102年 - 102 國立嘉義大學_碩士班(乙組)招生考試試題_生物事業管理學系：統計學#146553

一、1、何謂相對有效性(relative efficiency) ？(10 分)

2、繪製一個圖呈現兩個不偏估計式的抽樣分配，其中一個是相對有效的。此外，兩估計式均為常態分配，欲估計的參數為 θ。(10 分)

1. 假設不同肥料的農作物產量差異為常態分配，試問在 5% 的顯著水準下，能否推論新品種肥料的效果比目前使用的肥料好？(15 分)

2. 如果研究人員相信全縣市土地的土質都是相同的，則該如何進行這項實驗才能使自由度更高、更容易施行？(5 分)

1. Write down the names of the three statistics that can measurecentral location for the data. (5 分 ; Note: You do not need tocalculate the value of the three statistics.)

2. Which one of the above three statistics best describes the sickdays in the class. Explain your answer. (5 分)

1. Estimate the variance of the entire population of cereal boxweights with 95% confidence. (10 分)

2. What is the required condition for the statistical procedure in(1)? (5 分)

3. Describe how to check whether the required condition issatisfied. (5 分)

1. Fill out the blank cells in the above table. Calculate the samplelinear regression line () and describe what the slope coefficienttells you about relationship between the two variables. (15 分)(Please first calculate )

2. Is there evidence of a linear relationship between the numberof hours of television viewing and how overweight the child is?Please calculate the t-statistics, and use a two-tail test of at a5% significance level to support your judgment. Formulas tocalculate the t-statistics are provided as follows. (15 分)