Distribution of Sample Means 2011, 10, 20. Today ’ s Topics What is distribution of sample means?** Properties of distribution of sample means* How to.

Slides:

Advertisements

Similar presentations

Probability and Samples: The Distribution of Sample Means

Advertisements

Exponential Distribution. = mean interval between consequent events = rate = mean number of counts in the unit interval > 0 X = distance between events.

Sampling: Final and Initial Sample Size Determination

Sampling Distributions (§ )

Chapter 10: Sampling and Sampling Distributions

The Central Limit Theorem Today, we will learn a very powerful tool for sampling probabilities and inferential statistics: The Central Limit Theorem.

5.2 The Sampling Distribution of a Sample Mean

Distribution of Sample Means, the Central Limit Theorem If we take a new sample, the sample mean varies. Thus the sample mean has a distribution, called.

Statistics for the Social Sciences Psychology 340 Spring 2005 Sampling distribution.

Statistics Lecture 20. Last Day…completed 5.1 Today Parts of Section 5.3 and 5.4.

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 6-1 Introduction to Statistics Chapter 7 Sampling Distributions.

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

PROBABILITY AND SAMPLES: THE DISTRIBUTION OF SAMPLE MEANS.

6-5 The Central Limit Theorem

Chapter 7 Probability and Samples: The Distribution of Sample Means

Chapter 11: Random Sampling and Sampling Distributions

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.

Continuous Probability Distributions

From Last week.

Dan Piett STAT West Virginia University

AP Statistics Chapter 9 Notes.

Chap 6-1 A Course In Business Statistics, 4th © 2006 Prentice-Hall, Inc. A Course In Business Statistics 4 th Edition Chapter 6 Introduction to Sampling.

Chapter 11 – 1 Lecture 7 How certain are we? Sampling and the normal distribution.

Probability and Samples

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 6-1 Business Statistics: A Decision-Making Approach 6 th Edition Chapter.

Agresti/Franklin Statistics, 1e, 1 of 139  Section 6.4 How Likely Are the Possible Values of a Statistic? The Sampling Distribution.

Chapter 10 – Sampling Distributions Math 22 Introductory Statistics.

Distribution of the Sample Means

Statistics Workshop Tutorial 5 Sampling Distribution The Central Limit Theorem.

Statistics 300: Elementary Statistics Section 6-5.

Determination of Sample Size: A Review of Statistical Theory

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

Chapter 6.3 The central limit theorem. Sampling distribution of sample means A sampling distribution of sample means is a distribution using the means.

BUS304 – Chapter 6 Sample mean1 Chapter 6 Sample mean  In statistics, we are often interested in finding the population mean (µ):  Average Household.

Slide Slide 1 Section 6-5 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.

6.3 THE CENTRAL LIMIT THEOREM. DISTRIBUTION OF SAMPLE MEANS  A sampling distribution of sample means is a distribution using the means computed from.

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

Chapter 7 Statistical Inference: Estimating a Population Mean.

1 Competence and a new baby, M | mastery baby | 0 1 | Total | | 151 | | |

Chapter 7: The Distribution of Sample Means. Frequency of Scores Scores Frequency.

Sampling Theory and Some Important Sampling Distributions.

Lecture 5 Introduction to Sampling Distributions.

STA 2023 Section 5.4 Sampling Distributions and the Central Limit Theorem.

Distributions of Sample Means. z-scores for Samples  What do I mean by a “z-score” for a sample? This score would describe how a specific sample is.

Sec 6.3 Bluman, Chapter Review: Find the z values; the graph is symmetrical. Bluman, Chapter 63.

Lecture Slides Elementary Statistics Twelfth Edition

Ch5.4 Central Limit Theorem

6.39 Day 2: The Central Limit Theorem

Sampling Distributions

6-3The Central Limit Theorem.

Sec. 7-5: Central Limit Theorem

SAMPLING DISTRIBUTION. Probability and Samples Sampling Distributions Central Limit Theorem Standard Error Probability of Sample Means.

Inferring Population Parameters

Probability and the Sampling Distribution

Sampling Distributions

CHAPTER 15 SUMMARY Chapter Specifics

Sampling Distribution of the Mean

Use the graph of the given normal distribution to identify μ and σ.

Chapter 7: The Distribution of Sample Means

Central Limit Theorem Accelerated Math 3.

AGENDA: DG minutes Begin Part 2 Unit 1 Lesson 11.

The Central Limit Theorem

Sampling Distributions (§ )

Day 13 AGENDA: DG minutes Begin Part 2 Unit 1 Lesson 11.

The Normal Distribution

Presentation transcript:

Distribution of Sample Means 2011, 10, 20

Today ’ s Topics What is distribution of sample means?** Properties of distribution of sample means* How to find out the probability of a sample (mean)?**

The sales of food and drink in Jamie Joan’s vary from day to day. The distribution of daily sales is a normal distribution with mean of  = $900 and a standard deviation of  = $300. We plot all weekly mean sales Where would the weekly means fluctuate around? How much variability would you expect in the distribution of weekly means? Example 1: Jamie Joan ’ s ― Weekly Mean Distribution of Weekly Means

Distribution of Sample Means If the sample size is large (n > 30) PopulationDistribution of sample means “Good ”

Properties of distribution of sample means – Central Limit Theorem For any population with mean  and standard deviation , the distribution of sample means for sample size n will approach a normal distribution with a mean of  and a standard deviation of as n approaches infinity. (good approximation if n > 30). Mean: Standard Error:

The sales of food and drink in Jamie Joan’s vary from day to day. The distribution of daily sales has mean of  = $900 and a standard deviation of  = $300. Questions What is the probability that a weekly mean is between $560 and $1,240? What is the probability that a weekly mean is at or greater than $900? The mean sales for last week is $1,100. Did they have an exceptional week? (Hint: What is the probability of having a weekly mean of $1,100 or higher?) Example 1: Jamie Joan ’ s ― Weekly Means $560$1,240

Your Turn: IQ Score Population IQ: Distribution of Sample Means (n = 75) p = ?

How to Find out the Probability of a Sample Mean – Four Steps List the population parameters: Compute and list the mean and standard error of the distribution of sample means Compute the z score From the Unit Normal Table, look for the probability of z

Notations Sample X s Population   Distribution of sample means

Lecture Recap: Distribution of Sample Means What is a distribution of sample means? Central Limit Theorem (Properties of a distribution of sample means) Shape Mean Standard error How to use a distribution of sample means to find out the probability of a sample mean? Notations for population distribution, sample distribution, and distribution of sample means