Unit 5.5: Distributions of Differences Between Sample Means - Flashcards

Distribution of Difference Between Sample Means

When comparing two independent groups, we analyze the difference between their sample means (x̄₁ - x̄₂). Formula: μ(x̄₁-x̄₂) = μ₁ - μ₂

Standard Error of the Difference

Measures the variability of the difference between sample means. Formula: SE(x̄₁-x̄₂) = √(s₁²/n₁ + s₂²/n₂) where s₁, s₂ are sample standard deviations and n₁, n₂ are sample sizes.

Degrees of Freedom (Conservative Approach)

For t-procedures with two samples, use the conservative approach: df = smaller of (n₁ - 1) and (n₂ - 1)

The margin of error accounts for sampling variability in estimating the difference. Formula: E = t* × SE(x̄₁-x̄₂) where t* is the critical value from t-distribution based on confidence level and df

Confidence Interval Formula

A confidence interval estimates the range for the true difference between population means. Formula: (x̄₁ - x̄₂) ± E or (x̄₁ - x̄₂) ± t* × SE(x̄₁-x̄₂)