Hypothesis test
Hypothesis test is a formal procedure that uses sample evidence to decide between a null hypothesis, assumed true by default, and an alternative hypothesis, the claim under investigation.
Also known ashypothesis testing
FrameworkHypothesis testing
See it move
A five-rung ladder lays out the hypothesis-testing procedure in a fixed sequence. The first rung states H₀ (the null, or default, claim) and H₁ (the alternative being established); the second sets the significance level α, typically 0.05, which is the tolerated false-positive rate. The third rung computes the test statistic — for example t = (x̄ − μ₀) ÷ SE — to standardise the sample result; the fourth finds the p-value as the tail area beyond that statistic under H₀; and the fifth delivers the decision: reject H₀ if p-value ≤ α, otherwise fail to reject.
The formula
Variables
- Sample mean
- Hypothesised population mean under H₀
- Sample standard deviation
- Sample size
- Test statistic; compared with t-critical at n − 1 degrees of freedom
One-sample t-test for a population mean. Reject H₀ when |t| exceeds the two-tailed critical value at the chosen significance level α.
Check yourself
A researcher tests whether the mean invoice processing time at a logistics company differs from the claimed five minutes. She obtains a p-value of 0.031 from a two-tailed t-test and uses a significance level of 5%. Which conclusion is correct?