107年 - 107 國立臺北大學_碩士班一般入學考試試題_企業管理學系甲組：統計學#146960

(a) Compute 95 percent confidence interval for mean.

(b) How large a sample is needed to estimate the population mean within NT 10?

2. (10%) According to historical data, the probability of one disaster for every year is 10 percent. What is the probability less than two disasters in the next 5 years?

(a) If the mean of sample is less than or equal to 71.5, accept H₀; If the mean of sample is greater than 71.5, reject H₀. Please compute Type I error.

(b) Follow (a), The mean of population is 72.5. Please compute Type II error.

4. 某市調人員隨機調查 10 位消費者對於市場上五種主要品牌(A, B, C, D, E)的評價，依序從最高到最低 1-5 排序的結果彙整如下表：



請問該市調人員應該使用何種方法如何檢定消費者對這五種品牌的評價是否一致 (5%)？為什麼該使用這個方法 (10%)？檢定結果為何 (10%)？(α = 0.05)

5. 某研究生建立了一個線性避歸模式：Yᵢ = β₀ + β₁X₁ᵢ + β₂X₂ᵢ + β₃X₃ᵢ + εᵢ，β₀、β₁、β₂、β₃ 分別是截距項與解釋變數(x1-x3)的係數，εᵢ 是隨機誤差項，i = 1,2, ...,n，εᵢ 滿足避歸模式基本假設。該研究生想藉由變異數膨脹圈子(variance inflation factor, VIF)評估多重共線(multicollinearity)的問題，請問該生要如何計算 VIF 值(15%)？為什麼應該評估這個問題 (10%)？