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Test Configuration

Choose test type and specify your hypotheses

Test Type

Population Variance Status

Alternative Hypothesis

Significance Level (α)

Sample Data

Enter your sample statistics and null hypothesis values

Sample Mean (

\bar{x}

)

Null Hypothesis Mean (

\mu_0

)

Sample Size (n)

Sample Standard Deviation (s)

Testing Method

T-Test: Use when population variance σ² is unknown

Test Statistic: $T = \frac{\bar{X} - \mu_0}{S/\sqrt{n}} \sim t(n-1)$

Critical Values: Use t-distribution with n-1 degrees of freedom

Please fill in all required fields with valid positive numbers to perform the hypothesis test.

📊 Hypothesis Testing Theory

Understanding the statistical principles behind hypothesis testing

Type I & II Errors

Type I Error (α): Rejecting H₀ when it's true (false positive)

Significance Level: Maximum acceptable Type I error rate

Type II Error (β): Failing to reject H₀ when it's false (false negative)

Power: 1 - β, probability of correctly rejecting false H₀

P-value Interpretation

Definition: Probability of observing test statistic as extreme or more extreme, assuming H₀ is true

Decision Rule:

• P-value < α → Reject H₀

• P-value ≥ α → Fail to reject H₀

Note: P-value measures strength of evidence against H₀, not probability that H₀ is true

Test Selection

U-Test (Z-Test): Normal population, σ² known

T-Test: Normal population, σ² unknown

Chi-square Test: Test population variance

Assumptions: Random sampling, independence, normality (for small samples)

Large samples: Central Limit Theorem allows approximate normality

Common Mistakes

❌ Don't say: "Accept H₀" → Say: "Fail to reject H₀"

❌ Don't confuse: Statistical vs practical significance

❌ Don't interpret: P-value as P(H₀ is true)

✅ Do check: Assumptions before testing

✅ Do consider: Effect size and context