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/n​xˉ−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

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