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115年 - 115-2 司法官特種考試_三等_司法官及律師、專技高考_律師_各類科:民法與民事訴訟法(ㄧ)#147091(6題)

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10. An estimator that has small variance (but may be biased) is called precise. An estimator that has small MSE (Mean squared error) is called accurate. To illustrate: A standard 100-gm mass was weighted many, many times, on scale A. Similarly, on scale B, and finally on scale C. The distribution of measurements is summarized below Scale A: $\mu=100.08, \sigma=0.01$ Scale B: $\mu= 99.98, \sigma=0.02$ Scale C: $\mu=100.00, \sigma=0.05$ Which scale is most precise? Which scale is most accurate? (A) B is most precise, A is most accurate (B) A is most precise, B is most accurate (C) A is most precise and is also most accurate (D) B is most precise and is also most accurate e. Since the population mean is not given, there is no answer to this question. I

9. When the following hypotheses are being tested at a level of significance of a $H_5: \mu \ge 500$ $H_6: \mu < 500$ the null hypothesis will be rejected, if the p-value is (A) \( \leq a \) (B) \( >a \) (C) \( = a / 2 \) (D) \( \leq 1 - a / 2 \)

8. The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club. She would now like to determine whether or not the mean age of her customers is over 35. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are: (A) \( H_{5}:\mu \geq 35 \) vs. \( H_{6}:\mu < 35 \) (B) \( H_{5}:\mu \leq 35 \) vs. \( H_{6}:\mu >35 \) (C) \( H_{5}:\overline{\mathbf{X}}\geq 35 \) vs. \( H_{6}:\overline{\mathbf{X}} < 35 \) (D) \( H_{5}:\overline{\mathbf{X}}\leq 35 \) vs. \( H_{6}:\overline{\mathbf{X}} >35 \)

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