应用统计学英文课件 Business Statistics Ch08 Confidence Interval Estimation
合集下载
应用统计学PPT课件
10
2018/11/22
一、统计涵义
Statistics: （1）Numeric data, when used as plural of statistic. （2）A scientific procedure used in the study and evaluation of numeric data.
19
经 济 统 计
社 会 统 计
教 育 统 计
统
计
学
物 理 统 计
生 物 统 计
医 药 统 计
2018/11/22
2 统计学对象方法
对象：实质性学科与方法论学科
理论统计学与应用统计学
方法：特殊方法论与通用方法论
描述统计学与推断统计学
大量观察，平均分析，归纳推断
2018/11/22
20
统计学家与数学家的对话
数据→信息→知识→智慧
2018/11/22 15
四、统计科学 1 统计学发展简史 2 统计学对象方法 3 统计学基本概念
2018/11/22
16
1 统计学发展简史
英国（1690），威廉· 配第，政治算术 德国（1749），阿亨瓦尔，国势学 比利时（19世纪中），凯特勒，数理统计 德国（19世纪中），恩格尔，社会统计
2018/11/22 32
第三章 统计整理
一、整理程序 二、统计分组
三、频数分布 四、统计图表
格 罗 夫 纳
数 字 不 会 说 谎 ， 但 说 谎 的 人 会 想 出 办 法 。
33
2018/11/22
一、整理程序
审核：计算审核，逻辑审核 分组：分类，分组 汇总：手工汇总，电子汇总 表现：列表，图示
2018/11/22
一、统计涵义
Statistics: （1）Numeric data, when used as plural of statistic. （2）A scientific procedure used in the study and evaluation of numeric data.
19
经 济 统 计
社 会 统 计
教 育 统 计
统
计
学
物 理 统 计
生 物 统 计
医 药 统 计
2018/11/22
2 统计学对象方法
对象：实质性学科与方法论学科
理论统计学与应用统计学
方法：特殊方法论与通用方法论
描述统计学与推断统计学
大量观察，平均分析，归纳推断
2018/11/22
20
统计学家与数学家的对话
数据→信息→知识→智慧
2018/11/22 15
四、统计科学 1 统计学发展简史 2 统计学对象方法 3 统计学基本概念
2018/11/22
16
1 统计学发展简史
英国（1690），威廉· 配第，政治算术 德国（1749），阿亨瓦尔，国势学 比利时（19世纪中），凯特勒，数理统计 德国（19世纪中），恩格尔，社会统计
2018/11/22 32
第三章 统计整理
一、整理程序 二、统计分组
三、频数分布 四、统计图表
格 罗 夫 纳
数 字 不 会 说 谎 ， 但 说 谎 的 人 会 想 出 办 法 。
33
2018/11/22
一、整理程序
审核：计算审核，逻辑审核 分组：分类，分组 汇总：手工汇总，电子汇总 表现：列表，图示
商务统计学英文课件 (9)
e = the mathematical constant approximated by 2.71828 π = the mathematical constant approximated by 3.14159 Z = any value of the standardized normal distribution
n To use the normal probability plot to determine whether a set of data is approximately normally distributed
Continuous Probability Distributions
n A continuous random variable is a variable that can assume any value on a continuum (can assume an uncountable number of values)
X 8.0
8.6
Finding Normal Probabilities
(continued)
n Let X represent the time it takes to download an image file from the internet.
n Suppose X is normal with mean 8.0 and standard deviation 5.0. Find P(X < 8.6)
The random variable has an infinite theoretical range: + to
σ X
μ
Mean = Median = Mode
商务统计学最新英文版教学课件第4章
Venn Diagram For All Days In 2015
Sample Space (All Days In 2015)
Days That Are In January and Are Wednesdays
January Days
Wednesdays
Organizing & Visualizing Events
A = Weekday; B = Weekend; C = January; D = Spring;
Events A, B, C and D are collectively exhaustive (but not mutually exclusive – a weekday can be in January or in Spring)
total number of days in 2015
365
Jan.
Wed.
