Answer: 8.333; The YCS coefficient is statistically significantly different from zero

## Explanation To test the statistical significance of the YCS coefficient at the 10% significance level: 1. **Calculate the t-statistic**: - Coefficient for YCS = 0.20 - Standard error for YCS = 0.024 - t-statistic = Coefficient / Standard Error = 0.20 / 0.024 = 8.333 2. **Determine degrees of freedom**: - Sample size n = 46 - Number of independent variables (excluding intercept) = 2 (YCS and PR) - Degrees of freedom = n - k - 1 = 46 - 2 - 1 = 43 3. **Find critical t-value**: - For a two-tailed test at 10% significance level (α = 0.10) - With 43 degrees of freedom, the critical t-value ≈ 1.68 4. **Decision rule**: - Reject the null hypothesis if |t-statistic| > critical t-value - 8.333 > 1.68, so we reject the null hypothesis 5. **Conclusion**: - The YCS coefficient is statistically significantly different from zero at the 10% significance level **Note**: The text incorrectly states to test H₀: PR = 0 vs H₁: PR ≠ 0, but the question asks to test YCS, not PR. The correct hypothesis test should be: H₀: YCS coefficient = 0 vs H₁: YCS coefficient ≠ 0 The t-statistic calculation and conclusion remain correct despite this minor error in the explanation text.

Author: Nikitesh Somanthe