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Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions based on sample data.

What is hypothesis testing?

Hypothesis testing is a formal statistical procedure used to determine whether there is enough evidence in a sample to support a specific claim about a population parameter.

Null and alternative hypotheses

Hypothesis testing begins with two competing statements:

Steps of hypothesis testing

  1. State the null and alternative hypotheses
  2. Choose a significance level (α)
  3. Compute the test statistic (Z or t)
  4. Determine the critical value or p-value
  5. Make a decision: reject or fail to reject H₀

Test statistic

The test statistic measures how far the sample result deviates from what is expected under the null hypothesis.

Z = (x̄ − μ) / (σ / √n)
t = (x̄ − μ) / (s / √n)

Example

A company claims the average delivery time is 50 minutes.
Sample mean = 52, standard deviation = 8, sample size = 64.

Z = 2.00 → Reject H₀ at α = 0.05

How to interpret the result

Rejecting the null hypothesis means there is sufficient statistical evidence to support the alternative claim. Failing to reject H₀ does not prove it is true — only that evidence is insufficient.

Why is hypothesis testing important?

Hypothesis testing is fundamental in statistics, data science, research, quality control, and decision-making under uncertainty.