4
Not Wed. 27
Total
31
Not Jan. 48 286 334
Total 52 313 365
Marginal Probability Example
P(Wed.)
P(Jan.and Wed.) P(Not Jan.and Wed.) 4 48 52 365 365 365
(continued)
Contingency Tables -- For All Days in 2015
Jan. Not Jan. Total
Wed.
4
48
52
Not Wed. 27
286
313
Total
Decision Trees
Sample Space
应用统计学 第一课 英文
2
Keep in Touch
If you have a question, you are STRONGLY encouraged to ASK IT IN CLASS. You are probably not the only one that needs the question answered, and other students may benefit from your questions, too. Check our course website regularly. Announcements, assignments, and solutions etc will be posted online regularly. Drop by during office hours or book another time to see me in my office.
x P(x)
0.00 0.05 0.12 0.30 0.52
E ( X ) xi P( xi )
i 1
8
= 4.71 rooms
5
6 7 Total
0.20
0.15 0.26 1.00
1.00
0.90 1.82 = 4.71
14
Example: Bed and Breakfast
Business Data Analysis
73-102 Lecture 01
1
Agenda
Go through Course Outline (on CLEW) Brief Introduction to Statistics Review of Random Variable Review of Normal Distribution
应用统计学PPT课件
30.07.2020
15
数据计量
定距尺度是对现象类别或次序之间间距的测度。定距尺度不 但可以用数表示现象各类别的不同和顺序大小的差异，而且 可以用确切的数值反映现象之间在量方面的差异。定距尺度 使用的计量单位一般为实物单位（自然或物理）或者价值单 位。定距尺度的主要数学特征是“+”或“–”。统计中的总 量指标就是运用定距尺度计量的。
定比尺度是在定距尺度的基础上，确定相应的比较基数，然 后将两种相关的数加以对比而形成相对数(或平均数)，用于 反映现象的结构、比重、速度、密度等数量关系。例如，将 一个企业创造的增加值与该企业的职工人数对比，计算全员 劳动生产率，以此反映该企业的生产效率。定比尺度的主要 数学特征是“×”或“÷”。
数据计量：定类、定序，定距、定比。 定类尺度是按照客观现象的某种属性对其进行分
类。例如，人口按性别分为男女，用“1” 表示男 性，用“0” 表示女性。定类尺度的主要数学特征 是“=”或“≠”。 定序尺度是对客观现象各类之间的等级差或顺序 差的一种测度。例如，学生成绩可以分为优、良、 中、及格和不及格等五类。定序尺度的主要数学 特征是“<”或“>”。
30.07.2020
在在在
应用统计学
理抽终 性象极 的的的
基意分
础义析
上下中
，，，
所一一
有切切
的都知
判是识
断科都
C.R.
都学是
是数历
劳 统学史
计
学
1
整体概述
概况一
点击此处输入相关文本内容 点击此处输入相关文本内容
概况二
点击此处输入相关文本内容 点击此处输入相关文本内容
概况三
点击此处输入相关文本内容 点击此处输入相关文本内容
商务统计英文课件 (8)
§ A histogram with one peak is unimodal; two is bimodal; three or more is multimodal
§ A flat histogram with all bars about the same height is uniform
4.1 Summaries of Numerical Variables
The Variance
s 2 y1 y 2 y2 y 2 y n y 2
n 1
4.1 Summaries of Numerical Variables
The Standard Deviation (SD)
4.1 Summaries of Numerical Variables
The Mean (Average)
§ Arithmetic average; divide the sum of the values by the number of values (another typical value)
cv
s y
4M Example 4.1: MAKING M&M’s
Mechanics
Mean Weight = 0.86 gm SD = 0.04 gm
Cv = 0.04 gm / 0.86 gm = 0.0465
4M Example 4.1: MAKING M&M’s
Message
Since the SD is quite small compared to the mean (with a cv of about 5%) the results suggest that 53 pieces are usually enough to fill a bag.
