英文版统计学_Chapter2

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(完整word版)英文版概率论与数理统计重点单词

概率论与数理统计中的英文单词和短语概率论与数理统计Probability Theory and Mathematical Statistics第一章概率论的基本观点Chapter 1Introduction of Probability Theory不确立性indeterminacy必定现象certain phenomenon随机现象random phenomenon试验experiment结果outcome频次数frequency number样本空间sample space出现次数frequency of occurrencen 维样本空间n-dimensional sample space样本空间的点point in sample space随机事件random event / random occurrence基本领件elementary event必定事件certain event不行能事件impossible event等可能事件equally likely event事件运算律operational rules of events事件的包括implication of events并事件union events交事件intersection events互不相容事件、mutually exclusive exvents/互斥事件/incompatible events互逆的mutually inverse加法定理addition theorem古典概率classical probability古典概率模型classical probabilistic model几何概率geometric probability 乘法定理product theorem概率乘法multiplication of probabilities条件概率conditional probability全概率公式、全formula of total probability概率定理贝叶斯公式、逆Bayes formula概率公式后验概率posterior probability先验概率prior probability独立事件independent event独立随机事件independent random event独立实验independent experiment两两独立pairwise independent两两独立事件pairwise independent events第二章随机变量及其散布Chapter2Random Variables and Distributions随机变量random variables失散随机变量discrete random variables概率散布律law of probability distribution一维概率散布one-dimension probability distribution 概率散布probability distribution两点散布two-point distribution伯努利散布Bernoulli distribution二项散布 / 伯努Binomial distribution利散布超几何散布hypergeometric distribution三项散布trinomial distribution多项散布polynomial distribution泊松散布Poisson distribution泊松参数Poisson theorem散布函数distribution function概率散布函数probability density function连续随机变量continuous random variable概率密度probability density概率密度函数probability density function概率曲线probability curve平均散布uniform distribution指数散布exponential distribution指数散布密度函exponential distribution density 数function正态散布、高斯normal distribution散布标准正态散布standard normal distribution正态概率密度函normal probability density function数正态概率曲线normal probability curve标准正态曲线standard normal curve柯西散布Cauchy distribution散布密度density of distribution第三章多维随机变量及其散布Chapter 3 Multivariate Random Variables and Distributions二维随机变量two-dimensional random variable结合散布函数joint distribution function二维失散型随机two-dimensional discrete random 变量variable二维连续型随机two-dimensional continuous random 变量variable结合概率密度joint probability variablen 维随机变量n-dimensional random variablen 维散布函数n-dimensional distribution functionn 维概率散布n-dimensional probability distribution边沿散布marginal distribution边沿散布函数marginal distribution function边沿散布律law of marginal distribution边沿概率密度marginal probability density二维正态散布two-dimensional normal distribution二维正态概率密two-dimensional normal probability 度density 二维正态概率曲two-dimensional normal probability 线curve条件散布conditional distribution条件散布律law of conditional distribution条件概率散布conditional probability distribution条件概率密度conditional probability density边沿密度marginal density独立随机变量independent random variables第四章随机变量的数字特点Chapter 4 Numerical Characteristics fo Random Variables数学希望、均值mathematical expectation希望值expectation value方差variance标准差standard deviation随机变量的方差variance of random variables均方差mean square deviation有关关系dependence relation有关系数correlation coefficient协方差covariance协方差矩阵covariance matrix切比雪夫不等式Chebyshev inequality第五章大数定律及中心极限制理Chapter 5 Law of Large Numbers and Central Limit Theorem大数定律law of great numbers切比雪夫定理的special form of Chebyshev theorem特别形式依概率收敛convergence in probability伯努利大数定律Bernoulli law of large numbers同散布same distribution列维 - 林德伯格independent Levy-Lindberg theorem定理、独立同分布中心极限制理辛钦大数定律Khinchine law of large numbers利亚普诺夫定理Liapunov theorem棣莫弗 - 拉普拉De Moivre-Laplace theorem斯定理第六章样本及抽样分布Chapter 6 Samples and Sampling Distributions统计量statistic整体population个体individual样本sample容量capacity统计剖析statistical analysis统计散布statistical distribution统计整体statistical ensemble随机抽样stochastic sampling / random sampling 随机样本random sample简单随机抽样simple random sampling简单随机样本simple random sample经验散布函数empirical distribution function样本均值sample average / sample mean样本方差sample variance样本标准差sample standard deviation标准偏差standard error样本 k 阶矩sample moment of order k样本中心矩sample central moment样本值sample value样本大小、样本sample size容量样本统计量sampling statistics 随机抽样散布random sampling distribution抽样散布、样本sampling distribution散布自由度degree of freedomZ 散布Z-distributionU 散布U-distribution第七章参数预计Chapter 7Parameter Estimations统计推测statistical inference参数预计parameter estimation散布参数parameter of distribution参数统计推测parametric statistical inference点预计point estimate / point estimation整体中心距population central moment整体有关系数population correlation coefficient整体散布population covariance整体协方差population covariance点预计量point estimator预计量estimator无偏预计unbiased estimate/ unbiasedestimation预计量的有效性efficiency of estimator矩法预计moment estimation整体均值population mean整体矩population moment整体 k 阶矩population moment of order k整体参数population parameter极大似然预计maximum likelihood estimation极大似然预计量maximum likelihood estimator极大似然法maximum likelihood method /maximum-likelihood method似然方程likelihood equation似然函数likelihood function区间预计interval estimation置信区间confidence interval置信水平confidence level置信系数confidence coefficient单侧置信区间one-sided confidence interval置信上限置信下限U 预计正态整体整体方差的预计confidence upper limit confidence lower limitU-estimatornormal populationestimation of population variance置信度方差比degree of confidence variance ratio第八章假定查验Chapter 8Hypothesis Testings参数假定假定查验两类错误统计假定统计假定查验查验统计量明显性查验统计明显性parametric hypothesis hypothesis testingtwo types of errors statistical hypothesis statistical hypothesis testing test statisticstest of significance statistical significance单边查验、单侧one-sided test查验单侧假定、单边one-sided hypothesis 假定两侧假定两侧查验明显水平拒绝域 / 否认区two-sided hypothesis two-sided testing significant level rejection region域接受地区acceptance regionU 查验F 查验方差齐性的查验拟合优度查验U-testF-testhomogeneity test for variances test of goodness of fit。

