Example A population has a mean of 200 and a standard deviation of 50. A random sample of size 100 will be taken and the sample mean x̄ will be used to.

Slides:

Advertisements

Similar presentations

Samples The means of these samples

Advertisements

Estimation of Means and Proportions

Econ 338/envr 305 clicker questions

Sampling: Final and Initial Sample Size Determination

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

1 Test a hypothesis about a mean Formulate hypothesis about mean, e.g., mean starting income for graduates from WSU is $25,000. Get random sample, say.

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

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)

IEEM 3201 Two-Sample Estimation: Paired Observation, Difference.

Chapter Topics Confidence Interval Estimation for the Mean (s Known)

6-5 The Central Limit Theorem

Sampling Distributions

Population Proportion The fraction of values in a population which have a specific attribute p = Population proportion X = Number of items having the attribute.

BA 275 Quantitative Business Methods

Statistics Lecture 22. Last Day…completed 5.1 Today Parts of Section 5.3 and 5.4.

QM-1/2011/Estimation Page 1 Quantitative Methods Estimation.

Standard error of estimate & Confidence interval.

© 2010 Pearson Prentice Hall. All rights reserved Chapter Estimating the Value of a Parameter Using Confidence Intervals 9.

Review of normal distribution. Exercise Solution.

Sample Of size 2 Of size 3 1 A,B=3,1 2 A,B,C=3,1,5 3 A,C=3,5 4

An importer of Herbs and Spices claims that average weight of packets of Saffron is 20 grams. However packets are actually filled to an average weight,

Econ 3790: Business and Economics Statistics Instructor: Yogesh Uppal

Section 8.2 Estimating  When  is Unknown

When estimating the mean, how large a sample must be used in order to assure a given level of confidence? Use the formula:

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

FINAL REVIEW. The amount of coffee (in ounces) filled in a jar by a machine has a normal distribution with a mean amount of 16 ounces and a standard deviation.

Statistical Interval for a Single Sample

Review from before Christmas Break. Sampling Distributions Properties of a sampling distribution of means:

Ch 6 Introduction to Formal Statistical Inference

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

Confidence intervals for the mean - continued

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

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.

Estimation Chapter 8. Estimating µ When σ Is Known.

Confidence Intervals. Examples: Confidence Intervals 1. Among various ethnic groups, the standard deviation of heights is known to be approximately.

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

Introduction to Inferece BPS chapter 14 © 2010 W.H. Freeman and Company.

CHAPTER SEVEN ESTIMATION. 7.1 A Point Estimate: A point estimate of some population parameter is a single value of a statistic (parameter space). For.

1 BA 275 Quantitative Business Methods Quiz #2 Sampling Distribution of a Statistic Statistical Inference: Confidence Interval Estimation Introduction.

: An alternative representation of level of significance. - normal distribution applies. - α level of significance (e.g. 5% in two tails) determines the.

Example Random samples of size n =2 are drawn from a finite population that consists of the numbers 2, 4, 6 and 8 without replacement. a-) Calculate the.

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.

Exercise - 1 A package-filling process at a Cement company fills bags of cement to an average weight of µ but µ changes from time to time. The standard.

An importer of Herbs and Spices claims that average weight of packets of Saffron is 20 grams. However packets are actually filled to an average weight,

1 Mean Analysis. 2 Introduction l If we use sample mean (the mean of the sample) to approximate the population mean (the mean of the population), errors.

Section 9.2: Large-Sample Confidence Interval for a Population Proportion.

An importer of Herbs and Spices claims that average weight of packets of Saffron is 20 grams. However packets are actually filled to an average weight,

Confidence Intervals for a Population Mean, Standard Deviation Unknown.

Lesoon Statistics for Management Confidence Interval Estimation.

1 Chapter 8 Interval Estimation. 2 Chapter Outline  Population Mean: Known  Population Mean: Unknown  Population Proportion.

1 Probability and Statistics Confidence Intervals.

9-1 ESTIMATION Session Factors Affecting Confidence Interval Estimates The factors that determine the width of a confidence interval are: 1.The.

Chapter 8 Interval Estimates For Proportions, Mean Differences And Proportion Differences.

Chapter 8 Estimation ©. Estimator and Estimate estimator estimate An estimator of a population parameter is a random variable that depends on the sample.

Sample Size Needed to Achieve High Confidence (Means)

Properties of Normal Distributions

Chapter 4. Inference about Process Quality

Inference: Conclusion with Confidence

6-3The Central Limit Theorem.

Monthly utility bills factor into local cost of living measures

Estimating µ When σ is Known

Calculating Probabilities for Any Normal Variable

Lecture 7 Sampling and Sampling Distributions

Exercise - 1 A package-filling process at a Cement company fills bags of cement to an average weight of µ but µ changes from time to time. The standard.

Estimating µ When σ is Known

From Samples to Populations

Interval Estimation Download this presentation.

CONFIDENCE INTERVALS A confidence interval is an interval in which we are certain to a given probability of the mean lying in that interval. For example.

Presentation transcript:

Example A population has a mean of 200 and a standard deviation of 50. A random sample of size 100 will be taken and the sample mean x̄ will be used to estimate the the population mean. a-) What is the expected value of x̄ ? b-) what is the standard deviation of x̄ ? c-) Shoe the sampling distribution of x̄ ? d-) What does the sampling distribution of x̄ show?

Example Assume the population standard deviation is σ = 25 . Compute the standard error of the mean, σx̄ for sample sizes of 50, 100, 150 and 200. What can you say about the size of the standard error of the mean as the sample size is increased ?

Example A population has a mean of 200 and a standard deviation of 50. Suppose a random sample of size 100 is selected and the sample mean x̄ will be used to estimate the population mean. a-) What is the probability that the sample mean will be within ± 5 of the population mean ? b-) What is the probability that the sample mean will be within ± 10 of the population mean ?

Example 3: If a random sample of size 30 is taken from binomial distribution with n=9 and p= 0.5 Q: Find the probability that the sample mean exceeds 5.

Example 4: Suppose we have selected a random sample of n=36 observations from a population with mean equal to 80 and standard deviation equal to 6. Q: Find the probability that x̄ will be larger than 82.

Exercise - 1 A package-filling process at a Cement company fills bags of cement to an average weight of µ but µ changes from time to time. The standard deviation is σ = 3 pounds. A sample of 25 bags has been taken and their mean was found to be 150 pounds. Assume that the weights of the bags are normally distributed. Find the 90% confidence limits for µ.

Exercise - 3 An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the upper end point in a 99% confidence interval for the average income?

Exercise - 4 An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the width of the 90% confidence interval?

Exercise - 5 The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. If the head librarian knows that the population standard deviation is 150 books checked out per day, and she asked her assistant for a 95% confidence interval, approximately how large a sample did her assistant use to determine the interval estimate?