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1674Why the Percentile Interval Can Drift Off-CenterWhy can a percentile bootstrap interval end up noticeably off-center relative to the original estimate when the statistic is skewed?统计中等essay未尝试面试订阅1675Why the Basic Interval Reflects the Bootstrap Around the EstimateWhat conceptual idea makes the basic bootstrap interval differ from the percentile interval?统计中等essay未尝试面试订阅1676Why the Bootstrap Cannot Invent Unseen Tail EventsWhy is the nonparametric bootstrap often too optimistic about tail risk when the observed sample contains no truly extreme events?统计简单essay未尝试免费1677Why Studentization Can Improve Interval CalibrationWhy can studentizing a bootstrap statistic improve interval accuracy in skewed or scale-varying problems?统计困难essay未尝试面试订阅1678Why Block Bootstrap Is About Dependence, Not Just Bigger ChunksWhy is the point of a block bootstrap not merely to resample larger chunks, but to preserve local serial dependence?统计简单essay未尝试免费1679When a Parametric Bootstrap Beats a Nonparametric OneWhen can a parametric bootstrap be more informative than a nonparametric bootstrap?统计中等essay未尝试面试订阅1680Why Reusing the Same Bootstrap Draws for Many Design Choices Can MisleadWhy can a bootstrap study itself become overfit if you repeatedly choose tuning knobs by looking at the same resampled diagnostics?统计简单essay未尝试免费1681One-Sample z-Test with Known VolatilityA signal's average daily alpha over 25 days is 0.8, and the daily standard deviation is known to be 2. Test H 0: =0 against a two-sided alternative at the 5% level using a z-test.统计简单derivation未尝试免费1682One-Sided t-Test on a Small SampleFor n=10 independent observations, the sample mean is 1.5 and the sample standard deviation is 2. Test H 0: =0 against H 1: >0 at the 5% level using a t-test.统计简单derivation未尝试免费1683Two-Sample z-Test for Mean DifferenceTwo independent books produce average daily PnL of 102 and 100 over 100 days each. The daily standard deviation is known to be 5 for each book. Test whether the means are equal using a two-sided z-test.统计中等derivation未尝试面试订阅1684Chi-Square Goodness-of-Fit for a DieA six-sided die is rolled 60 times, and the counts are (14,8,11,9,10,8). Test fairness using a chi-square goodness-of-fit test.统计简单derivation未尝试免费1685Power of a One-Sided z-TestConsider testing H 0: =0 versus H 1: >0 with known =10 and sample size n=25 at significance level =0.05. What is the power when the true mean is =4?统计中等derivation未尝试面试订阅1686Sample Size for a z-TestYou want a two-sided z-test of H 0: =0 with known =4 to detect a true mean of 1 at 5% significance and 80% power. Approximately what sample size is needed?统计中等derivation未尝试面试订阅1687Paired t-Test on Trade-Cost DifferencesFor 16 paired executions, the mean cost difference (strategy A minus strategy B) is -1.2 and the sample standard deviation of the differences is 1.5. Test whether strategy A has lower mean cost using a 5% one-sided paired t-test.统计简单derivation未尝试免费1688Chi-Square Test for a Normal VarianceAssume normal data with n=20 and sample variance s 2=9. Test H 0: 2=4 using the classical chi-square variance test.统计中等derivation未尝试面试订阅1689Approximate Fair-Coin Test with a Normal ApproximationA coin is flipped 20 times and lands heads 14 times. Use the normal approximation to test fairness at the 5% two-sided level.统计简单derivation未尝试免费1690Likelihood-Ratio Test for an Exponential RateSuppose X 1,\dots,X 10 \sim Exp ( ) and X i=5. Use a likelihood-ratio test of H 0: =1 against the unrestricted alternative.统计困难derivation未尝试面试订阅1691Confidence Interval and Test DecisionA two-sided test for a coefficient gives z = 1.8. Without doing a separate interval calculation, what can you say about whether the 95% confidence interval contains zero?统计简单essay未尝试免费1692Type I vs Type II Tradeoff from Changing a ThresholdA one-sided z-test for H 0: =0 with n=25 and known variance 1 rejects when X>c. Compare the thresholds c=0.33 and c=0.66 in terms of Type I error and power when the true mean is 0.5.统计困难derivation未尝试面试订阅1693Chi-Square Test of Independence in a 2x2 TableA 2x2 contingency table of outcomes is \begin pmatrix 30 & 20\\ 10 & 40\end pmatrix . Test independence using the classical chi-square test.统计中等derivation未尝试面试订阅