Statistics - Hypothesis Testing
Hypothesis testing is a systematic procedure used in statistics and data science to decide whether a claim about a population is supported by sample data or not.
What is Hypothesis testing ?
Hypothesis testing is a statistical method used to make inferences about a population based on sample data. It involves formulating two competing hypotheses and using statistical techniques to determine which one is more likely to be true.
STEP 1: State the Problem Clearly
First, identify what you want to test.
📌 Example question:
Is the average score of students equal to 70?
STEP 2: Formulate the Hypotheses
(a) Null Hypothesis (H₀)
Assumes no change / no effect
Always contains equality (=, ≤, ≥)
H₀: μ = 70
(b) Alternative Hypothesis (H₁)
Opposite of H₀
Represents what we want to prove
H₁: μ ≠ 70 (two-tailed test)
STEP 3: Choose the Significance Level (α)
Probability of rejecting a true null hypothesis
Common values:
α = 0.05 (5%)
α = 0.01 (1%)
📌 Meaning:
There is a 5% risk of making a wrong decision.
STEP 4: Select the Appropriate Test
Choose the test based on:
Sample size
Type of data
Known or unknown population variance
| Situation | Test Used |
| Large sample, known variance | Z-test |
| Small sample, unknown variance | t-test |
| Categorical data | Chi-square |
| More than two means | ANOVA |
STEP 5: Collect Sample Data
Gather data randomly from the population.
📌 Example:
Sample of 40 students’ scores.
STEP 6: Compute the Test Statistic
This value shows how far the sample result is from the assumed population value.
Examples:
Z statistic
t statistic
χ² statistic
📌 Formula (example – Z-test):
Z=xˉ−μσ/nZ = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}Z=σ/nxˉ−μ
STEP 7: Determine the p-Value
- p-value = Probability of observing the sample result assuming H₀ is true
📌 Interpretation:
Small p-value → Strong evidence against H₀
Large p-value → Weak evidence against H₀
STEP 8: Make the Decision
Decision Rule
If p-value ≤ α → Reject H₀
If p-value > α → Fail to reject H₀
📌 Example:
p-value = 0.03
α = 0.05
👉 Reject H₀
STEP 9: Draw a Statistical Conclusion
State the result in words, not symbols.
📌 Example:
“There is sufficient statistical evidence that the average score is different from 70.”
STEP 10: Interpret the Result in Context
Relate the conclusion to the real-world problem.
📌 Example:
The teaching method has a significant impact on students’ performance.
Flow Summary
1️⃣ Define the problem
2️⃣ State H₀ and H₁
3️⃣ Choose α
4️⃣ Select test
5️⃣ Collect data
6️⃣ Calculate test statistic
7️⃣ Find p-value
8️⃣ Decision (Reject / Accept H₀)
9️⃣ Conclusion
🔟 Real-world interpretation
Important Notes
“Fail to reject H₀” ≠ “Accept H₀”
Statistical significance ≠ Practical importance
Always check assumptions of the test
