GATE Testing of Hypotheses: Likelihood Ratio and Large Sample Tests – Previous Year Questions
7 GATE previous year questions on Likelihood Ratio and Large Sample Tests (Testing of Hypotheses, Statistics) with answers and explanations, from every paper.
- GATE 2021 ST Q31 – The observations 0,2 are a sample of size two from Binomial(2,p). Test p=1/2 against p≠1/2. Find the observed likelihood-ratio statistic,to two…
- GATE 2024 ST Q25 – Which statement about hypothesis-test errors is true?
- GATE 2024 ST Q63 – Four iid uniform(0,θ) observations test H₀:θ=1 against H₁:θ=.1 by rejecting if their maximum is below .3. If p is the Type-I error probability, find…
- GATE 2024 ST Q64 – Four observations from N(μ,1),μ unknown, have sample mean .16. Given Φ(2.28)=.989,Φ(1.96)=.975,Φ(1.64)=.95, a size-.05 LRT tests μ=0 against μ≠0. Find…
- GATE 2025 ST Q19 – For iid X₁,X₂~N(θ,1),θ∈ℝ, let φ be the size-.05 likelihood-ratio test of H₀:θ=0 against H₁:θ≠0. Which holds?
- GATE 2025 ST Q63 – X~Bin(3,θ),0<θ<1. To test H₀:1/4≤θ≤3/4 against the outside alternatives, reject for X=0 or 3. Find the test size to two decimals.
- GATE 2026 ST Q44 – An iid sample of size n≥2 is used to test H₀:density (2π)(−1/2)e(−x²/2) against H₁:density e(− x )/2. At level 0.05, the likelihood-ratio critical…