QB_PH_121: Bose-Einstein and Fermi-Dirac statistics

In hypothesis testing, the probability of rejecting the null hypothesis $H_0$ when it is actually true is known as:

Correct Answer

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Governing Concept & Domain Context:** * This question evaluates **Fundamentals of Bose-Einstein and Fermi-Dirac statistics** under *Bose-Einstein and Fermi-Dirac statistics* in GATE PH. 2. **Stage 2: Mathematical Derivation:** * By definition of Neyman-Pearson statistical hypothesis testing: $\alpha = P(\text{Reject } H_0 \mid H_0 \text{ is True})$. Option A is correct. 3. **Stage 3: Distractor Elimination Forensics:** * The evaluated correct answer is derived using standard physical equations. * Distractor values correspond to typical unit conversion omissions or inverted formulas. 4. **Stage 4: Common Student Trap:** * *Trap:* Confusing Type I error with Type II error. *Reference: R.K. Pathria, Paul D. Beale, Statistical Mechanics (Academic Press).*