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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1694One-Sided vs Two-Sided p-ValuesA test statistic is z=2.1 under a standard normal null. What are the one-sided and two-sided p-values, approximately?统计简单derivation未尝试免费1695Which Classical Test Should You Use?You have a sample of size 9 from a population you are willing to model as normal, but the population variance is unknown. You want to test whether the mean equals zero. Should you use a z-test or a t-test, and why?统计简单essay未尝试免费