§ A flat histogram with all bars about the same height is uniform
4.1 Summaries of Numerical Variables
The Variance
s 2 y1 y 2 y2 y 2 y n y 2
n 1
4.1 Summaries of Numerical Variables
The Standard Deviation (SD)
4.1 Summaries of Numerical Variables
The Mean (Average)
§ Arithmetic average; divide the sum of the values by the number of values (another typical value)
cv
s y
4M Example 4.1: MAKING M&M’s
Mechanics
Mean Weight = 0.86 gm SD = 0.04 gm
Cv = 0.04 gm / 0.86 gm = 0.0465
4M Example 4.1: MAKING M&M’s
Message
Since the SD is quite small compared to the mean (with a cv of about 5%) the results suggest that 53 pieces are usually enough to fill a bag.
应用统计学英文课件 Business Statistics Ch03 Numerical Descriptive Measures
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Mode = 9
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
0123456
No Mode
Chap 3-11
Measures of Central Tendency: The Mode
Chap 3-13
Measures of Central Tendency: Which Measure to Choose?
The mean is generally used, unless extreme values (outliers) exist.
The median is often used, since the median is not sensitive to extreme values. For example, median home prices may be reported for a region; it is less sensitive to outliers.
Chap 3-8
Measures of Central Tendency: Locating the Median
If the number of values is even, the median is the average of the two middle numbers
Note that n 1 is not the value of the median, 2
Mean = sum of values divided by the number of values
应用统计学PPT课件
统计应用
质量管理中的6
统计在许多领域都有应用:在统计中，表示一个总体的标 准差，它说的是数据之间的差异程度。比如，在企业生产 的产品中，同一种产品也没有两个是完全一样的，因为在 生产过程中，由于各种因素的影响而使产品质量产生波动。 在服务领域就更是如此。产品或服务的这种差异称为质量 的波动性，也正是由于波动性的存在才需要进行质量管理
一个统计顾问提交给茶叶委员会的报告中，含 有标题为“饮茶人数的估计值(含标准误差)”的 附表。不久，一封信被送到这个统计学者手中， 问道什么是人们喝红茶时的“标准误差”
1-8
2019-7-11
应用统计学
Applied Statistics
理解统计对管理者更重要
皇家委员会审查一份统计报告，报告中提到中产阶级 家庭平均有2.2个子女，委员会评述说：“每一个成人 女性有2.2个子女的数字是荒谬的。这是为要求对中产 阶级提供财政援助以便通过四舍五入把平均值提高到 一个更合适的整数
避免尴尬
☻假定你是市场部的新任经理，一次广告活动的统 计结果摆到了你面前，声称某个结果是“统计显著 ”的。你如何解释这份报告而又是暴露你对该术语 的无知？
赶快学点统计，这对你和你的事业都非常有用。
Gudmund R. Iversen
1 - 10
2019-7-11
应用统计学
Applied Statistics 几乎所有的领域都要用统计
应用统计学
Applied Statistics
应用统计学
Applied Statistics
1-1
2019-7-11
应用统计学
Applied Statistics
统计名言
统计思维总有一天会像读与写一样 成为一个有效率公民的必备能力。
商务统计学最新英文版教学课件第6章
Z X μ 18.6 18.0 0.12
σ
5.0
μ = 18 σ= 5
μ=0 σ= 1
18 18.6
X
P(X < 18.6)
0 0.12
Z
P(Z < 0.12)
Solution: Finding P(Z < 0.12)
Standardized Normal Probability Table (Portion)
The standardized normal distribution (Z) has a mean of 0 and a standard deviation of 1
Translation to the Standardized Normal Distribution
Translate from X to the standardized normal (the “Z” distribution) by subtracting the mean of X and dividing by its standard deviation:
f(Z) 1 e(1/2)Z2 2π
Where
e = the mathematical constant approximated by 2.71828 π = the mathematical constant approximated by 3.14159 Z = any value of the standardized normal distribution
Any normal distribution (with any mean and standard deviation combination) can be transformed into the standardized normal distribution (Z)
应用统计学英文课件BusinessStatisticsCh08ConfidenceIntervalEstima
Chapter Problem
Saxon Home Improvement
Saxon Home Improvement
Learning Objectives
In this chapter, you learn:
To construct and interpret confidence interval estimates for the mean and the proportion
Point Estimates
We can estimate a Population Parameter …
Mean
μ
Proportion
π
with a Sample Statistic
(a Point Estimate)
X
p
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Point and Interval Estimates
A point estimate is a single number a confidence interval provides additional
information about the variability of the estimate
Business Statistics: A First Course
5th Edition
Chapter 8
Confidence Interval Estimation
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc.
