Agricultural Economics- ICAR JRF/SRF 2024

• Type I Error and Level of Significance:
• In statistical hypothesis testing, the Level of Significance (denoted by $\alpha$) is defined as the maximum tolerable probability of committing a Type I error:

• It represents the rejection probability of the Null Hypothesis when it is genuinely true. Common levels of significance are $5\%$ (0.05) and $1\%$ (0.01).
• Distractors:
• Level of Confidence: Given by $(1 - \alpha)$, representing the probability of accepting $H_0$ when it is true.
• Power of the Test: Given by $(1 - \beta)$, the probability of rejecting $H_0$ when $H_0$ is false.

Correct option: (2) Level of Significance

• Diagnostic Tests for Heteroscedasticity vs. Autocorrelation:
• Durbin-Watson Test: Used exclusively to detect the presence of first-order autocorrelation (serial correlation) among regression error residuals ($u_t = \rho u_{t-1} + \varepsilon_t$), not heteroscedasticity.
• Standard Tests for Heteroscedasticity:
• Goldfeld-Quandt Test: Tests whether error variances differ across two sorted subsamples.
• Glejser Test: Regresses absolute residuals $|e_i|$ on explanatory variables.
• Park Test: Regresses logarithm of squared residuals $\ln(e_i^2)$ on $\ln(X_i)$.
• White's General Test & Breusch-Pagan-Godfrey Test.

Correct option: (4) Durbin Watson Test

• Directional Hypothesis Testing: One-Tailed Tests:
• hypothesis test testing $H_0: \theta = 5$ against the alternative hypothesis $H_1: \theta \lt 5$ is a Left-Tailed Test.
• The inequality symbol in the alternative hypothesis ($\lt $) points strictly to the left, concentrating the entire rejection region (critical region of size $\alpha$) in the lower (left) tail of the sampling distribution.
• Distractors:
• Right-Tailed Test: Alternative hypothesis has the form $H_1: \theta \gt 5$.
• Two-Tailed Test: Alternative hypothesis has the form $H_1: \theta \neq 5$.

Correct option: (2) Left tailed