GATE 2021 ST – Question 34
Three iid observations from a bivariate normal population with unknown mean μ and positive definite covariance Σ are (1,2)ᵀ,(4,−2)ᵀ,(−5,0)ᵀ. Find the p-value for the likelihood-ratio test μ=0 against μ≠0,to two decimals.
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Correct answer: 1.00 to 1.00
Explanation
The sample mean is exactly zero. Thus the constrained and unrestricted mean estimates coincide,and their maximized likelihoods agree. The discrepancy statistic is its minimum zero (Hotelling T² is also zero),so the upper-tail p-value is **1.00**.