108年 - 108 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#146909

(a) 請分別說明違反這些假設，該模式估計或檢定會產生甚麼問題？(15%)

(b) 請寫出這個模式 F-value 的式子及其所檢定的虛無(null)與對立(alternative)假設為何？(5%)

(c) 如果無法拒絕虛無假設，並不表示 Y 與 X₁, X₂ 沒有關係？為什麼？(10%)

2. 變異數分析模式可分成固定效果模式(fixed-effect model)與隨機效果模式(random-effect model)，請以單因子模式為例，說明兩種模式(符號自訂)及用途上的差異？(20%)

(1) Find the margin of error for a \( 95\% \) confidence interval. \( (10\%) \)

(2) We expect that the margin of error is not greater than 0.02. How many people should be surveyed? (95% confidence interval) (10%)

4. The employee with low productivity in KID company is \( 5\% \). For the employee marked as low productivity, the attendance system showed that the probability of personal leave twice in a month is \( 100\% \). In contrast, the probability of personal leave twice in a month for other employees is \( 20\% \). Mary took the personal leave twice in the last month. What is the probability that Mary is an employee with low productivity? (10%)

5. One survey of education level in Taipei showed that 33 persons are elementary school, 44 persons are junior high school, 89 persons are senior high school, 14 persons are undergraduate and 20 persons are graduate. In Taiwan, the survey of education level showed that \( 10.2\% \) of population is elementary school, \( 12.3\% \) of population is junior high school, \( 57.9\% \) of population is senior high school, \( 7\% \) of population is undergraduate and \( 12.6\% \) of population is graduate. Is the education level in Taipei significantly different from the education level in Taiwan? (95% confidence interval) (20%)