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115年 - 115 灌溉管理組織新進農田水利事業人員甄試試題_灌溉管理人員灌溉管理組/機電組/水質組:農田灌溉排水概要#144183(28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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