→ deyugo:太感謝了! :) 推 140.112.42.55 01/04
心統(上)期末考 2001/1/5
Part.1
1. 請完成下表：
┌─（ ）
統計─┤ ┌─（ ）
└─推論統計─┤ ┌（ ）
└─（ ）─┤
└（ ）
2. 請說明什麼是z分配、t分配、卡方分配（chi-square distribution）。
此三分配的平均數為何？
3. 假設X、Y、Z為三個互相獨立的變項，其分配如下
X ~ N(0, 1) Y ~ N(μ, σ^2) Z ~ χ5^2
請問你如何以X、Y、Z三個變項產生U與V兩個不同分配的新變項？
U ~ x2^2 V ~ t5 (X、Y、Z可同時出現於U、V中)
4. 列聯相關係數C，Cramer's Phi，等關聯指標的目的為何？
5. Yates' correction適合於什麼樣的資料分析情境？
6. 專職運動員在比賽後照例會作禁藥使用檢測。請以統計檢驗的角度，用文字
說明（1）此檢驗的虛無假設，（2）犯第一類錯誤之情形，（3）犯第二類錯誤
之情形，與（4）此檢驗之檢定力(power)。
7. 假設X的分配為常態分配，平均數為μ，標準差為σ，N為樣本人數，X.bar
與s為樣本的平均數和標準差。
(a) 當σ已知時，( X.bar - μ ) / ( σ /√N) 的分配為何？
(b) 當σ未知時，( X.bar - μ ) / ( s /√N) 的分配為何？
8. Suppose two random variables X1 and X2 are independent with X1~N(μ1, σ1^2)
and X2 ~ N(μ2, σ2^2). Let us take N1 observations on X1 and N2 observations
on X2. What is the sampling distribution of the difference between these two
normally distributed independent means(X1.bar - X2.bar)? What is its standard
error of X1.bar - X2.bar?
9. 檢驗兩個獨立樣本的平均數時，
(a)你會用什麼統計方法來檢驗？
(b)作此檢定有何假設(assumptions)？請清楚解釋這些假設的意義。
(c)請討論此檢定的強韌性(robustness)，亦即當我們的資料不符合(b)之假設時
會有什麼影響。
心統(上)期末考 2001/1/5
Part.2
1.Which of the following two statements is technically more correct?
(1) We are 95% confident that the population mean lies in the interval 80-90,or
(2) We are 95% confident that the interval 80-90 contains the population means.
Explain.
2. (a)以下為100戶三洲人士家中分別養貓或狗的數目，有一國際愛貓協會想
以統計檢定瞭解各洲人士飼養貓與狗的偏好是否一樣，please help them!
亞洲 歐洲 美洲
貓 8 20 2
狗 12 30 28
(b)該協會會長認為各洲愛養貓與狗的比例約為2：3。請問在此假設下，
各細格的期望值為多少？
(c)該協會後來發現有6戶人家同時飼養貓和狗，以致於總戶數實僅94。
他們不知道這樣有沒有問題而來請教你。請問你會如何答覆呢？
3. Someone wishes to test whether a die is fair and rolls it 600 times. On each
roll, he just records whether the result was even or odd, and large (4,5,6)
or small (1,2,3). The observed frequencies turn out as follows:
Large Small
Even 183 113
Odd 88 216
Make a chi-square test to see if the die if fair. (α = 0.05)
4. A set of sample scores from an experiment has an N = 30 and an Xobt.bar = 19.
a. Can we reject the null hypothesis that the sample is a random sample from
anormal population withμ= 22 andσ= 8? Useα= 0.01(1 tail).Assume the
sample mean is in the correct direction.
b. What is the power of the experiment to detect a real effect such that
μreal=20?
c. What is the power to detect a μreal=20 if N is increased to 100?
d. What value dose N have to equal to achieve a power of 0.8000 to detect a
μreal=20? Use the nearest table for z.obt.
5.You wanted to estimate the mean number of vehicles crossing a busy bridge in
your neighborhood each morning during rush hour for the past year. To
accomplish this, you stationed yourself and a few assistants at one end of
the bridge on 18 randomly selected mornings during the year and counted the
number of vehicles crossing the bridge in a 10-minute period during rush
hour. You found the mean to be 125 vehicles per minute with a standard
deviation of 32.
a. Construct the 95% confidence limits for the population mean.
(vehicles per minute)
b. Construct the 99% confidence limits for the population mean.
(vehicles per minute)
6.A leading toothpaste manufacturer advertises that, in a recent medical study,
70% of the people tested had brighter teeth after using its toothpaste(called
Very Bright) as compared to using the leading competitor's brand(called Brand
X).The advertisement continues, "Therefore, use Very Bright and get brighter
teeth." In point of fact, the data upon which the above statements were based
were collected from the Pasadena plant. In the experiment, each employees
used both toothpastes.Half of the employees used Brand X for 3 weeks,
followed by Very Bright for the same time period. The other half used Very
Bright first, followed by Brand X. A brightness test was given at the end of
each 3-week period. Thus, there were two scores for each employee, one from
the brightness test following use of Brand X and one following the use of
Very Bright. The following table shows the scores(the higher, the brighter):
Subject Very Bright Brand X
1 5 4
2 4 3
3 4 2
4 2 3
5 3 1
6 4 1
7 1 3
8 3 4
9 6 5
10 6 4
Using a dependent t test to answer following question:
a. What is the alternative hypothesis? Use a directional hypothesis.
b. What is the null hypothesis?
c. Usingα= 0.05(1 tail), what do you conclude?
d. What error may you be making by your conclusion in part c.
e. Does the advertising seem misleading?
7.Based on previous research and sound theoretical considerations, an
experimental psychologist believes that memory for pictures is superior to
memory for words. To test this hypothesis, the psychologist performs an
experiment in which students from an introductory psychology class are used
as subjects. Eight randomly selected students view 30 slides with nouns
printed on them, and another group of eight randomly selected students view
30 slides with actual pictures of the same nouns. Each slide contains either
one noun or one picture, and is viewed for 4 seconds. After viewing the
slides, subjects are given a recall test, and the number of correctly
remembered items is measured. The data are shown here:
No. of Pictures No. of Nouns
Recalled Recalled
18 12
21 9
14 21
25 17
23 16
19 10
26 19
15 22
a. What is the alternative hypothesis? Assume that a directional hypothesis
is warranted.
b. What is the null hypothesis?
c. Usingα= 0.01(1 tail), what do you conclude?
type by Kbilly
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