Chap 8-1
Chap 8-7
统计学英文教学课件Chapter 1(商科)What is Statistics
Judgement Convenience
Probability Samples
Simple Random
Systematic
Stratified
Cluster
16
Simple Random Sampling
• Every possible subset of n units has the same chance of being selected
and levels of measurement 3. Describe key data collection methods 4. Identify common sampling methods 5. Distinguish the different areas of statistics 6. Explain why you study statistics
11
Data Collection Issues - Errors
Sampling
Bad Luck
Non-sampling
Interviewer/Instrument Bias Non-response Bias Selection Bias Interviewee Lie Measurement Error Observer Bias
8
Levels of Measurement
Interval
Similar to ordinal data, WITH differences between data values being meaningful, BUT ratio of two data values not meaningful
N/n = 5000/200 = 25. Select a random number from 1 to 25. Suppose you randomly select the 16th student. Then select every 25th student from there: 41, 66, 91, …
Probability Samples
Simple Random
Systematic
Stratified
Cluster
16
Simple Random Sampling
• Every possible subset of n units has the same chance of being selected
and levels of measurement 3. Describe key data collection methods 4. Identify common sampling methods 5. Distinguish the different areas of statistics 6. Explain why you study statistics
11
Data Collection Issues - Errors
Sampling
Bad Luck
Non-sampling
Interviewer/Instrument Bias Non-response Bias Selection Bias Interviewee Lie Measurement Error Observer Bias
8
Levels of Measurement
Interval
Similar to ordinal data, WITH differences between data values being meaningful, BUT ratio of two data values not meaningful
N/n = 5000/200 = 25. Select a random number from 1 to 25. Suppose you randomly select the 16th student. Then select every 25th student from there: 41, 66, 91, …
应用统计学英文课件 Business Statistics Ch03 Numerical Descriptive Measures
Me pd oi s a n in 1 tp io on is n tih o tie r od d ne arte 2
If the number of values is odd, the median is the middle number
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Standard Deviation
Coefficient of Variation
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Same center, different variation
Chap 3-16
Measures of Variation: The Range
In some situations it makes sense to report both the mean and the median.
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Chap 3-14
12.3 12.1 12.2 12.3 12.2
Hale Waihona Puke x x1.3 21.1 21.21.3 21.21.22
n
5
Th meeaneiv s1o2lo .u 2zm 2 .
Measures of Central Tendency:
The Mean
(continued)
The most common measure of central tendency
If the number of values is odd, the median is the middle number
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Standard Deviation
Coefficient of Variation
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Same center, different variation
Chap 3-16
Measures of Variation: The Range
In some situations it makes sense to report both the mean and the median.
Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc.
Chap 3-14
12.3 12.1 12.2 12.3 12.2
Hale Waihona Puke x x1.3 21.1 21.21.3 21.21.22
n
5
Th meeaneiv s1o2lo .u 2zm 2 .
Measures of Central Tendency:
The Mean
(continued)
The most common measure of central tendency
统计学课件-英文版
LO4-1: Explain the concepts of center, variability, and shape.
Three key characteristics of numerical data:
4-5
Chapter 4
LO4-2
4.1 Numerical Description
LO4-2: Use Excel to obtain descriptive statistics and visual displays.
•
For the J.D. Power quality data:
•
Here, the midrange (126.5) is higher than the mean (114.70) or median (113).
4-14
Chapter 4
LO4-3
4.2 Measures of Center
Growth Rates A variation on the geometric mean used to find the average growth rate for a time series.
