Statistics Graduate Level Quiz
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A researcher plans to use the large-sample test statistic Tn=n(Xˉ−1)/ST_n=\sqrt{n}(\bar X-1)/S and reject the null hypothesis of mean 11 when ∣Tn∣>1.96|T_n|>1.96. Under the scientific null model, the observations are independent and satisfy log⁡Xi∼N(−1/2,1)\log X_i\sim N(-1/2,1), so the population mean is exactly 11. The sample size is n=40n=40.
Which simulation design most directly assesses the finite-sample validity of the proposed asymptotic rejection rule under the stated null model?
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