5.4 Sampling Distributions and the Central Limit Theorem Key Concepts: –How to find sampling distributions and verify their properties –The Central Limit.

Slides:

Advertisements

Similar presentations

Sampling: Final and Initial Sample Size Determination

Advertisements

Sampling Distributions (§ )

Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide

Sampling distributions. Example Take random sample of students. Ask “how many courses did you study for this past weekend?” Calculate a statistic, say,

CHAPTER 8: Sampling Distributions

Section 5.3 Normal Distributions: Finding Values.

Chapter Six Sampling Distributions McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.

T T Population Sampling Distribution Purpose Allows the analyst to determine the mean and standard deviation of a sampling distribution.

Standard Normal Distribution

Lesson #17 Sampling Distributions. The mean of a sampling distribution is called the expected value of the statistic. The standard deviation of a sampling.

T T07-01 Sample Size Effect – Normal Distribution Purpose Allows the analyst to analyze the effect that sample size has on a sampling distribution.

PROBABILITY AND SAMPLES: THE DISTRIBUTION OF SAMPLE MEANS.

Today Today: Chapter 8, start Chapter 9 Assignment: Recommended Questions: 9.1, 9.8, 9.20, 9.23, 9.25.

The Central Limit Theorem For simple random samples from any population with finite mean and variance, as n becomes increasingly large, the sampling distribution.

Clt1 CENTRAL LIMIT THEOREM  specifies a theoretical distribution  formulated by the selection of all possible random samples of a fixed size n  a sample.

Sample Distribution Models for Means and Proportions

Normal and Sampling Distributions A normal distribution is uniquely determined by its mean, , and variance,  2 The random variable Z = (X-  /  is.

Probability and the Sampling Distribution Quantitative Methods in HPELS 440:210.

Chapter 6: Sampling Distributions

AP Statistics Chapter 9 Notes.

Introduction to Statistical Inference Chapter 11 Announcement: Read chapter 12 to page 299.

AP Statistics 9.3 Sample Means.

Copyright © Cengage Learning. All rights reserved. 7 Sample Variability.

Normal Probability Distributions Chapter 5. § 5.4 Sampling Distributions and the Central Limit Theorem.

Normal Probability Distributions

Chapter 10 – Sampling Distributions Math 22 Introductory Statistics.

Chapter 7: Sample Variability Empirical Distribution of Sample Means.

Statistics Workshop Tutorial 5 Sampling Distribution The Central Limit Theorem.

Statistics 300: Elementary Statistics Section 6-5.

The Central Limit Theorem and the Normal Distribution.

Section 5.4 Sampling Distributions and the Central Limit Theorem Larson/Farber 4th ed.

Lecture 2 Review Probabilities Probability Distributions Normal probability distributions Sampling distributions and estimation.

Population and Sample The entire group of individuals that we want information about is called population. A sample is a part of the population that we.

Chapter 7 Sampling and Sampling Distributions ©. Simple Random Sample simple random sample Suppose that we want to select a sample of n objects from a.

Chapter 7: Introduction to Sampling Distributions Section 2: The Central Limit Theorem.

Section 6-5 The Central Limit Theorem. THE CENTRAL LIMIT THEOREM Given: 1.The random variable x has a distribution (which may or may not be normal) with.

8 Sampling Distribution of the Mean Chapter8 p Sampling Distributions Population mean and standard deviation,  and   unknown Maximal Likelihood.

BUS216 Spring  Simple Random Sample  Systematic Random Sampling  Stratified Random Sampling  Cluster Sampling.

Estimation Chapter 8. Estimating µ When σ Is Known.

Sampling Error SAMPLING ERROR-SINGLE MEAN The difference between a value (a statistic) computed from a sample and the corresponding value (a parameter)

PSY 307 – Statistics for the Behavioral Sciences Chapter 9 – Sampling Distribution of the Mean.

Chapter 18: Sampling Distribution Models

SAMPLING DISTRIBUTIONS

Chapter 5 Sampling Distributions. The Concept of Sampling Distributions Parameter – numerical descriptive measure of a population. It is usually unknown.

Chapter 18: The Central Limit Theorem Objective: To apply the Central Limit Theorem to the Normal Model CHS Statistics.

Chapter 9 Inferences Based on Two Samples: Confidence Intervals and Tests of Hypothesis.

Sampling Distributions

MATH Section 4.4.

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.

THE CENTRAL LIMIT THEOREM. Sampling Distribution of Sample Means Definition: A distribution obtained by using the means computed from random samples of.

Kuliah 6: Taburan Persampelan

Chapter 6: Sampling Distributions

Sampling and Sampling Distributions

Ch5.4 Central Limit Theorem

Chapter 7 Review.

Section 7.1 Central Limit Theorem

Central Limit Theorem Sample Proportions.

Introduction to Sampling Distributions

Sec. 7-5: Central Limit Theorem

Chapter 6: Sampling Distributions

Chapter 18: Sampling Distribution Models

Statistics in Applied Science and Technology

Probability and the Sampling Distribution

CENTRAL LIMIT THEOREM specifies a theoretical distribution

Sampling Distributions

Central Limit Theorem Accelerated Math 3.

Sampling Distributions (§ )

Quantitative Methods Varsha Varde.

Review of Hypothesis Testing

How Confident Are You?.

Presentation transcript:

5.4 Sampling Distributions and the Central Limit Theorem Key Concepts: –How to find sampling distributions and verify their properties –The Central Limit Theorem –Using the Central Limit Theorem to find probabilities

5.4 Sampling Distributions and the Central Limit Theorem What is a sampling distribution? –The probability distribution of a sample statistic that is formed when samples of size n are repeatedly taken from a population. Examples of sample statistics:

5.4 Sampling Distributions and the Central Limit Theorem Properties of sampling distributions of sample means: 1. The mean of the sample means,, is equal to the population mean : 2. The standard deviation of the sample means,, is proportional to σ : (valid when n ≤ 0.05N) Note: is known as the standard error of the mean.

According to Forbes Magazine, the top five wealthiest women in the world in 2010 were: Christy Walton: $22.5 billion Alice Walton: $20.6 billion Liliane Bettencourt: $20.0 billion Birgit Rausing: $13.0 billion Savitri Jindal: $12.2 billion 1. Let X = wealth (in billions of dollars). Find the mean and standard deviation of X.

5.4 Sampling Distributions and the Central Limit Theorem 2. List all possible samples of size 2 from this population of 5 and list the sample mean for each sample. 3. Find the mean and standard deviation of the sample means in column three. SampleWealth Sample Mean {C, A }22.5, { C,L }22.5, { C,B }22.5, { C,S }22.5, { A,L }20.6, { A,B}20.6, { A,S }20.6, { L,B }20.0, { L,S }20.0, { B,S }13.0,

5.4 Sampling Distributions and the Central Limit Theorem Where does the Central Limit Theorem fit in? –We use the CLT to make a statement about the shape of the distribution of the sample means (see p. 263) If samples of size 30 or more are drawn from any population with mean µ and standard deviation σ, then the sampling distribution of the sample means will be approximately normal. If the population itself is normally distributed, then the sampling distribution of the sample means is normally distributed for any sample size n.

5.4 Sampling Distributions and the Central Limit Theorem Practice using the Central Limit Theorem #10 p. 270 (Annual Snowfall) #24 p. 271 (Canned Vegetables) #30 p. 272 (Gas Prices: California) #36 p. 272 (Make a Decision)