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115年 - 115 外交特種考試_三等_外交領事人員類科英文組一、外交領事人員類科法文組、外交領事人員類科德文組、外交領事人員類科日文組、外交領事人員類科西班牙文組、外交領事人員類科阿拉伯文組、外交領事人員類科韓文組、外交領事人員類科俄文組、外交領事人員類科義大利文組、外交領事人員類科土耳其文組、外交領事人員類科葡萄牙文組、外交領事人員類科國際法組:國際關係與近代外交史#144520(24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 belowScale 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_0: \mu \ge 500$$H_a: \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) \( H_{0}:\mu \geq 35 \) vs. \( H_{a}:\mu < 35 \) (B) \( H_{0}:\mu \leq 35 \) vs. \( H_{a}:\mu >35 \) (C) \( H_{0}:\overline{\mathbf{X}}\geq 35 \) vs. \( H_{a}:\overline{\mathbf{X}} < 35 \) (D) \( H_{0}:\overline{\mathbf{X}}\leq 35 \) vs. \( H_{a}:\overline{\mathbf{X}} >35 \)

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