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115年 - 115 國營臺灣鐵路股份有限公司工務處_從業人員甄試試題_第 8 階-助理工程師-建築工程:建築營造與估價及建築結構系統#145953(33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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