Calculator Inputs
Example Data Table
| Test | Input values | Statistic formula | Use case |
|---|---|---|---|
| One Mean Z | x̄ = 52, μ₀ = 50, σ = 10, n = 36 | z = (x̄ - μ₀) / (σ / √n) | Known population deviation |
| One Mean T | x̄ = 52, μ₀ = 50, s = 9, n = 36 | t = (x̄ - μ₀) / (s / √n) | Unknown population deviation |
| One Proportion Z | p̂ = 0.54, p₀ = 0.50, n = 400 | z = (p̂ - p₀) / √(p₀(1 - p₀) / n) | Single sample proportion |
| Chi Square Variance | s² = 16, σ₀² = 12, n = 25 | χ² = (n - 1)s² / σ₀² | Variance claim test |
| F Variance Ratio | s₁ = 6, s₂ = 4, n₁ = 18, n₂ = 16 | F = s₁² / s₂² | Compare two variances |
Formula Used
Z mean test: z = (x̄ - μ₀) / (σ / √n)
T mean test: t = (x̄ - μ₀) / (s / √n), with df = n - 1
Z proportion test: z = (p̂ - p₀) / √(p₀(1 - p₀) / n)
Chi square variance test: χ² = (n - 1)s² / σ₀², with df = n - 1
F variance ratio test: F = s₁² / s₂², with df1 = n₁ - 1 and df2 = n₂ - 1
The calculator uses the selected tail and alpha level to estimate critical values, p value, and the hypothesis decision.
How to Use This Calculator
Choose the test type first. Then select the tail direction and significance level. Enter the required sample values for that test. Press the calculate button. The result appears above the form. Review the graph, p value, critical values, and final decision. Use the CSV or PDF button to save the report.
Test Statistic Graphing Calculator Guide
What This Calculator Does
A test statistic graphing calculator helps you connect sample data with a probability distribution. It shows where your statistic falls on the curve. It also compares that statistic with critical values. This makes hypothesis testing easier to read and explain.
Why Graphs Matter
A p value alone can feel abstract. A graph gives it context. You can see whether the statistic sits near the center, inside a tail, or beyond a rejection boundary. This visual check helps students, analysts, and researchers catch mistakes before writing conclusions.
Supported Test Types
This tool supports common statistics tests. Use the z mean test when population standard deviation is known. Use the t mean test when it is unknown. Use the proportion z test for one sample proportion. Use chi square for variance claims. Use the F test for two variance comparisons.
Understanding Tail Choices
The tail option controls the rejection region. A left tailed test checks for unusually small values. A right tailed test checks for unusually large values. A two tailed test checks both sides. Choose the tail that matches the alternative hypothesis before calculating.
Reading the Result
The calculator reports the statistic, p value, critical value, degrees of freedom, and decision. If the p value is less than or equal to alpha, the null hypothesis is rejected. Otherwise, the result fails to reject the null hypothesis. This wording avoids claiming proof.
Good Input Practice
Always check units and sample size. Standard deviations and variances must be positive. Proportions must stay between zero and one. For small samples, confirm that your course or project allows the chosen model. A calculator gives fast results, but assumptions still matter.
Saving Your Work
Use the export buttons after calculation. The CSV file is useful for spreadsheets. The PDF file is better for reports, assignments, and records. Include the formula and tail choice when sharing results. That makes your statistical conclusion easier to verify.
FAQs
What is a test statistic?
A test statistic is a standardized value from sample data. It measures how far the sample result is from the null hypothesis value.
What does the p value mean?
The p value estimates how unusual the test statistic is under the null hypothesis. Smaller values give stronger evidence against the null claim.
When should I use a z test?
Use a z test when the population standard deviation is known, or when testing one sample proportion with suitable sample conditions.
When should I use a t test?
Use a t test for a mean when the population standard deviation is unknown and the sample standard deviation is used instead.
What is a two tailed test?
A two tailed test checks both directions. It is used when the alternative hypothesis says the value is different, not just greater or smaller.
What is alpha?
Alpha is the significance level. Common choices are 0.10, 0.05, and 0.01. It sets the rejection boundary for the test.
Can this calculator prove a hypothesis?
No. Hypothesis tests give statistical evidence. They do not prove that a claim is true or false with absolute certainty.
Why are degrees of freedom shown?
Degrees of freedom shape t, chi square, and F distributions. They affect p values and critical values, especially for smaller samples.