4-12
Chapter 4
LO4-3
4.2 Measures of Center
Year Revenue (mil)
Formulas> Insert Function (������������ ) >Statistical>MEDIAN
4-9
Chapter 4
LO4-3 Mode
• • •
4.2 Measures of Center
The most frequently occurring data value. May have multiple modes or no mode. The mode is most useful for discrete or categorical data with only a few distinct data values. For continuous data or data with a wide range, the mode is rarely useful.
商务统计学课件第1章(ISEC)
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Hale Waihona Puke Chap 1-4附注在商业世界中，统计学有4种重要的应用。
· 总结商业数据 · 根据数据得出结论 · 作出商业行动的可靠预测 · 改进运营过程
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 1-10
为什么要收集数据？
市场调研者需要了解一个新的旅游产品的效果； 消费者的消费行为方面的信息数据，如：消费者购买产 品的花费、选择的产品渠道、偏好产品的类型、产品使 用周期、购买产品的目的、消费者家庭背景、工作和生 活环境、个人消费观和价值观等。如果企业收集到了这 些数据，建立消费者大数据库，便可通过统计和分析来 掌握消费者的消费行为、兴趣偏好和产品的市场口碑现 状，再根据这些总结出来的行为、兴趣爱好和产品口碑 现状制定有针对性的营销方案和营销战略，投消费者所 好，那么其带来的营销效应是可想而知的。
Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc.
Chap 1-16
Types of Data（数据类型）
Data
（属性） Categorical
Examples:
Numerical （数值）
gender belief (Defined categories) 定义属性类别
Probability Theory & Mathematical Statistics 概率论与数理统计
相关主题
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
Note: 95% confidence is based on the fact that we used Z = 1.96.
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 8-13
Estimation Process
No probability involved in a specific interval
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 8-17
Confidence Intervals
Confidence Intervals
correct statement about µ.
But what about the intervals from other possible samples of size 25?
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
368 ± 1.96 * 15 / 25 = (362.12, 373.88) contains 95% of the sample means
When you don’t know µ, you use X to estimate µ
If X = 362.3 the interval is 362.3 ± 1.96 * 15 / 25 = (356.42, 368.18) Since 356.42 ≤ µ ≤ 368.18, the interval based on this sample makes a
Assumptions Population standard deviation σ is known Population is normally distributed If population is not normal, use large sample
Random Sample
Population
(mean, μ, is unknown)
Mean X = 50
Sample
I am 95% confident that μ is between 40 & 60.
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
• Critical Value is a table value based on the sampling distribution of the point estimate and the desired confidence level
• Standard Error is the standard deviation of the point estimate
Such interval estimates are called confidence intervals
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 8-8
Confidence Interval Estimate
Chapter Problem
Saxon Home Improvement
Saxon Home Improvement
Learning Objectives
In this chapter, you learn:
To construct and interpret confidence interval estimates for the mean and the proportion
Point and Interval Estimates
A point estimate is a single number a confidence interval provides additional
information about the variability of the estimate
(continued)
In practice you only take one sample of size n In practice you do not know µ so you do not
know if the interval actually contains µ However you do know that 95% of the intervalrmula
The general formula for all confidence intervals is:
Point Estimate ± (Critical Value)(Standard Error)
Where: • Point Estimate is the sample statistic estimating the population parameter of interest
formed in this manner will contain µ Thus, based on the one sample, you actually
selected you can be 95% confident your interval will contain µ (this is a 95% confidence interval)
Gives information about closeness to unknown population parameters
Stated in terms of level of confidence
e.g. 95% confident, 99% confident Can never be 100% confident
Chap 8-4
Chapter Outline
Content of this chapter
Confidence Intervals for the Population Mean, μ when Population Standard Deviation σ is Known when Population Standard Deviation σ is Unknown
95% of all the confidence intervals that can be constructed will contain the unknown true parameter
A specific interval either will contain or will not contain the true parameter
Lower Confidence Limit
Point Estimate Width of
confidence interval
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Upper Confidence Limit
Chap 8-6
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 8-15
Confidence Level
Confidence Level The confidence that the interval will contain the unknown population parameter A percentage (less than 100%)
Chap 8-10
Confidence Interval Example
(continued)
Sample #
X
Lower Limit
Upper Limit
Contain µ?
