Calculator Form
Example Data Table
| Case | Test Type | Main Inputs | Tail | Alpha | Expected Use |
|---|---|---|---|---|---|
| Mean score claim | One sample t | x̄ = 52, μ0 = 50, s = 8, n = 36 | Two tailed | 0.05 | Test whether a mean differs from a claim. |
| Conversion rate claim | One proportion z | x = 64, n = 100, p0 = 0.50 | Right tailed | 0.05 | Test whether a proportion is higher. |
| Two group comparison | Welch two sample t | x̄1 = 82, x̄2 = 78, s1 = 10, s2 = 11 | Two tailed | 0.05 | Compare means with unequal variation. |
Formula Used
Step 1: State hypotheses
H0: parameter = null value. H1 depends on the selected tail.
Step 2: Set significance level
Alpha is the maximum chosen risk for rejecting a true null hypothesis.
Step 3: Compute statistic
One mean z: z = (x̄ - μ0) / (σ / √n)
One mean t: t = (x̄ - μ0) / (s / √n)
One proportion z: z = (p̂ - p0) / √(p0(1 - p0) / n)
Two mean test: statistic = ((x̄1 - x̄2) - d0) / SE
Two proportion test: z = ((p̂1 - p̂2) - d0) / SE
Step 4: Compare evidence
Reject H0 when p value ≤ alpha. You may also use the critical rule.
Step 5: Make conclusion
The final conclusion states whether evidence supports the alternative claim.
How To Use This Calculator
- Select the test type that matches your data.
- Choose the alternative direction.
- Enter alpha and confidence level.
- Fill only the inputs needed for your selected test.
- Press Calculate to show the result above the form.
- Use CSV or PDF buttons to save the calculated report.
What Is Five Step Hypothesis Testing?
Five step hypothesis testing gives structure to a statistical decision. It starts with a claim about a population. It ends with a decision based on sample evidence. The method keeps the work clear, repeatable, and fair.
Why This Calculator Helps
This calculator supports common mean and proportion tests. It can handle one sample, two samples, known variation, unknown variation, and paired style comparisons through entered summaries. You choose the test direction. Then you enter the sample evidence, null value, sample size, and significance level. The tool returns the statistic, p value, critical region, confidence interval, and decision.
The Five Steps
The first step states the null and alternative hypotheses. The null usually represents no change, no difference, or the claimed value. The alternative represents the effect you want to test. The second step sets alpha. Alpha is the risk of rejecting a true null claim. The third step selects the correct statistic. A z test is used when conditions support normal standard errors. A t test is useful when the population standard deviation is unknown. The fourth step compares evidence. You may compare the p value with alpha, or compare the statistic with a critical value. The fifth step states the conclusion in practical words.
Reading The Output
A small p value means the sample would be unusual if the null claim were true. If the p value is less than or equal to alpha, reject the null hypothesis. If it is larger, do not reject the null hypothesis. This does not prove the null claim. It only means the sample did not give enough evidence against it.
Good Practice
Check assumptions before trusting any result. Samples should be random or representative. Observations should be independent. Proportion tests need enough expected successes and failures. Mean tests should have normal data or a large sample. Report both the p value and the effect estimate. Also review the confidence interval. It shows likely values for the tested difference. A clear conclusion should mention the context, the direction, and the strength of evidence. This makes the test useful for reports, studies, dashboards, and classroom work. Always combine statistical results with subject knowledge before making important decisions today.
FAQs
What are the five steps of hypothesis testing?
The five steps are state hypotheses, set alpha, calculate the statistic, compare evidence, and write the conclusion. This structure keeps the test clear and consistent.
When should I use a z test?
Use a z test when the standard error follows a normal model. It is common for known population standard deviation, large samples, and proportion tests with enough expected counts.
When should I use a t test?
Use a t test when testing means with unknown population standard deviation. It uses sample standard deviation and degrees of freedom to adjust uncertainty.
What does p value mean?
The p value measures how unusual the sample result is under the null hypothesis. Smaller p values give stronger evidence against the null claim.
What does alpha mean?
Alpha is the chosen significance level. It is the risk limit for rejecting a true null hypothesis. Common values are 0.10, 0.05, and 0.01.
What is a two tailed test?
A two tailed test checks for a difference in either direction. It is used when the alternative claim says the parameter is not equal to the null value.
Can this calculator prove the null hypothesis?
No. A failed rejection does not prove the null hypothesis. It means the sample did not provide enough evidence against the null at the selected alpha.
Why are assumptions important?
Assumptions protect the accuracy of the test. Random sampling, independence, normality, and expected count rules help make p values and critical values reliable.