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%)

1. (10%) Find the limit: \( \lim_{x\to 1}\frac{x^{1 / 3} - 1}{\sqrt{x} - 1} \).

2. (10%) Find the limit of \( g(x) \) as \( x \) approaches the indicated values: $\lim_{x \to \sqrt{5}} \frac{1}{x+g(x)} = 2.$

3. (10%) Find \( dy / dx \) by implicit differentiation: \( y^2 = \sqrt{\frac{1 + x}{1 - x}} \).

4. (10%) Show that the function \( f(x) = x + \sin^2\left(\frac{x}{3}\right) - 8 \) has exactly one zero in the interval \( (-\infty, \infty) \).

5. (15%) Graph the function: \( y = \frac{\sqrt{1 - x^2}}{2x + 1} \). (Find where the curve is increasing and where it is decreasing. Find the local extreme points. Find the points of inflection, if any occur, and determine the concavity of the curve. Identify any asymptotes.)

6. (10%) Find the area of the triangular region bounded on the left by \( x + y = 2 \), on the right by \( y = x^2 \), and above by \( y = 2 \).

115年 - 115 國立臺北大學_碩士班一般入學考試試題_金融與合作經營學系：統計學#146920

115年 - [無官方正解]115 國立臺北大學_碩士班一般入學考試試題_經濟學系：統計學#146534

115年 - [無官方正解]115 國立嘉義大學_碩士班招生考試試題_財務金融學系：統計學#143862

115年 - 115 中央警察大學_碩士班入學考試試題：統計學#139759

114年 - 114 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#146907

114年 - 114 中央警察大學_碩士班入學考試試題_警察政策研究所、刑事警察研究所、資訊管理研究所、鑑識科學研究所、行政管理研究所、防災研究所、水上警察研究所海洋科技組：統計學(同等學力加考)#146791

114年 - [無官方正解]114 國立嘉義大學_碩士班招生考試試題_財務金融學系：統計學#144015

114年 - [無官方正解]114 臺灣綜合大學系統_學士班轉學生考試試題:統計學#138278

113年 - 113 國立臺北大學_碩士班一般入學考試試題_自然資源與環境管理研究所：統計學#146880

113年 - 113 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#146878