应用数理统计课件(配庄楚强版教材)第二章

（ξ1,ξ2,..,ξn), 则（ξ1,ξ2,…,ξn)的联合分布函
数为： F ( x1 , x2 ,L , xn )
= P { ξ1 < x1 , ξ 2 < x2 , ..., ξ n < xn }
= P { ξ1 < x1}P{ ξ 2 < x2 } ⋅ ... ⋅ P{ ξ n < xn }
（2）χ2 分布（Chi-square distribution）
χ 2 ～χ 2 (n)
{ } p分位点：χ p2 (n ) 满足P
χ
2
<
χ
2 p
(n)
=p
p53（9 347）表 4
χ
2 0.95
(9
)
=
16.91（9
p540)
表p 4 χ2 分布分位数表
n
p
8
9
0 ．90 13．362 14．684
又如：α = 0.1，uα = u0.1 = ? (表中没有)
u0.1 = −u1−0.1 = −u0.9 = −1.282
对称性(symmetricy)：
0.1
uα = −u1−α
α = 0.1
u0.1
u1− 0.1
习题或附表中α通常是指分位点之外的概率（面积）
单侧分位点：α放在分位点u1−α的一侧双侧分位点: α分割放在正负对称的
2 +L +
)
m
1
9
二. t 分布 (t distribution)
Definition: 若ξ～N(0,1), η～χ2(n)且相互独立,
则有
t=
ξ η
～ t (n )

统计学要点摘要英文版-Statistic-Review

Chapter 2 Statistic ReviewA.Random variables;1.expected value:Define ：X is a discrete random variable，“ the mean （or expected value）of X " is the weighted average of the possible outcomes，where the probabilities of theoutcome serve as the appropriate weight。

p i is ith of prob。

, i=1，2，……nInterpretation: The random variable is a variable that have a probability associated with each outcome. Outcome is not controlled.Discrete random Var. ：has finite outcome，or outcome is countable infinite。

Continuous random Var。

: uncountable infinite outcome, the probability of each outcome is small because of too many numbers.For normal random Var.，probability density function is used to calculate the probability between the are。

E（)：the expectations operator,→… “ sample mean”, used to estimateThe is changed from sample to sample。

英文商务统计学ppt课件_Ch02

Categorical Байду номын сангаасata
Tabulating Data
Graphing Data
Summary Table
Bar Charts
Pie Charts
Pareto Chart
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Banking Preference
16% 24% 2%
ATM Automated or live telephone Drive-through service at branch In person at branch Internet
17%
41%
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Chap 2-5
Organizing Categorical Data: Bar Chart

In a bar chart, a bar shows each category, the length of which represents the amount, frequency or percentage of values falling into a category.
Chap 2-3
Organizing Categorical Data: Summary Table

A summary table indicates the frequency, amount, or percentage of items in a set of categories so that you can see differences between categories.

基础统计学简介(英文版)

1-5 5
Who Uses Statistics?
Statistical techniques are used extensively by managers in marketing, accounting, quality control, consumers, professional sports people, hospital administrators, educators, politicians, physicians, gamblers, etc...
1-9 9
Types of Statistics
– This is why younger people pay more for insurance…
• Knowledge of statistical methods at least helps you understand why decisions are made
– In future you will make decisions that involve data
1-6 6
Types of Statistics
Descriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.
EXAMPLE 1: A Gallup poll found that 49% of the people in a survey knew the name of the first book of the Bible. The statistic 49 describes the number out of every 100 persons who knew the answerstics?

