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Q46Section I (Objective (Q1–Q80))45 of 79

Statistical Inference — computing a one-sided t-statistic

Let x1,x2,…,x9x_1,x_2,…,x_9 be a random sample from Normal distribution N(μ,σ2)N(\mu,\sigma^2), μ\mu and σ\sigma are unknown parameters, μ∈R,σ>0\mu\in\mathbb{R},\sigma>0. The observed values of xˉ=∑i=19xi9=9.8\bar x=\frac{\sum_{i=1}^9 x_i}{9}=9.8 and 18∑i=19(xi−xˉ)2=1.69\frac{1}{8}\sum_{i=1}^9(x_i-\bar x)^2=1.69. If LRT is used to test H0:μ=8.8H_0:\mu=8.8 versus H1:μ>8.8H_1:\mu>8.8, then what is the calculated value of the statistic?

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