Answer: n-2.

## Explanation For a hypothesis test concerning the correlation coefficient between two normally distributed variables, the degrees of freedom is calculated as **n-2**, where n is the sample size. ### Why n-2? 1. **Statistical reasoning**: When testing the correlation coefficient (Pearson's r), we use a t-test with degrees of freedom = n-2. 2. **Mathematical basis**: The correlation coefficient is estimated from the data, and we lose 2 degrees of freedom because we need to estimate two parameters - the means of both variables. 3. **Test statistic formula**: The test statistic for testing the correlation coefficient ρ is: $$t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$$ where r is the sample correlation coefficient and the degrees of freedom is n-2. ### Comparison with other options: - **Option B (n-1)**: This is typically used for one-sample t-tests or tests involving a single variable. - **Option C (2n-2)**: This would be relevant for comparing means of two independent samples (two-sample t-test with equal variances). ### Practical application: In hypothesis testing for correlation: - Null hypothesis: H₀: ρ = 0 (no correlation) - Alternative hypothesis: H₁: ρ ≠ 0 (correlation exists) - Degrees of freedom: df = n-2 - Critical t-value: t-critical with df = n-2 at chosen significance level This is a fundamental concept in regression and correlation analysis in statistics.

Author: LeetQuiz .