社会统计学02

5
Definition
❖ Frequency Distribution (or Frequency Table)
shows how a data set is partitioned among all of several categories (or classes) by listing all of the categories along with the number of data values in each of the categories.
two consecutive
lower class
boundarHale Waihona Puke es10Class
10
Width
10
10
10
10
14
Reasons for Constructing Frequency Distributions
1. Large data sets can be summarized. 2. We can analyze the nature of data. 3. We have a basis for constructing
90
4. Outliers: Sample values that lie 80
70
very far away from the vast
60
majority of other sample values. 50
East
40
West
5. Time: Changing characteristics 30
class width
(maximum value) – (minimum value) number of classes

统计学(中英文)_ch01

Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 1-12
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n
i
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 1-8
Inferential Statistics 推断统计
Estimation 估计 e.g., Estimate the population mean weight using the sample mean weight 例如：利用采样的平均重量估计人口的平均体重 Hypothesis testing 假设检验 e.g., Test the claim that the population mean weight is 120 pounds 例如：根据测试的要求，人口平均体重是120 磅
英文翻译乃自己所做，英文翻译乃自己所做，有错误之处请自行查证。之处请自行查证。
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 1-1
Business Statistics, A First Course
Defined descriptive vs. inferential statistics 描述性统计和推理统计 Reviewed data types 回顾数据类型
♦ ♦ ♦ ♦
Categorical vs. Numerical data 绝对的和数值的数据 Discrete vs. Continuous data 离散的和连续的数据

基础统计学英文版

This is why younger people pay more for insurance…
Knowledge of statistical methods at least helps you understand why decisions are made
In future you will make decisions that involve data
Types of Statistics
❖ Descriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.
EXAMPLE 2: According to Consumer Reports, General Electric washing machine owners reported 9 problems per 100 machines during 2002. The statistic 9 describes the number of problems out of every 100 machines.
Types of Statistics
❖ Descriptive Statistics: Methods of organizing, summarizing, and presenting data in an informative way.
EXAMPLE 1: A Gallup poll found that 49% of the people in a survey knew the name of the first book of the Bible. The statistic 49 describes the number out of every 100 persons who knew the answer.

统计学英文版教材课件

Combining Events
There are some important ways in which events can be combined that we will encounter repeatedly throughout this course. Suppose we have two events, A and B .
For example, A ∪ B = {1, 3, 4, 5}.
S A 1 5 2
STAT7055 - Lecture 2
B 3 4
6
February 17, 2016 13 / 64
Introduction
Intersection, Union and Complement
Complement
STAT7055 - Lecture 2
February 17, 2016
3 / 64
Introduction
Deﬁnitions
Probabilities of Outcomes
The probability of an outcome occurring on a single trial is written as P (Oi ). Probabilities associated with the outcomes in a sample space must satisfy two important requirements:
STAT7055 - Lecture 2
February 17, 2016
7 / 64
Introduction
Events
Events
A simple event is an individual outcome from the sample space. An event is a collection of one or more simple events (or outcomes).

统计学课件(英文)

5
Descriptive vs. Inferential Statistics
Descriptive statistics: involves arranging, summarizing, and presenting a set of data in such a way that useful information is produced. Its methods make use of graphical techniques and numerical descriptive measures (such as averages) to summarize and present the data Inferential statistics: generalizing from a sample to a population, estimating unknown population parameters, drawing conclusions, making decisions.
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Scale of Measurement: Ratio
The data have the properties of interval data and the ratio of two values is meaningful. Contains a meaningful zero value that indicates that nothing exists for the variable at the zero point .
15
Kinds of Data (variables)
Qualitative (Categorical) data:

第二章双变量回归分析基本概念

1-14
第七节样本回归函数（SRF）
对应(2.3.2)的SRF
Yˆi ˆ1 ˆ2 Xi 其中 Yˆ读为Y-帽，是 E(Y 的Xi估) 计量。
• 注意，一个估计量(estimator)，又称(样本)统计量 (statistic)，是指一个规则或公式或方法。在一项应用中，由估计量算出的一个具体的数值，称为估计值 (estimate) 。
1-12
第七节样本回归函数（SRF）
总体是观测不到的，大多数情况下，对应于一个解释变量X，只能观测到被解释变量Y的一个值。
• 我们只能得到对应于某些固定X 值的Y 值的一个（有限个）样本。
1-13
第七节样本回归函数（SRF）
样本回归函数(sample regression function, SRF)
（2.3.1）
PRF的形式是一个经验问题，线性方程是常
用的形式：
E(Y Xi ) f ( Xi ) 1 2 Xi （2.3.2）
• 其中 1 和 2为未知但却固定的参数，称为回归系数( regression coefficient)。1 和 2 分别称为截距
和斜率系数。方程(2.3.2）本身则称为线性总体回归函数或简称线性总体回归。
Yi 1 2 X i ui
(2.5.2)
(2.5.2)为PFR的随机设定形式，与（2.3.2）等价。
1-11
第六节随机扰动项的意义
为什么要引入随机扰动项？
• 理论的含糊性 • 数据的缺失 • 变量的解释力（核心变量与周边变量） • 人类行为的内在随机性 • 糟糕的替代变量（永久消费与当前消费等） • 节省原则 • 错误的函数形式
• 父母身高、子女身高 • 儿女的身高趋向人口总体平均，普遍回归定律(law of

