GATE ST 2025 Problem-19 Hypothesis Testing | Likelihood Ratio Test & Power Function Explained
Автор: RitwikMath
Загружено: 2025-10-22
Просмотров: 61
Описание:
This video analyzes a GATE 2025 statistical hypothesis testing problem involving a two-sided test for the mean of a normal distribution based on sample sum \(X_{ar} = X_1 + X_2\). We derive the likelihood ratio test (LRT) for significance level 0.05, explain the power function's behavior as an even and strictly increasing function in \(\theta\), and show why the minimum power occurs at \(\theta = 0\) with value 0.05. We clarify why LRT here is not a Uniformly Most Powerful (UMP) test for two-sided alternatives. This explanation is essential for GATE and Indian Statistical Service aspirants mastering hypothesis testing concepts.
#gate2025 #hypothesistesting #likelihoodratiotest #powerfunction #gatestatistics #upscaspirants #indianstatisticalservice #statistics #gatereasoning
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