PROBABILITY AND STATISTICS

Slides:

Advertisements

Similar presentations

Central Limit Theorem Given:

Advertisements

THE CENTRAL LIMIT THEOREM

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

Sampling distributions. Example Take random sample of 1 hour periods in an ER. Ask “how many patients arrived in that one hour period ?” Calculate statistic,

5.2 The Sampling Distribution of a Sample Mean

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

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

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.

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.

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.

Sampling Distribution of the Sample Mean. Example a Let X denote the lifetime of a battery Suppose the distribution of battery battery lifetimes has 

Chapter 21 Basic Statistics.

Chapter 10 – Sampling Distributions Math 22 Introductory Statistics.

Section 5.2 The Sampling Distribution of the Sample Mean.

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

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

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

Sample Variability Consider the small population of integers {0, 2, 4, 6, 8} It is clear that the mean, μ = 4. Suppose we did not know the population mean.

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.

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.

PROBABILITY AND STATISTICS WEEK 9-10 Onur Doğan. The sampling distribution of the sample statistics Onur Doğan.

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

Review of Statistical Terms Population Sample Parameter Statistic.

Sampling Theory and Some Important Sampling Distributions.

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

Central Limit Theorem Let X 1, X 2, …, X n be n independent, identically distributed random variables with mean  and standard deviation . For large n:

CHAPTER 7 Sampling Distributions

Section 8.2: The Sampling Distribution of a Sample Mean

Chapter 7 Probability and Samples

Ch5.4 Central Limit Theorem

Central Limit Theorem Section 5-5

Sampling Distribution Estimation Hypothesis Testing

Sampling Distribution of a sample Means

Sec. 7-5: Central Limit Theorem

Chapter 6: Sampling Distributions

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

Sample Mean Distributions

Chapter 7 Sampling Distributions.

Central limit theorem Let’s work with it..

Continuous Probability Distributions

Sample vs Population comparing mean and standard deviations

BUS7010 Quant Prep Statistics in Business and Economics

Sampling Distribution

Sampling Distribution

Lecture Slides Elementary Statistics Twelfth Edition

From Simulations to the Central Limit Theorem

Lecture Slides Elementary Statistics Twelfth Edition

Sampling Distributions

Probability and Statistics (week-9)

Sampling Distribution of a Sample Proportion

Sampling Distributions

CHAPTER 15 SUMMARY Chapter Specifics

Sampling Distribution of the Mean

Chapter 7: The Distribution of Sample Means

CHAPTER 7 Sampling Distributions

The Central Limit Theorem

Sampling Distribution of a Sample Proportion

Sample Means Section 9.3.

CHAPTER 7 Sampling Distributions

How Confident Are You?.

Presentation transcript:

PROBABILITY AND STATISTICS WEEK 9 Onur Doğan 2016-2017

The sampling distribution of the sample statistics Onur Doğan 2016-2017

The sampling distribution of the sample statistics Consider a population of N elements from which we can obtain the following distinct data: {0, 2, 4, 6, 8}. Form samples of size 2 for this population. Define their means and figure the bar chart of the means. Define the sampling distribution of the sample ranges and figure bar chart. Onur Doğan 2016-2017

The Central Limit Theorem The mean is the most commonly used sample statistic and thus it is very important. The central limit theorem is about the sampling distribution of sample means of random samples of size n. Let us establish what we are interested in when studying this distribution: 1) Where is the center? 2) How wide is the dispersion? 3) What are the characteristics of the distribution? The central limit theorem gives us an answer to all these questions. Onur Doğan 2016-2017

The Central Limit Theorem Let µ be the mean and σ the standard deviation of a population variable. If we consider all possible random sample of size n taken from this population, the sampling distribution of sample means will have the following properties: c) if the population is normally distributed the sampling distribution of the sample means is normal; if the population is not normally distributed, the sampling distribution of the sample means is approximately normal for samples of size 30 or more. The approximation to the normal distribution improves with samples of larger size. Onur Doğan 2016-2017

The Central Limit Theorem Onur Doğan 2016-2017

The Central Limit Theorem Onur Doğan 2016-2017

The Central Limit Theorem Onur Doğan 2016-2017

Example Consider a normal population with µ=100 and σ=25. If we choose a random sample of size n = 36, what is the probability that the mean value of this sample is between 90 and 110? In other words, what is P(90 < x < 110)? Onur Doğan 2016-2017

Example The average male drinks 2L of water when active outdoor s(with standard deviation of 0,7 L). You are planning a full day nature trip for 50 men and bring 110 L of water. What is the probability that you will run out? Onur Doğan 2016-2017