Hypothesis Testing: Types, Steps & Statistical Decisions

What is Hypothesis Testing?

Hypothesis testing is a statistical method used to make decisions or inferences about a population based on sample data. It helps researchers determine whether a claim (hypothesis) about a population parameter is supported by evidence or should be rejected.

Key Definitions

• Null Hypothesis (H₀): The default assumption (usually "no effect" or "no difference"). Example: "The new marketing strategy does not increase sales."
• Alternative Hypothesis (H₁ or Ha): The claim we want to test. Example: "The new marketing strategy increases sales."
• Test Statistic: A standardized value (e.g., z-score, t-score) calculated from sample data to compare against a critical value.
• p-value: The probability of observing the test statistic (or more extreme) if H₀ is true. A low p-value (typically ≤ 0.05) suggests rejecting H₀.
• Significance Level (α): The threshold probability (e.g., 5%) for rejecting H₀. Common choices: 0.01, 0.05, 0.10.

Types of Hypothesis Tests

Hypothesis tests are classified based on:

1. Number of Tails:
   • One-tailed (one-sided): Tests for an effect in one direction (e.g., "sales increase").
   • Two-tailed (two-sided): Tests for any effect (e.g., "sales differ" from baseline).
2. Population Parameters Tested:
   • Mean (t-test, z-test): For continuous data (e.g., average income, customer satisfaction scores).
   • Proportion (z-test): For categorical data (e.g., % of voters supporting a candidate).
   • Variance (Chi-square test): For dispersion in data (e.g., consistency of product quality).
3. Sample Size & Distribution:
   • Z-test: For large samples (n > 30) or known population variance.
   • t-test: For small samples (n ≤ 30) or unknown variance.
   • Chi-square test: For categorical data or testing goodness-of-fit.

Steps in Hypothesis Testing

flowchart TD
    A["1. State Hypotheses"] --> B["2. Choose Significance Level (α)"]
    B --> C["3. Select Test Statistic"]
    C --> D["4. Collect & Prepare Data"]
    D --> E["5. Calculate Test Statistic"]
    E --> F["6. Determine Critical Value or p-value"]
    F --> G["7. Make Decision: Reject or Fail to Reject H₀"]
    G --> H["8. Draw Conclusion"]

Worked Example: Daraz’s Delivery Time Hypothesis

Scenario: Daraz claims its new logistics system reduces delivery time from 5 days to ≤4 days (95% confidence).

• H₀: μ ≥ 5 days (no improvement).
• H₁: μ < 5 days (improvement).
• Test: One-tailed t-test (small sample, unknown variance).
• Data: Sample of 25 orders shows mean = 4.2 days, s = 0.8 days.
• Calculation:
  • t = (4.2 – 5) / (0.8 / √25) = –2.5.
  • Critical t-value (α = 0.05, df = 24) = –1.711.
• Decision: Since –2.5 < –1.711, reject H₀.
• Conclusion: Daraz’s claim is supported (p < 0.05).

Type I and Type II Errors

Trade-off: Reducing α (e.g., from 0.05 to 0.01) increases β (harder to detect true effects).

Choosing the Right Test

mindmap
  root((Hypothesis Test Selection))
    --- Data Type
      --- Continuous: Mean (t-test, z-test)
      --- Categorical: Proportion (z-test), Chi-square
    --- Sample Size
      --- Large (n > 30): z-test
      --- Small (n ≤ 30): t-test
    --- Population Variance
      --- Known: z-test
      --- Unknown: t-test
    --- Test Direction
      --- One-tailed: Directional claim (e.g., "increase")
      --- Two-tailed: Non-directional claim (e.g., "difference")

In the Real World

1. Nabil Bank’s Loan Approval:

   • Idea: Hypothesis testing for credit risk.
   • How: Tests whether applicants with scores >700 have a default rate ≤5% (H₀: p ≥ 0.05). If rejected, stricter criteria are applied.

2. Pathao’s Driver Earnings:

   • Idea: Comparing mean earnings before/after a surge pricing algorithm.
   • How: Paired t-test to check if earnings increased significantly (H₁: μ₁ > μ₂).

3. NEPSE Stock Returns:

   • Idea: Testing if a new trading strategy outperforms the market.
   • How: Two-tailed t-test on monthly returns (H₁: μ ≠ market return).

Common Statistical Tests in Business

Exam Tip

1. Always state H₀ and H₁ clearly—examiners check for logical consistency.
2. Show calculations step-by-step (e.g., t-score formula, p-value lookup).
3. Interpret results in business terms:
   • "Reject H₀" → "The evidence supports the claim."
   • "Fail to reject H₀" → "Insufficient evidence to support the claim."
4. Common pitfalls:
   • Confusing one-tailed vs. two-tailed tests.
   • Misinterpreting p-values (e.g., p = 0.06 ≠ "significant" at α = 0.05).
5. Practice with real data: Use TU/PU past papers (e.g., 2022 PU question on testing mean salary differences).