🧪 Hypothesis Testing

Last Updated: Jan 2026

Hypothesis Testing is a statistical method used to make decisions about a population using sample data.

We test an assumption (hypothesis) and decide whether there is enough evidence to:

  • Accept it, or
  • Reject it

🗣 Hinglish Tip: Hypothesis testing = ek claim ko data ke through prove ya disprove karna

Used when we want to:

  • Compare values
  • Check claims
  • Validate assumptions
  • Make decisions with confidence

Real-World Use Cases

  • Medicine → Is new drug effective?
  • Manufacturing → Is defect rate acceptable?
  • Business → Did sales increase after campaign?
  • ML / Data Science → Model performance comparison

Basic Terminology

  • Population → Entire data
  • Sample → Part of population
  • Test Statistic → Value calculated from sample
  • Significance Level (α) → Probability of rejecting true hypothesis (Common: 0.05)

Symbols Use in Hypothesis Testing:

  • H0 = Null Hypothesis/default assumption
  • H1 = Alternative Hypothesis
  • α = Significance Level
  • p-value/critical value = Probability of rejecting true hypothesis

Types of Hypothesis

Every hypothesis test has two hypotheses:

Null Hypothesis (H₀)

  • Default assumption
  • States no effect or no difference

Examples:

H₀: μ = 50
H₀: p = 0.4

🗣 Hinglish Tip: Null hypothesis = kuch bhi change nahi hua

Alternative Hypothesis (H₁ or Hₐ)

  • Opposite of null hypothesis
  • Indicates effect or difference

Examples:

H₁: μ ≠ 50
H₁: μ > 50
H₁: μ < 50

Types of Alternative Hypothesis (Based on Direction)

Two-Tailed Test

  • Tests both sides
  • Checks for any difference
H₀: μ = μ₀
H₁: μ ≠ μ₀

Use case:

  • Quality control
  • Equality check

Right-Tailed Test

  • Tests greater than
  • Focus on right side
H₀: μ ≤ μ₀
H₁: μ > μ₀

Use case:

  • Performance improvement
  • Sales increase

Left-Tailed Test

  • Tests less than
  • Focus on left side
H₀: μ ≥ μ₀
H₁: μ < μ₀

Use case:

  • Defect reduction
  • Cost decrease

Types of Hypothesis Testing (Based on Data & Condition)

Z-Test

Used when:

  • Sample size n ≥ 30
  • Population standard deviation (σ) known
  • Data is normal or CLT applies

Use case:

  • Large sample testing

t-Test

Used when:

  • Sample size n < 30
  • Population standard deviation unknown

Types:

  • One-sample t-test
  • Two-sample t-test
  • Paired t-test

Use case:

  • Small samples

Chi-Square Test (χ²)

Used for:

  • Categorical data
  • Independence testing
  • Goodness of fit

Use case:

  • Gender vs preference
  • Survey analysis

ANOVA (F-Test)

Used to:

  • Compare more than two means

Use case:

  • Multiple group comparison

Hypothesis Testing Workflow

  1. State hypotheses (H₀ & H₁)
  2. Choose significance level (α)
  3. Select appropriate test
  4. Compute test statistic
  5. Find p-value or critical value
  6. Make decision (Reject or Fail to Reject H₀)

Decision Rule

  • If p-value ≤ α → Reject H₀
  • If p-value > α → Fail to reject H₀

🗣 Hinglish Tip: Chhota p-value = strong evidence against H₀

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