Estimation Lesson 3 Aims:

Slides:



Advertisements
Similar presentations
Normal Distribution 2 To be able to transform a normal distribution into Z and use tables To be able to use normal tables to find and To use the normal.
Advertisements

Chap 8-1 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chapter 8 Estimation: Single Population Statistics for Business and Economics.
Sample Means W~N(980, 1002) μ=980 σ / √n = P(W>1000)= We only expect 2 samples in every 100 to be this big.
BCOR 1020 Business Statistics Lecture 17 – March 18, 2008.
Estimation Procedures Point Estimation Confidence Interval Estimation.
Statistical inference form observational data Parameter estimation: Method of moments Use the data you have to calculate first and second moment To fit.
IEEM 3201 One and Two-Sample Estimation Problems.
Chapter 8 Estimation: Single Population
1 Inference About a Population Variance Sometimes we are interested in making inference about the variability of processes. Examples: –Investors use variance.
1 Confidence Intervals for Means. 2 When the sample size n< 30 case1-1. the underlying distribution is normal with known variance case1-2. the underlying.
How confident are we that our sample means make sense? Confidence intervals.
Chapter 9: Introduction to the t statistic
Chapter 7 Estimation: Single Population
Section 7-4 Estimating a Population Mean: σ Not Known.
7.2 Confidence Intervals When SD is unknown. The value of , when it is not known, must be estimated by using s, the standard deviation of the sample.
Today’s lesson Confidence intervals for the expected value of a random variable. Determining the sample size needed to have a specified probability of.
Confidence Intervals (Chapter 8) Confidence Intervals for numerical data: –Standard deviation known –Standard deviation unknown Confidence Intervals for.
Introduction to Biostatistics and Bioinformatics Estimation II This Lecture By Judy Zhong Assistant Professor Division of Biostatistics Department of Population.
AP STATISTICS LESSON 10 – 1 (DAY 2)
H1H1 H1H1 HoHo Z = 0 Two Tailed test. Z score where 2.5% of the distribution lies in the tail: Z = Critical value for a two tailed test.
CHAPTER SIX Confidence Intervals.
Topic 6 - Confidence intervals based on a single sample Sampling distribution of the sample mean - pages Sampling distribution of the.
Sampling Theory The procedure for drawing a random sample a distribution is that numbers 1, 2, … are assigned to the elements of the distribution and tables.
Determination of Sample Size: A Review of Statistical Theory
Estimation Chapter 8. Estimating µ When σ Is Known.
© Copyright McGraw-Hill 2000
11/18/2015 IENG 486 Statistical Quality & Process Control 1 IENG Lecture 07 Comparison of Location (Means)
Estimating the Area Under a Curve Aims: To be able to calculate an estimate for the area under a curve. To decide if this is an over estimate or an under.
Ch 12 – Inference for Proportions YMS 12.1
Section 6-3 Estimating a Population Mean: σ Known.
Section 7-3 Estimating a Population Mean: σ Known.
MeanVariance Sample Population Size n N IME 301. b = is a random value = is probability means For example: IME 301 Also: For example means Then from standard.
8.2 Testing the Difference Between Means (Independent Samples,  1 and  2 Unknown) Key Concepts: –Sampling Distribution of the Difference of the Sample.
By the end of this lesson you will be able to explain/calculate the following: 1. Mean for data in frequency table 2. Mode for data in frequency table.
Chapter 5 Sampling Distributions. The Concept of Sampling Distributions Parameter – numerical descriptive measure of a population. It is usually unknown.
Lesson Estimating a Population Proportion.
Confidence Intervals for a Population Proportion Excel.
Lecture 4 Confidence Intervals. Lecture Summary Last lecture, we talked about summary statistics and how “good” they were in estimating the parameters.
Exam Question Starter/Recap. Improper Integration Lesson 3 Aims: To know what an improper integral is. To be able to find the value of an improper integral.
10.1 – Estimating with Confidence. Recall: The Law of Large Numbers says the sample mean from a large SRS will be close to the unknown population mean.
Feed Back from Test. Sum of Cubed Numbers. Lesson 3 Aims: To introduce the sum of cubes formula. To recap the sum of natural numbers and the sum of squares.
Ex St 801 Statistical Methods Inference about a Single Population Mean (CI)
The Normal Distribution AS Mathematics Statistics 1 Module.
Review Confidence Intervals Sample Size. Estimator and Point Estimate An estimator is a “sample statistic” (such as the sample mean, or sample standard.
Recall on whiteboards What type of data is the normal distribution used to model? Discrete or continuous? About what percentage of the data values will.
Binomial Test now I want to check your probability and binomial Moodle work, so please have this on the table Homework Today and for half term - Probability.
Lab Chapter 9: Confidence Interval E370 Spring 2013.
Unit 4 Review. Starter Write the characteristics of the binomial setting. What is the difference between the binomial setting and the geometric setting?
Confidence Intervals. Point Estimate u A specific numerical value estimate of a parameter. u The best point estimate for the population mean is the sample.
© 2001 Prentice-Hall, Inc.Chap 8-1 BA 201 Lecture 12 Confidence Interval Estimation.
Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 9 Section 4 – Slide 1 of 11 Chapter 9 Section 4 Putting It All Together: Which Procedure.
Statistics for Business and Economics 7 th Edition Chapter 7 Estimation: Single Population Copyright © 2010 Pearson Education, Inc. Publishing as Prentice.
Chapter 8 Confidence Interval Estimation. 8.1 Confidence Interval Estimation of the Mean This section deals with the case of known σ. There are two kinds.
Intro to Normal Distribution AS Maths with Liz Stats 1.
X AND R CHART EXAMPLE IN-CLASS EXERCISE
t distribution Suppose Z ~ N(0,1) independent of X ~ χ2(n). Then,
Tests for Two Means – Normal Populations
Random Sampling Population Random sample: Statistics Point estimate
Confidence Intervals Tobias Econ 472.
CI for μ When σ is Unknown
Introduction to Inference
Year-3 The standard deviation plus or minus 3 for 99.2% for year three will cover a standard deviation from to To calculate the normal.
CHAPTER 15 SUMMARY Chapter Specifics
Confidence Intervals Tobias Econ 472.
Upcoming Schedule PSU Stat Jan 2015
Determining Which Method to use
Chapter 6 Confidence Intervals.
Introduction to the t Test
Section 9.2: Sample Proportions
Confidence Intervals Usually set at 95 % What does that mean ?
Presentation transcript:

Estimation Lesson 3 Aims: • To be able to decide which distribution to use when constructing a C.I. • To practice exam style questions. • To be able to calculate the unbiased estimates for the mean and variance.

Assumptions or Theory for Summary table of which CI formula to use Parent Distribution Variance Assumptions or Theory for C I Normal X~(µ,σ2) Known Not normal Unknown Unknown Note: If sample is < 30 and not from a normal distribution we can’t use either the z or t distribution to model the situation

Unbiased Estimates of the Mean & Variance The unbiased estimate of the mean from a sample is calculated using: The variance if unknown can be calculated by using the formula below and we call it s2 rather than σ2

Jan 08 Exam Question 6 mins have a go! of Nadal’s of Nadal’s on Nadal’s

Complete relay race Do revision Exercise page 107. Qu 1 to 5 compulsory, 5 to 9 optional