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研究所、轉學考(插大)◆統計學
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93年 - 93 國立交通大學管碩士班考試入學試題_交通運輸研究所、運輸科技與管理學系：統計學#124804
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(1) 何謂中央極限定理(Central Limit Theorem)?
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5. (10%) The chi-square test statistic X² is based on a comparison of the sample frequenciesfi with the corresponding expected frequencies Fiunder the null hypothesis H0. Show that test statisticcan be written as the following weighted sum of the residuals fi - Fi, that is
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(a) (5%) Use the t ratio to test the hypothesis that X is a statistically significant variable.
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(b) (5%) Determine the estimated standard deviations of the parameter estimators.
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(c) (5%) Construct a 95 percent confidence interval for the coefficient of X. Does this interval include zero?
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(2) 母體中位數(Median)之推論有何重要意義?
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(3) χ²(ν)分配之期望值與變異數各為何?
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(4) t(ν)分配之期望值與變異數各為何?
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(5) 一組資料為右偏(Skewed to the right)分配時，其眾數(Mode)、中位數(Median)、及平均數(Mean)之相關位置為何?
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(a) 求算 E(X) 與 σ(X)
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(b) 當隨機抽樣數為 n=2 時，之抽樣分配為何?
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