Statistics Graduate Level Quiz
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HYPOTHESIS TESTING
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Suppose θ^∼N(θ,s2)\widehat\theta\sim N(\theta,s^2) with known ss. An equivalence test of H0:∣θ∣≥ΔH_0:|\theta|\geq\Delta against H1:∣θ∣<ΔH_1:|\theta|<\Delta uses the two one-sided tests (TOST) procedure at one-sided level 0.050.05. Let Δ=2s\Delta=2s and use z0.95=1.645z_{0.95}=1.645.
Which pair gives the actual size of the equivalence test and its power at θ=0\theta=0, respectively?
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