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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

ByHoang TruongUpdated

FrameworkHypothesis testing

See it move

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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.

Where it fits
SubjectData Analysis & StatisticsCoreTopicHypothesis TestingCore

The formula

LaTeX
t=xˉμ0s/nt = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}

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

PracticeCORE

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?

Select an answer to check your understanding.
Hypothesis Test — Five-Step Procedure