of-fit) or whether two categorical variables are independent. Widely used in social science and biology research.

How to Read a Hypothesis Test Result

Every hypothesis test produces a test statistic and a p-value. The test statistic measures how far the sample result is from what the null hypothesis predicts. If the p-value is less than α, reject H₀. If greater, fail to reject. Failing to reject does not mean the null is true — it means the data didn’t provide enough evidence to rule it out. The solver shows both the p-value and critical value approaches, since either may be required depending on your course.

Common Mistakes in Hypothesis Testing

Confusing one-tailed and two-tailed tests — the direction of H₁ determines which tail to use
Wrong degrees of freedom — df = n−1 for one-sample t; formula differs for two-sample
Interpreting “fail to reject” as “accept H₀” — they are not the same
Ignoring effect size — a significant result with tiny effect may not be practically meaningful

FAQ

Common questions

A two-tailed test checks whether the parameter differs in either direction. A one-tailed test checks only one direction. The choice depends on the wording of the alternative hypothesis.

It means the data didn’t provide sufficient evidence to conclude H₀ is false. It does not mean H₀ is true — only that you couldn’t rule it out at the chosen significance level.

Yes. Select “Two-Sample t-Test” from the options. You’ll need the mean, standard deviation, and sample size for both groups.

α = 0.05 is the standard in most undergraduate courses. Medical research often uses α = 0.01. Use whatever your assignment specifies.

Yes. The full solution includes both the p-value comparison (p vs α) and the critical value comparison (test statistic vs critical value). Both lead to the same decision.

Get the full test result — every step explained.

No more guessing at p-values or critical values. Run your hypothesis test now.