Understanding CI for Means Ayona Chatterjee Math 2063 University of West Georgia.

Slides:

Advertisements

Similar presentations

Chapter 6 Confidence Intervals.

Advertisements

Statistics Versus Parameters

Sampling: Final and Initial Sample Size Determination

CHAPTER 7.1 Confidence Intervals for the mean. ESTIMATION  Estimation is one aspect of inferential statistics. It is the process of estimating the value.

Hypothesis Testing I 2/8/12 More on bootstrapping Random chance

ESTIMATION AND HYPOTHESIS TESTING

Ch 6 Introduction to Formal Statistical Inference.

EPIDEMIOLOGY AND BIOSTATISTICS DEPT Esimating Population Value with Hypothesis Testing.

Chapter 11 Problems of Estimation

Estimation from Samples Find a likely range of values for a population parameter (e.g. average, %) Find a likely range of values for a population parameter.

1 Business 90: Business Statistics Professor David Mease Sec 03, T R 7:30-8:45AM BBC 204 Lecture 23 = Finish Chapter “Confidence Interval Estimation” (CIE)

Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc., 2000 LIND MASON MARCHAL 1-1 Chapter Seven Sampling Methods and Sampling Distributions GOALS When you.

Sampling Methods and Sampling Distributions Chapter.

Why sample? Diversity in populations Practicality and cost.

1 Business 90: Business Statistics Professor David Mease Sec 03, T R 7:30-8:45AM BBC 204 Lecture 22 = More of Chapter “Confidence Interval Estimation”

Chapter 7 Estimation Procedures. Chapter Outline  A Summary of the Computation of Confidence Intervals  Controlling the Width of Interval Estimates.

Lecture Slides Elementary Statistics Twelfth Edition

BCOR 1020 Business Statistics

 a fixed measure for a given population  ie: Mean, variance, or standard deviation.

Confidence Intervals W&W, Chapter 8. Confidence Intervals Although on average, M (the sample mean) is on target (or unbiased), the specific sample mean.

Standard error of estimate & Confidence interval.

Review of normal distribution. Exercise Solution.

Statistical Inference Dr. Mona Hassan Ahmed Prof. of Biostatistics HIPH, Alexandria University.

1/2555 สมศักดิ์ ศิวดำรงพงศ์

ESTIMATING with confidence. Confidence INterval A confidence interval gives an estimated range of values which is likely to include an unknown population.

Estimation of Statistical Parameters

Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc. Chap 8-1 Confidence Interval Estimation.

1 SAMPLE MEAN and its distribution. 2 CENTRAL LIMIT THEOREM: If sufficiently large sample is taken from population with any distribution with mean  and.

Inferences in Regression and Correlation Analysis Ayona Chatterjee Spring 2008 Math 4803/5803.

6.1 - One Sample One Sample  Mean μ, Variance σ 2, Proportion π Two Samples Two Samples  Means, Variances, Proportions μ 1 vs. μ 2.

Section 8.1 Estimating  When  is Known In this section, we develop techniques for estimating the population mean μ using sample data. We assume that.

Ch 8 Estimating with Confidence. Today’s Objectives ✓ I can interpret a confidence level. ✓ I can interpret a confidence interval in context. ✓ I can.

Statistical Interval for a Single Sample

MATH 1107 Elementary Statistics Lecture 8 Confidence Intervals for proportions and parameters.

Dan Piett STAT West Virginia University Lecture 9.

Estimating the Value of a Parameter Using Confidence Intervals

Ch 6 Introduction to Formal Statistical Inference

Large sample CI for μ Small sample CI for μ Large sample CI for p

Module 14: Confidence Intervals This module explores the development and interpretation of confidence intervals, with a focus on confidence intervals.

Section 8.2 ~ Estimating Population Means Introduction to Probability and Statistics Ms. Young.

 The point estimators of population parameters ( and in our case) are random variables and they follow a normal distribution. Their expected values are.

Review Normal Distributions –Draw a picture. –Convert to standard normal (if necessary) –Use the binomial tables to look up the value. –In the case of.

Chapter 7 Estimation Procedures. Basic Logic  In estimation procedures, statistics calculated from random samples are used to estimate the value of population.

Confidence Interval Estimation For statistical inference in decision making: Chapter 9.

Elementary Statistics

Chapter 7 Confidence Intervals and Sample Size McGraw-Hill, Bluman, 7 th ed., Chapter 7 1.

Chapter 7: Statistical Data Treatment & Evaluation CHE 321: Quantitative Chemical Analysis Dr. Jerome Williams, Ph.D. Saint Leo University.

INFERENCE Farrokh Alemi Ph.D.. Point Estimates Point Estimates Vary.

Lab Chapter 9: Confidence Interval E370 Spring 2013.

Chapter 9 – Statistical Estimation Statistical estimation involves estimating a population parameter with a sample statistic. Two types of estimation:

8.2 Estimating Population Means

Sampling Why use sampling? Terms and definitions

Target for Today Know what can go wrong with a survey and simulation

Inference: Conclusion with Confidence

Chapter 11: Simple Linear Regression

Week 10 Chapter 16. Confidence Intervals for Proportions

Towson University - J. Jung

Chapter Review Problems

Calculating Probabilities for Any Normal Variable

Estimating the Value of a Parameter Using Confidence Intervals

Confidence Intervals Accelerated Math 3.

Lecture 7 Sampling and Sampling Distributions

MATH 2311 Section 7.1.

Determining Which Method to use

Confidence Interval.

I can determine the different sampling techniques used in real life.

The Normal Distribution

How Confident Are You?.

MATH 2311 Section 7.1.

Presentation transcript:

Understanding CI for Means Ayona Chatterjee Math 2063 University of West Georgia

Why do we need CI? We want to estimate the mean of the population, since we cannot measure the whole population, we use sample mean to estimate the population mean. Assume we have a small city with 20 houses and this is our whole population. We want to find an estimate for the average house price in this city.

House Prices House prices The house prices for all the houses in the population are given in thousands of dollars. Here the population mean is In real life the population size is so large that we cannot find the true mean. There are about 90 million homes in USA. In 2007 the average house price in USA was

House prices Suppose we can only sample 10 houses from the population to find an estimate for the population mean. Sample 1 mean: 301

Suppose we can only sample 8 houses from the population to find an estimate for the population mean. Sample 1 mean: 301 Sample 2 mean: House prices

Suppose we can only sample 8 houses from the population to find an estimate for the population mean. Sample 1 mean: 301 Sample 2 mean: Sample 3 mean: House prices

Suppose we can only sample 8 houses from the population to find an estimate for the population mean. Sample 1 mean: 301 Sample 2 mean: Sample 3 mean: Sample 4 mean: House prices

Suppose we can only sample 8 houses from the population to find an estimate for the population mean. Sample 1 mean: 301 Sample 2 mean: Sample 3 mean: Sample 4 mean: Sample 5: mean: House prices

Note We have now five DIFFERENT estimates for the same population mean. Are all of the correct? How large or how small can the sample estimate get? It would be helpful to have an interval such that we can conclude that the population mean will lie within this interval with some confidence.

Confidence Interval A confidence interval is a range of values used to estimate the true value of a population parameter. A CI estimate of a parameter consists of an interval of numbers generated by a point estimate, together with an associated confidence level.

Confidence Level The confidence level is the probability 1-α that is the proportion of times the CI will actually contain the population parameter. Most common confidence levels are 90%, 95% and 99%. A 95% confidence interval means that in the long run, the proportion of intervals that will contain the parameter will equal 95%.