基础统计学(英文版)(ppt 31页)

EXAMPLE: the number of bedrooms in a house, or the number of hammers sold at the local Home Depot (1,2,3,…,etc). But you cannot have 2.3 bedrooms or 10.6 hammers…Thus discrete variables result from counting.
1-3
Why study statistics?
• Numerical info is everywhere
– But how do we know if conclusions reported are accurate?
• Statistical techniques are used to make decisions that affect our lives
1-18
Types of Variables
A continuous variable can assume any value within a specified range.
Examples are: The pressure in a tire, the weight of a pork chop, or the height of students in a class. Typically, continuous variables are the result of measuring something.
1-15
Types of Variables
For a Qualitative or Attribute variable the characteristic being studied is nonnumeric.

第2章Descriptive Statistics描述统计学表格和图形法-B

• one variable is categorical and the other is quantitative,
一个变量是分类的，另一份是数量的，
• both variables are categorical, or 都是分类变量，
• both variables are quantitative. 或都是数量变量。
Summarizing Data for Two Variables using Tables
▪ Thus far we have focused on methods that are used to summarize the data for one variable at a time.
之前我们关注怎么汇总一个变量的数据。
1
otherwise on a password-protected website or school-approved learning management system for classroom use.
Essentials of Modern Business Statistics (7e)
▪ Often a manager is interested in tabular and graphical methods that will help understand the relationship between two variables.
管理人员往往需要汇总两个变量的数据来揭示变量之间的关系。
2
otherwise on a password-protected website or school-approved learning management system for classroom use.

统计学课件英语

1
Financial Accounting and Accounting Standards
LEARNING OBJECTIVES
After studying this chapter, you should be able to: 1. Identify the major financial statements and other means of financial reporting. 2. Explain how accounting assists in the efficient use of scarce resources. 3. Identify the objective of financial reporting. 4. Explain the need for accounting standards. 5. Identify the major policy-setting bodies and their role in the standard-setting process.
in making decisions in their capacity as capital providers.
Illustration 1-1 Capital Allocation Process
It promotes productivity, encourages innovation, and provides an efficient and liquid market for buying and selling securities and obtaining and granting credit.
1-6
LO 2 Explain how accounting assists in the efficient use of scare resources.

应用商务统计学讲义第二章中英文对照

Errors
Total
Amount
Small
89.47% 10.53% 100.0%
Total
335
65
400
Amount
Medium invoices have a larger chance (28.57%) of having errors than small (10.53%) or
Medium Amount
DCOVA
Percent 37% 29% 18% 13% 3%
Source: Data extracted and adapted from “Main Reason Young Adults Shop Online?”
USA Today, December 5, 2012, p. 1A. 来源：数据提取和改编自“主要原因年轻人网上购物吗？“ 今日美国，2012年12月5日，1a P.。
Large Amount
Total
71.43% 92.86% 83.75%
28.57% 7.14%
16.25%
100.0% 100.0% 100.0%
l中a型rg发e票(比7小.1（41%0.5)3i%n）vo或i大ce（s7.14%）发票的出错机会大（28.57%）。
LLL Tables Used For Organizing
Numerical Data
用于组织数值数据的表
DCOVA
Numerical Data 数据
Ordered Array 有序阵列
Frequency Distributions
频数分布图
Cumulative Distributions
累积分布
Organizing Numerical Data:

