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

科目：研究所、轉學考(插大)◆統計學 | 年份：102年 | 選擇題數：0 | 申論題數：10

試卷資訊

所屬科目：研究所、轉學考(插大)◆統計學

選擇題 (0)

申論題 (10)

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)
二、為了瞭解新品種的肥料是否比目前使用的種類更有效，研究人員找到 5 塊、每塊為兩畝的田地，其分散在縣市各地。每一塊地被分割為兩個大小相等的次區塊，隨機選取其中之一次區塊施加目前使用的肥料，另一次區塊則施加新品種肥料。接著在這些地上種植某農作物，收成後對農作物產量進行測量結果如下表：土地編號 1 2 3 4 5目前肥料 56 45 68 72 61新品種肥料 60 49 66 73 59
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)
三 、 The number sick days due to colds and flu in a class wasrecorded by a sample of 9 students. These data are:5 7 1 3 6 70 5 9 31. 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)
四 、 The weights of a random sample of cereal boxes that aresupposed to weigh 10 gram are listed here:5 7 6 12 9 12 8 11 4 16 (sample mean=9; samplevariance=14)
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)
五、Studies suggest there are several detrimental effects of televisionviewing on children. One of the problems may be that watchingtelevision reduces the amount of physical exercise and causesobesity. A sample of five 10-year-old children was taken. Thenumber of overweight kilograms (y) to each child was recorded.In addition, the number of hours of television viewing per week(x) was also recorded. These data are listed in the followingtable:
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)