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Inferential Statisticshard
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Given Xi∼N(μ,σ2)X_i \sim N(\mu, \sigma^2)Xi​∼N(μ,σ2) for i=1...ni=1...ni=1...n, we test H0:μ=0H_0: \mu = 0H0​:μ=0 using the Likelihood Ratio Test. For a large sample, what is the value of the LRT statistic λ=−2ln⁡(L(θ^0)/L(θ^))\lambda = -2 \ln(L(\hat{\theta}_0)/L(\hat{\theta}))λ=−2ln(L(θ^0​)/L(θ^)) if the ttt-statistic is t=2t=2t=2?