Sampling and sampling distibutions. Sampling from a finite and an infinite population Simple random sample (finite population) – Population size N, sample.

Slides:

Advertisements

Similar presentations

THE CENTRAL LIMIT THEOREM

Advertisements

How many movies do you watch? Does the CLT apply to means?  The Central Limit Theorem states that the more samples you take, the more Normal your.

Sampling: Final and Initial Sample Size Determination

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.

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

Statistical Inference and Sampling Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing.

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

1 Pertemuan 06 Sebaran Penarikan Contoh Matakuliah: I0272 – Statistik Probabilitas Tahun: 2005 Versi: Revisi.

PROBABILITY AND SAMPLES: THE DISTRIBUTION OF SAMPLE MEANS.

Modular 13 Ch 8.1 to 8.2.

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

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

Standard error of estimate & Confidence interval.

The Central Limit Theorem. 1. The random variable x has a distribution (which may or may not be normal) with mean and standard deviation. 2. Simple random.

Chapter 7 Sampling Distribution

Many times in statistical analysis, we do not know the TRUE mean of a population of interest. This is why we use sampling to be able to generalize the.

AP Statistics Chapter 9 Notes.

Econ 3790: Business and Economics Statistics Instructor: Yogesh Uppal

Chapter 10 – Sampling Distributions Math 22 Introductory Statistics.

Statistics Workshop Tutorial 5 Sampling Distribution The Central Limit Theorem.

Statistics 300: Elementary Statistics Section 6-5.

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.

1 Chapter 7 Sampling Distributions. 2 Chapter Outline  Selecting A Sample  Point Estimation  Introduction to Sampling Distributions  Sampling Distribution.

Distribution of the Sample Mean (Central Limit Theorem)

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.

The Central Limit Theorem 1. The random variable x has a distribution (which may or may not be normal) with mean and standard deviation. 2. Simple random.

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

Sampling Distributions. Essential Question: How is the mean of a sampling distribution related to the population mean or proportion?

Chap 7-1 Basic Business Statistics (10 th Edition) Chapter 7 Sampling Distributions.

Stat 13 Lecture 19 discrete random variables, binomial A random variable is discrete if it takes values that have gaps : most often, integers Probability.

7 sum of RVs. 7-1: variance of Z Find the variance of Z = X+Y by using Var(X), Var(Y), and Cov(X,Y)

Chapter 7 Sampling Distributions. Sampling Distribution of the Mean Inferential statistics –conclusions about population Distributions –if you examined.

Conditions and Formulas Are you confident?. 1 proportion z-interval what variable(s) need to be defined? write the formula.

1 Sampling distributions The probability distribution of a statistic is called a sampling distribution. : the sampling distribution of the mean.

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:

Sampling Distributions

MATH Section 4.4.

Sampling and Sampling Distributions

Ch5.4 Central Limit Theorem

Introduction to Sampling Distributions

Sec. 7-5: Central Limit Theorem

CHAPTER 7 Sampling Distributions

Review of Hypothesis Testing

Distribution of the Sample Proportion

MATH 2311 Section 4.4.

Lecture Slides Elementary Statistics Twelfth Edition

Sampling Distribution Models

Sampling Distributions

CHAPTER 15 SUMMARY Chapter Specifics

Sampling Distribution of the Mean

The estimate of the proportion (“p-hat”) based on the sample can be a variety of values, and we don’t expect to get the same value every time, but the.

CHAPTER 7 Sampling Distributions

Exam 2 - Review Chapters

CHAPTER 7 Sampling Distributions

Central Limit Theorem Accelerated Math 3.

Sampling Distribution Models

The Central Limit Theorem

CHAPTER 7 Sampling Distributions

CHAPTER 7 Sampling Distributions

CHAPTER 7 Sampling Distributions

Sample Proportions Section 9.2.

Sample Means Section 9.3.

Central Limit Theorem cHapter 18 part 2.

Review of Hypothesis Testing

The Normal Distribution

Presentation transcript:

Sampling and sampling distibutions

Sampling from a finite and an infinite population Simple random sample (finite population) – Population size N, sample size n – Each possible sample of size n has the same probability of being selected Random sample (infinite population) – Each element comes from the same population Making sure all the cereal boxes have the same weight at the plant – Each element is selected independently Sampling customers of a McDonalds restaurant

The number of different possible samples N=2500, n = 30 N!/(n!*(N-n)!)=2.57*10^69

Point estimation Finding the sample mean Population mean = $51,800 Population standard deviation = $4000

Sampling distributions

An example, sample size 30, population standard deviation 4000

Central limit theorem

TETC-110B

Sampling distributions

The distribution function for sample proportion Can be approximated by a normal distribution – If np>=5 – and n(1-p)>=5