《统计学基础(英文版·第7版)》题库答案les7e_ptb_01

Chapter 1Introduction to Statistics1.1An Overview of Statistics1Distinguish Between a Population and a SampleMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the data set is a population or a sample.1)The age of every fourth person entering a department storeA)sample B)population2)The age of each employee at a local grocery storeA)population B)sampleSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.Identify the population and the sample.3)A survey of 1212 American households found that 52% of the households own a computer.4)When 1348 American households were surveyed, it was found that 57% of them owned two cars.5)A survey of 2625 elementary school children found that 28% of the children could be classified as obese. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Use the Venn diagram to identify the population and the sample.6)A)Population: Magazine subscribers; Sample; Magazine subscribers who renew their subscriptionB)Population: Magazine subscribers who renew their subscription; Sample: Magazine subscribers2Distinguish Between a Parameter and a StatisticSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Determine whether the numerical value is a parameter or a statistic. Explain your reasoning.7)A recent survey by the alumni of a major university indicated that the average salary of 10,500 of its 200,000graduates was $130,000.8)The average salary of all assembly-line employees at a certain car manufacturer is $44,000.9)A survey of 1040 students was taken from a university with 19,000students.3Distinguish Between Descriptive Statistics and Inferential StatisticsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify whether the statement describes inferential statistics or descriptive statistics.10)The average age of the students in a statistics class is 20years.A)descriptive statistics B)inferential statistics11)The chances of winning the California Lottery are one chance in twenty-two million.A)inferential statistics B)descriptive statistics12)There is a relationship between smoking cigarettes and getting emphysema.A)inferential statistics B)descriptive statistics13)From past figures, it is predicted that 31% of the registered voters in California will vote in the June primary.A)inferential statistics B)descriptive statistics14)Based on previous clients, a marriage counselor concludes that the majority of marriages that begin withcohabitation before marriage will result in divorce.A)inferential statistics B)descriptive statistics4ConceptsSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.Provide an appropriate response.15)Explain the difference between a sample and a population.16)If you had to do a statistical study, would you use a sample or a population? Why?1.2Data Classification1Distinguish Between Qualitative and Quantitative DataMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the data are qualitative or quantitative.1)the colors of automobiles on a used car lotA)qualitative B)quantitative2) the number of complaint letters received by the United States Postal Service in a given dayA)quantitative B)qualitative3)the number of seats in a movie theaterA)quantitative B)qualitative4)the numbers on the shirts of a girlʹs soccer teamA)qualitative B)quantitative2Classify Data with Respect to the Four Levels of MeasurementMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify the data setʹs level of measurement.5)hair color of women on a high school tennis teamA)nominal B)ordinal C)interval D)ratio6)numbers on the shirts of a girlʹs soccer teamA)nominal B)ordinal C)interval D)ratio7)ages of students in a statistic classA)ratio B)ordinal C)interval D)nominal8)temperatures of 26 selected refrigeratorsA)interval B)ordinal C)nominal D)ratio9)number of milligrams of tar in 30 cigarettesA)ratio B)ordinal C)interval D)nominal10)number of pages in your statistics bookA)ratio B)ordinal C)interval D)nominal11)marriage status (married, single, or divorced) of the faculty at the University of ColoradoA)nominal B)ordinal C)interval D)ratio12)list of 1240 social security numbersA)nominal B)ordinal C)interval D)ratio13)the ratings of a movie ranging from ʺpoorʺ to ʺgoodʺ to ʺexcellentʺA)ordinal B)nominal C)interval D)ratio14)the final grades (A, B, C, D, and F) for students in a statistics classA)ordinal B)nominal C)interval D)ratio15)the annual salaries for all teachers in CaliforniaA)ratio B)ordinal C)interval D)nominal16)list of zip codes for ChicagoA)nominal B)ordinal C)interval D)ratio17)the nationalities listed in a recent survey (for example, Asian, European, or Hispanic).A)nominal B)ordinal C)interval D)ratio18)the amounts of fat (in grams) in 37 cookiesA)ratio B)ordinal C)interval D)nominal19)the years the summer Olympics were held in the United StatesA)interval B)ordinal C)nominal D)ratio20)numbers of touchdowns scored by a major university in five randomly selected games53134A)ratio B)ordinal C)interval D)nominal21)the average daily temperatures (in degrees Fahrenheit) on five randomly selected days2123213027A)interval B)nominal C)ordinal D)ratio22)manuscripts rated ʺacceptableʺ or ʺunacceptableʺA)ordinal B)nominal C)ratio D)interval23)the lengths (in minutes) of the top ten movies with respect to ticket sales in 2007A)ratio B)nominal C)ordinal D)interval24)the data listed on the horizontal axis in the graphA)nominal B)interval C)ordinal D)ratio25)the data listed on the horizontal axis in the graphA)ratio B)nominal C)ordinal D)interval3ConceptsSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.Provide an appropriate response.26)Explain the differences between the interval and ratio levels of measurement.27)Explain why data expressed with