中原大學九十二學年度二技進修在職班招生考試

92年7月26日 第2節 (14:00~15:30)   誠實是我們珍視的美德,
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科目:統計學  

一、 選擇題(每題3分)
1.
The variance of a sample of 169 observations equals 576. The standard deviation of the sample equals
  a. 13 b. 24 c. 576 d. 28,461
   
2.
From a group of six people, two individuals are to be selected at random. How many possible selections are there?
  a. 12 b. 36 c. 15 d. 8
   
3.
If A and B are independent events with P(A) = 0.65 and P(AB)= 0.26, then, P(B) =
  a. 0.400 b. 0.169 c. 0.390 d. 0.650
   
4. The intersection of two mutually exclusive events
  a. can be any value between 0 to 1
  b. must always be equal to 1
  c. must always be equal to 0
  d. can be any positive value
   
5. A measure of the average value of a random variable is called a(n)
  a. variance b. standard deviation
  c. expected value d. coefficient of variation
   
6. For a standard normal distribution, the probability of z < 0 is
  a. zero b. -0.5 c. 0.5 d. one
   
7. A population has a mean of 75 and a standard deviation of 8. A random sample of 800 is selected. The expected value of is
  a. 8 b. 75 c. 800 d. None of the above is correct.
   
8. The level of significance is the
  a. maximum allowable probability of Type II error
  b. maximum allowable probability of Type I error
  c. same as the confidence coefficient
  d. same as the p-value
   
9.
The error of rejecting a true null hypothesis is
  a. a Type I error
  b. a Type II error
  c. is the same as ß
  d. committed when not enough information is available
   
10.
The collection of all possible sample points in an experiment is
  a. the sample space b. a sample point
  c. an experiment d. the population
                      
二、 填空題(答題請標明格號,每格3分)
1.
設有一樣本資料如下
 
5      12 6  8 5
6  7 5 12 4
其中位數(median)為 (1) ,眾數(mode)為 (2) ,第75百分位數(percentile)為 (3)
   
2.
令X為一隨機變數,其機率分配如下:
 
x
f(x)
 
 
0
0.80
 
 
1
0.15
 
 
2
0.04
 
 
3
0.01
 
  則X的期望值為 (4) ,變異數為 (5)
     
3.
某農場生產的橘子每個平均重量為100克,標準差為25克,若將10個橘子裝成一箱,則每箱橘子的平均重量等於 (6) 克,變異數等於 (7) 克。
     
4.
小明發現其所任職的出版社的人員,平常都用五種中文輸入法(注音、倉頡、大易、速成及無蝦米)之一來做文書處理,他想知道這五種輸入法的輸入速度是否相同。經隨機抽選部份人員調查其每分鐘打字的字數後,小明得到下列變異數分析表:
  表一:中文輸入速度變異數分析表
 
上表中空格(8)、(9)、(10)之數值分別為, (8) (9) (10)
   
三、
問答題(共40分)
1.
(1) 何謂相關係數(correlation coefficient)?其需要如何求算得到? (10分)
  (2) 如要分析兩個隨機變數間的相關性時,以共變數(covariance)及以相關係數分析,就所得到的結果而言,有哪些相同及不同的地方? (10分)
   
2.
請簡要說明區間估計與假說檢定之間的關係。 (20分)
     
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