GATE 2021 ST – Question 14
A realization of n≥2 iid N(μ,σ²) observations is given,μ∈ℝ,σ>0. P:a 95% confidence interval for μ is unique when σ is known. Q:a 95% confidence interval for μ is not unique when σ is unknown. Which hold?
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Correct answer: (B) Q only
Explanation
Coverage alone does not specify a unique interval. Even with known σ,choose any tail split α_L+α_U=.05 and invert the normal pivot;different splits give different 95% intervals. Similarly the t pivot permits different tail splits with unknown σ. Thus P is false,Q true. **B**.