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:
- Null hypothesis (H₀): assumes no effect or no difference
- Alternative hypothesis (H₁): represents the claim being tested
Steps of hypothesis testing
- State the null and alternative hypotheses
- Choose a significance level (α)
- Compute the test statistic (Z or t)
- Determine the critical value or p-value
- 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.
t = (x̄ − μ) / (s / √n)
Example
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.