the Celsius temperature scale is at the interval level of measurement ratherthan the ratio level.1.3Data Collection and Experimental Design1Decide Whether Study is Observational Study or ExperimentMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Determine whether the study is an observational study or an experiment.1)A medical researcher obtains a sample of adults suffering from diabetes. She randomly assigns 89people to atreatment group and 89 to a placebo group. The treatment group receives a medication over a period of threemonths and the placebo group receives a placebo over the same time frame. At the end of three months thepatientsʹ symptoms are evaluated.A)experiment B)observational study2)A poll is conducted in which professional musicians are asked their ages.A)observational study B)experiment3)A pollster obtains a sample of students and asks them how they will vote on an upcoming referendum.A)observational study B)experiment4)The personnel director at a large company would like to determine whether the company cafeteria is widelyused by employees. She calls each employee and asks them whether they usually bring their own lunch, eat at the company cafeteria, or go out for lunch.A)observational study B)experiment5)A scientist was studying the effects of a new fertilizer on crop yield. She randomly assigned half of the plots ona farm to group one and the remaining plots to group two. On the plots in group one, the new fertilizer wasused for a year. On the plots in group two, the old fertilizer was used. At the end of the year the average cropyield for the plots in group one was compared with the average crop yield for the plots in group two.A)experiment B)observational study6)A researcher obtained a random sample of 100 smokers and a random sample of 100 nonsmokers. Afterinterviewing all 200 participants in the study, the researcher compared the rate of depression among thesmokers with the rate of depression among nonsmokers.A)observational study B)experimentSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.Identify the experimental units and treatments used in the experiment.7)A medical researcher center wants to test the effectiveness of a new diabetes medication. The companyidentifies 98 adults suffering from a similar form of diabetes. The subjects are randomly assigned to twogroups. One group is given a medication and the other is given a placebo that looks exactly like the medication.After three months, the subjectsʹ symptoms are studied and compared.2Identify a Biased SampleSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.Provide an appropriate response.8)Explain what bias there is in a study done entirely online.9)A report sponsored by the California Citrus Commission stated that cholesterol levels can be lowered bydrinking at least one glass of a citrus product each day. Determine if the report is biased.10)A local newspaper ran a survey by asking, ʺDo you support the deployment of a weapon that could killmillions of innocent people?ʺ Determine whether the survey question is biased.3Identify Sampling TechniquesMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Identify the sampling technique used.11)Thirty-five sophomores, 30 juniors and 33seniors are randomly selected from 281 sophomores, 242juniors and529 seniors at a certain high school.A)stratified B)random C)cluster D)convenience E)systematic12)Every fifth person boarding a plane is searched thoroughly.A)systematic B)random C)cluster D)convenience E)stratified13)At a local community college, five statistics classes are randomly selected out of 20 and all of the students fromeach class are interviewed.A)cluster B)random C)convenience D)systematic E)stratified14)A researcher randomly selects and interviews fifty male and fifty female teachers.A)stratified B)random C)cluster D)convenience E)systematic15)A researcher for an airline interviews all of the passengers on five randomly selected flights.A)cluster B)random C)convenience D)systematic E)stratified16)A community college student interviews everyone in a particular statistics class to determine the percentage ofstudents that own a car.A)convenience B)random C)cluster D)systematic E)stratified17)Based on 12,500 responses from 36,500questionnaires sent to its alumni, a major university estimated that theannual salary of its alumni was $116,000 per year.A)random B)stratified C)cluster D)convenience E)systematic18)In a recent television survey, participants were asked to answer ʺyesʺ or ʺnoʺ to the question ʺAre you in favorof the death penalty?ʺ Six thousand five hundred responded ʺyesʺ while 4700 responded ʺnoʺ. There was afifty-cent charge for the call.A)convenience B)random C)cluster D)stratified E)systematic19)A lobbyist for a major airspace firm assigns a number to each legislator and then uses a computer to randomlygenerate ten numbers. The lobbyist contacts the legislators corresponding to these numbers.A)random B)convenience C)cluster D)stratified E)systematic20)To ensure customer satisfaction, every 20th phone call received by customer service will be monitored.A)systematic B)random C)cluster D)stratified E)convenience21)A market researcher randomly selects 400 drivers under 45years of age and 100 drivers over 45years of age.A)stratified B)random C)cluster D)convenience E)systematic22)To avoid working late, the quality control manager inspects the last 60 items produced that day.A)convenience B)random C)cluster D)stratified E)systematic23)The names of 70 contestants are written on 70 cards. The cards are placed in a bag, and three names are pickedfrom the bag.A)random B)stratified C)cluster D)convenience E)systematic24)A researcher randomly selected 70 