Correct answer: (C) The power function depends on θ.
Explanation
Under the continuous null,P(X>θ₀)=1/2,so S∼Binomial(n,1/2) regardless of f. Under an alternative,S∼Binomial(n,p),p=1−F(θ₀),and power is Σ_(j>c) binom(n,j)p^j(1−p)^(n−j). Thus it depends on the alternative distribution and its median parameter,as intended by **C**; the median alone does not specify a unique numerical power without a distributional family.
More Rank and Sign Tests questions
GATE 2022 ST Q51– Independent size-seven samples are population 1:(18,20,16,20,17,18,14) and population…
GATE 2022 ST Q56– For n paired observations used in Spearman rank correlation,x i are distinct for i≥2 and…
GATE 2021 ST Q64– X₁,…,X₁₀ are iid with density f θ(x)=f(x−θ),where f is symmetric about zero. For testing…
GATE 2026 ST Q46– Five iid observations come from a continuous distribution with population median θ (1/2).…
GATE 2025 ST Q34– Three independent observed pairs are (1,3),(2,4),(7,8). Find their Spearman rank…
GATE 2024 ST Q27– An iid sample n≥11 has a continuous strictly increasing CDF and median M. Test H₀:M=10…