1
362.30 356.42 368.18
Yes
2
369.50 363.62 375.38
Yes
3
360.00 354.12 365.88
An interval gives a range of values:
Takes into consideration variation in sample statistics from sample to sample
Based on observations from 1 sample
Business Statistics: A First Course
5th Edition
Chapter 8
Confidence Interval Estimation
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc.
Chap 8-1
Population Mean
Population Proportion
σ Known σ Unknown
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 8-18
Confidence Interval for μ (σ Known)
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 8-9
Confidence Interval Example
Cereal fill example Population has µ = 368 and σ = 15. If you take a sample of size n = 25 you know
Chap 8-7
Confidence Intervals
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 8-13
Estimation Process
No probability involved in a specific interval
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 8-17
Confidence Intervals
Confidence Intervals
correct statement about µ.
But what about the intervals from other possible samples of size 25?
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
368 ± 1.96 * 15 / 25 = (362.12, 373.88) contains 95% of the sample means
When you don’t know µ, you use X to estimate µ
If X = 362.3 the interval is 362.3 ± 1.96 * 15 / 25 = (356.42, 368.18) Since 356.42 ≤ µ ≤ 368.18, the interval based on this sample makes a
Assumptions Population standard deviation σ is known Population is normally distributed If population is not normal, use large sample
Random Sample
Population
(mean, μ, is unknown)
Mean X = 50
Sample
I am 95% confident that μ is between 40 & 60.
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
• Critical Value is a table value based on the sampling distribution of the point estimate and the desired confidence level
• Standard Error is the standard deviation of the point estimate
Such interval estimates are called confidence intervals
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 8-8
Confidence Interval Estimate
Chapter Problem
Saxon Home Improvement
Saxon Home Improvement
Learning Objectives
In this chapter, you learn:
To construct and interpret confidence interval estimates for the mean and the proportion
Point and Interval Estimates
A point estimate is a single number a confidence interval provides additional
information about the variability of the estimate
(continued)
In practice you only take one sample of size n In practice you do not know µ so you do not
know if the interval actually contains µ However you do know that 95% of the intervalrmula
The general formula for all confidence intervals is:
Point Estimate ± (Critical Value)(Standard Error)
Where: • Point Estimate is the sample statistic estimating the population parameter of interest
formed in this manner will contain µ Thus, based on the one sample, you actually
selected you can be 95% confident your interval will contain µ (this is a 95% confidence interval)
Gives information about closeness to unknown population parameters
Stated in terms of level of confidence
e.g. 95% confident, 99% confident Can never be 100% confident
Chap 8-4
Chapter Outline
Content of this chapter
Confidence Intervals for the Population Mean, μ when Population Standard Deviation σ is Known when Population Standard Deviation σ is Unknown
95% of all the confidence intervals that can be constructed will contain the unknown true parameter
A specific interval either will contain or will not contain the true parameter
Lower Confidence Limit
Point Estimate Width of
confidence interval
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Upper Confidence Limit
Chap 8-6
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 8-15
Confidence Level
Confidence Level The confidence that the interval will contain the unknown population parameter A percentage (less than 100%)
Chap 8-10
Confidence Interval Example
(continued)
Sample #
X
Lower Limit
Upper Limit
Contain µ?
1
362.30 356.42 368.18
Yes
2
369.50 363.62 375.38
Yes
3
360.00 354.12 365.88
An interval gives a range of values:
Takes into consideration variation in sample statistics from sample to sample
Based on observations from 1 sample
Business Statistics: A First Course
5th Edition
Chapter 8
Confidence Interval Estimation
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc.
Chap 8-1
Population Mean
Population Proportion
σ Known σ Unknown
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 8-18
Confidence Interval for μ (σ Known)
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 8-9
Confidence Interval Example
Cereal fill example Population has µ = 368 and σ = 15. If you take a sample of size n = 25 you know
Chap 8-7
Confidence Intervals