of the nationʹs middle schools and interviewed all of the teachers at eachschool.A)cluster B)random C)stratified D)convenience E)systematicSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.Provide an appropriate response.25)After a hurricane, a disaster area is divided into 200 equal grids. Thirty of the grids are selected and everyoccupied household in the grid is interviewed to help focus relief efforts. Select the numbers of the first fivegrids that belong to the cluster sample.163487693890169513925588771015092097915726)There are 750 incoming freshmen attending a university this fall. A researcher wishes to send questionnaires toa sample of 30 of them to complete regarding their drinking habits. Select the numbers of the first fivefreshmen who belong to the simple random sample.163487693890169513925588771015092097915727)A college employs 85 faculty members. Without replacement, select the numbers of the five members who willserve on the tenure committee next year.163487693890169513925588771015092097915728)Of the 5000 outpatients released from a local hospital in the past year, one hundred were contacted and askedtheir opinion on the care they received. Select the first five patients who belong to the simple random sample.1634876938901695139255887710150920979157MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether you would take a census or use a sampling. If you would use a sampling, decide what sampling technique you would use.29)The average age of the 80 residents of an assisted living center.A)census B)random sampling C)stratified sampling D)cluster sampling 4ConceptsSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.Provide an appropriate response.30)Explain the differences between cluster sampling and stratified sampling.31)Explain the difference between a census and a sampling and describe the advantages and disadvantages ofeach.Chapter 1Introduction to StatisticsAnswer Key1.1An Overview of Statistics1Distinguish Between a Population and a Sample1)A2)A3)population: collection of all American households; sample: collection of 1212American households surveyed4)population: collection of all American households; sample: collection of 1348American households surveyed5)population: elementary school children; sample: collection of 2625 elementary school children surveyed.6)A2Distinguish Between a Parameter and a Statistic7)It describes a statistic because the number $130,000is based on a subset of the population.8)It describes a parameter because the $44,000is based on all the workers at the car manufacturer.9)It describes a statistic because the number 1040is based on a subset of the population.3Distinguish Between Descriptive Statistics and Inferential Statistics10)A11)A12)A13)A14)A4Concepts15)A population is the collection of all outcomes, responses, measurements, or counts that are of interest.. A sample is asubset of a population.16)A sample would be used. It is usually impractical to obtain all the population data.1.2Data Classification1Distinguish Between Qualitative and Quantitative Data1)A2)A3)A4)A2Classify Data with Respect to the Four Levels of Measurement5)A6)A7)A8)A9)A10)A11)A12)A13)A14)A15)A16)A17)A18)A19)A20)A21)A22)A23)A24)A25)A3Concepts26)Data at the ratio level are similar to data at the interval level, but with the added property that a zero entry is aninherent zero (implies ʺnoneʺ). Also, for data at the ratio level a ratio of two data values can be formed so that one data value can be expressed as a multiple of another.27)Such data is at the interval level rather than the ratio level because the temperature of 0°C does not represent acondition where no heat is present, so it is not an inherent zero as required by the ratio level. Also, ratios of twotemperatures cannot be formed so that one data value is expressed as a multiple of the other. The temperature 2°C is not twice as warm as 1°C.1.3Data Collection and Experimental Design1Decide Whether Study is Observational Study or Experiment1)A2)A3)A4)A5)A6)A7)The experimental units are the 98 adults in the study. The treatment is the new diabetes medication.2Identify a Biased Sample8)The study may be biased because it is limited to people with computers.9)A report sponsored by the citrus industry is much more likely to reach conclusions favorable to the industry.10)The wording of the question is biased, as it tends to encourage negative responses.3Identify Sampling Techniques11)A12)A13)A14)A15)A16)A17)A18)A19)A20)A21)A22)A23)A24)A25)163, 169, 15, 92, 9726)163, 487, 693, 169, 51327)16, 34, 69, 38, 1328)1634, 3890, 1695, 1392, 150929)A4Concepts30)In stratified sampling, members of the population are divided into two or more subsets, or strata, that share a similarcharacteristic. A sample is then randomly selected from each of the strata. A stratified sample has members from each segment of the population. In cluster sampling, the population is divided into naturally occurring subgroups, each having similar characteristics. All of the members in one or more (but not all) of the clusters are then selected. In a cluster sample, care must be taken to ensure that all clusters have similar characteristics.31)A census is a count or measure of an entire population, while a sampling is a count or measure of part of a population.A census provides complete information but is often expensive, difficult, and time consuming to perform especially ifthe population is large. A sampling is less expensive and time consuming, however appropriate sampling techniques must be used to ensure that unbiased data are collected and that the sample is representative of the population. Even with the best sampling methods, sampling error can occur.。

概率论与数理统计(英文) 第二章

2. Probability （概率）2.1 Sample Space 样本空间statistical experiment (random experiment)----repeating----more than one outcome----know all the outcomes, but don ’t predict whichoutcome will be occurexample :toss an honest coin---- In this experiment there are only two possible outcomes:{head}, {tail}toss two honest coins---- In this experiment there are 4 possible outcomes:{H, H}, {H, T}, {T, H}, {T, T}Each outcome in a sample space is called a sample point of the sample space.Example 2.1.1 Consider the experiment of tossing a die. If we are interested in the number thatshows on the top face, the sample space would be{}11,2,3,4,5,6S =If we are interested only in whether the numbers is even or odd, the sample space is simply{}2,S even odd =Example 2.1.3 An experiment consists of flipping a coin and then flipping it a second time if ahead occurs. If a tail occurs on the first flip then a die is tossing once. To list the elements of thesample space providing the most information,we construct a diagram of Fig 2.1.1, which is called a tree diagram. Now the various paths alongthe branches of the tree give the distinct sample points. Starting with the top left branch andmoving to the right along the first path, we get the sample point HH, indicating the possibility thatheads occurs on two successive flips of the coin. The possibility that coin will show a tail followedby a 4 on the toss of the die is indicated by T4. Thus the sample space is{,,1,2,3,4,5,6}S HH HT T T T T T T =Fig .2.1.1 Tree diagram for Example 2.1.3 Definition 2.2.1 An event is a subset of a sample space.Example 2.2.1 Given the sample space {|0}S t t =≥. where t is the life in hours of a certainbulb, we are interest in the event B that a bulb burnt out before 200 hrs, i.e. the subset{|0200}B t t =≤< of S .Example 2.2.2 Assume that the unemployment rate r of a region is between 0 and 15%，i.e. wehave the sample space {|00.15}S r r =≤≤. If the event C “unemployment rate is low ”means that 0.04r ≤, then we have the subset {|00.04}C r r =≤≤ of S .You may have known operation of subsets, i.e.the complement of a subset （余集）,the union of subset,(并集)the difference of subset （差集）intersection of subsets （交集）,so we can say about the complement of an event, the union, difference and intersection ofevents.certain event （必然事件）：The sample space S itself, is certainly an event, which is called a certain event, means thatit always occurs in the experiment.impossible event （不可能事件）：The empty set, denoted by ∅, is also an event, called an impossible event, means that it neveroccurs in the experiment.Example 2.2.3 Consider the experiment of tossing a die, then{1,2,3,4,5,6}S =Let x be the number that shows on the top face, then the event {|,10}A x x S x =∈≤, isthe certain event, i.e. A S =.Then even {|,B x x S x =∈ is an irrational number }, (irrational-无理数)is the impossible event, i.e.B =∅.Let be the event consisting of all even numbers and be the event consisting of numbers divisible by 3. Find A , ,,A B A B A B .Solution We have {2,4,6,8},{3,6,9}.A B ==Thus{1,3,5,7,9}A = {2,3,4,6,8,9}A B = {6}A B = {3,9}A B = The relationship between events and the corresponding sample space can be illustrated graphical by means of Venn diagrams. In a Venn diagram, we represent the sample space by a rectangle and represent events by circles drawn inside the rectangle.Example 2.2.5 In Figure 2.2.1A B = regions 1 and 2, A D = regions 1,2 ,3 ,4 ,5 and 7,A B D = regions 2, 6 and 7A B D 1234567Fig 2.2.1 Venn diagram of Example 2.2.5The following list summarizes the rules of the operations of events.1. A ∅=∅2. A A ∅=3. A A A =4. A A =∅5. A A S =6. S =∅7. S ∅=8. A A =9. _________A B A B =10. _________A B A B =11. AB B A = 12. ()()AB C A B C = 13. ()()()AB C A C B C = 14. ()()()A B C A C B C =2.3 Probability of events1. relative frequency --------probability用频率定义概率Considering an Example.We plant 100 untreated cotton seeds.If 49 seeds germinate, that is, if there are 49 success (by success in statistics we mean the occurrence of the event under discussion) in 100 trials, we say that the relative frequency of success is 0.49.If we plant more and more seeds, a whole sequence of values for the respective relative frequencies is obtained. In general, these relative frequencies approach a limit value, we call this limit the probability of success in a single trial. From the data of Table 2.3.1 it appears that the relative frequencies are approaching the value 0.51, which we call the probability of a cotton seedling emerging from an untreated seed.relative frequencies are approaching the value 0.5252.0→n salways 1. Similarly, the probability of the impossible event is 0, and the probability of any event is always between 0 and 1.Note. In this definition , the word“limit”has a meaning which is different from the meaning you may have learned in calculus. We will discuss this problem later.Example 2.3.1Select 200 bulbs produced by company X at random of them 150 having life longer than 300hrs. Find the probability that the bulbs produced by company X have life longer than 300hrs.Solution.1500.75200p==Jixie-9-42.”equally likely to occur”------probability（古典概率，有限、等可能性）In many cases, the probability may be stated without experience. If we toss a properly balanced coin, we believe that the probability of getting a head is 0.5. We make this statement since in tossing a properly balanced coin, only two outcomes are possible and both outcome areIt should be pointed out that this definition is in a sense circular in nature, since the expression “equally likely to occur”itself involves the idea of probability. However, since this term is generally intuitively understood, the concept of “equally likely” will be left undefined.Solution.The sample space S consists of 20 sample points. The event {A= a white ball is drawn}consists of 4 sample points, thus the probability of drawing a white ball is4()0.2P A==.Solution The sample space is{S =(,)|,m n m n are positive integers 6}≤thus S consists of 36 sample points .Let {A =getting a total of 9},{B =getting a total greater of 9}Then we have{(3,6),(4,5),(5,4),(6,3)}A ={(4,6),(5,5),(6,4),(5,6),(6,5),(6,6)}B =Thus41()369P A == , 61()366P B ==. where ()p A is the probability that the event A occurs ./*******/Example 2.3.4 抽球问题Consecutively draw ballFrom a big pack which contains a white balls and b black balls, a ball is consecutively draw at random. what is the probability that the ball which be drawn in m-th time is white?抽球问题袋中有a 个白球，b 个黑球，从中依次任取一个球，且每次取出的球不再放回去，求第m 次取出的球是白球的概率。