Sample Size and CI’s for the Population Mean (  and the Population Proportion (p)

Slides:

Advertisements

Similar presentations

Ch. 8 – Practical Examples of Confidence Intervals for z, t, p.

Advertisements

Choosing Sample Size and Using Your Calculator Presentation 9.3.

Chapter 8 Interval Estimation Population Mean:  Known Population Mean:  Known Population Mean:  Unknown Population Mean:  Unknown n Determining the.

Chapter 19 Confidence Intervals for Proportions.

Lecture 14 Dustin Lueker.  This interval will contain μ with a 100(1-α)% confidence ◦ If we are estimating µ, then why it is unreasonable for us to know.

Summary of Confidence Intervals for Estimating  and p.

Class notes for ISE 201 San Jose State University

Estimating the Population Mean Assumptions 1.The sample is a simple random sample 2.The value of the population standard deviation (σ) is known 3.Either.

Point and Confidence Interval Estimation of a Population Proportion, p

Sample Size I: 1 Sample Size Determination In the Context of Estimation.

Inference on averages Data are collected to learn about certain numerical characteristics of a process or phenomenon that in most cases are unknown. Example:

Quiz 6 Confidence intervals z Distribution t Distribution.

Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 8-1 Chapter 8 Confidence Interval Estimation Business Statistics, A First Course.

Standard Error of the Mean

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

Review of normal distribution. Exercise Solution.

Chapter 7 Confidence Intervals and Sample Sizes

Confidence Interval Estimation

9 Confidence intervals Chapter9 p218 Confidence intervals Point estimation  The first method involves using the sample mean to estimate population mean.

Inference for a Single Population Proportion (p).

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

Statistics: Concepts and Controversies What Is a Confidence Interval?

Confidence Interval Estimation

Understanding Inferential Statistics—Estimation

Chap 8-1 Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall Chapter 8 Confidence Interval Estimation Business Statistics: A First Course.

Confidence Intervals 1 Chapter 6. Chapter Outline Confidence Intervals for the Mean (Large Samples) 6.2 Confidence Intervals for the Mean (Small.

Confidence Intervals for Means. point estimate – using a single value (or point) to approximate a population parameter. –the sample mean is the best point.

Estimates and Sample Sizes Lecture – 7.4

Introduction to Biostatistics and Bioinformatics Estimation II This Lecture By Judy Zhong Assistant Professor Division of Biostatistics Department of Population.

2.6 Confidence Intervals and Margins of Error. What you often see in reports about studies… These results are accurate to within +/- 3.7%, 19 times out.

STA291 Statistical Methods Lecture 18. Last time… Confidence intervals for proportions. Suppose we survey likely voters and ask if they plan to vote for.

Large sample CI for μ Small sample CI for μ Large sample CI for p

Estimation Chapter 8. Estimating µ When σ Is Known.

ESTIMATING APPROPRIATE SAMPLE SIZE. Determining sample Size z* σ √n ≤m.

Unit 6 Confidence Intervals If you arrive late (or leave early) please do not announce it to everyone as we get side tracked, instead send me an .

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 8-1 Confidence Interval Estimation.

Lecture 7 Dustin Lueker. 2  Point Estimate ◦ A single number that is the best guess for the parameter  Sample mean is usually at good guess for the.

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 7-1 4th Lesson Estimating Population Values part 2.

Confidence Intervals for Proportions Chapter 19. Rate your confidence Name my age within 10 years? within 5 years? within 1 year? Shooting a basketball.

Introduction to Inference: Confidence Intervals and Hypothesis Testing Presentation 8 First Part.

Introduction to Inference: Confidence Intervals and Hypothesis Testing Presentation 4 First Part.

 The point estimators of population parameters ( and in our case) are random variables and they follow a normal distribution. Their expected values are.

Ch 12 – Inference for Proportions YMS 12.1

Confidence intervals. Want to estimate parameters such as  (population mean) or p (population proportion) Obtain a SRS and use our estimators, and Even.

Determining the Appropriate Sample Size

Confidence Intervals Inferences about Population Means and Proportions.

M35 C.I. for proportions 1  Department of ISM, University of Alabama, Proportions How do “polls” work and what do they tell you?

CONFIDENCE INTERVALS.

4.4.2 Normal Approximations to Binomial Distributions

1 Chapter 18 Inference about a Population Proportion.

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.

One Sample Mean Inference (Chapter 5)

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

Point Estimates point estimate A point estimate is a single number determined from a sample that is used to estimate the corresponding population parameter.

Confidence Intervals for Proportions Chapter 19. Rate your confidence Name my age within 10 years? within 5 years? within 1 year? Shooting a basketball.

Inference for Proportions Section Starter Do dogs who are house pets have higher cholesterol than dogs who live in a research clinic? A.

1 Probability and Statistics Confidence Intervals.

Sample Size Needed to Achieve High Confidence (Means)

Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc. Chap 8-1 Chapter 8 Confidence Interval Estimation Business Statistics: A First Course 5 th Edition.

Sample Size and CI’s for the Population Mean ( .

Inference for a Single Population Proportion (p)

Confidence intervals for µ

Confidence Interval Estimation

Inferences Based on a Single Sample

Statistics Confidence Intervals

Confidence Interval Estimation

An overview to this point

Inference for Proportions

STA 291 Summer 2008 Lecture 15 Dustin Lueker.

Mar. 24 Statistic for the day: The number of heartbeats in a lifetime for any animal (mouse to elephant): Approximately 1 billion Assignment: Read Chapter.

Presentation transcript:

Sample Size and CI’s for the Population Mean (  and the Population Proportion (p)

Sample Size and CI’s for  Suppose we wish to estimate a population mean  using a 95% CI and have a margin of error no larger than E units. What sample size do we need to use? Suppose we wish to estimate a population mean  using a 95% CI and have a margin of error no larger than E units. What sample size do we need to use? Recall the “large” sample CI for  is given by: Recall the “large” sample CI for  is given by: MARGIN OF ERROR (E) Note: The z-value should actually be a t-distribution value, but for sample size planning purposes we will use a standard normal value. 95% z = % z = % z = 2.576

Sample Size and CI’s for  For a 95% CI if we want margin of error, E we have For a 95% CI if we want margin of error, E we have After some wonderful algebraic manipulation After some wonderful algebraic manipulation Oh, oh! We don’t know s !! 1.“Guesstimate” 2.Use sample SD from pilot or prior study. 3.Use fact 95% of observations generally lie with 2 SD’s of the mean thus where Range represents the expected maximum – minimum we would see in sample. Could also use fact that 99% lie within 3 SD’s and use 6 instead of 4 in our crude approximation.

Example: Estimating Mean Cholesterol Level of Females 30 – 40 yrs. of age Q: What sample size would be necessary to estimate the mean cholesterol level for the population of females between the ages of 30 – 40 with a 95% confidence interval that has a margin of error no larger than E = 3 mg/dl?

Sample Size and CI’s for   Suppose from a pilot study we find s = 19.8 mg/dl We can use this estimate to find the sample size that will give E = 3 mg/dl. We can use this estimate to find the sample size that will give E = 3 mg/dl. Standard normal values 90% = % = % = 2.576

Sample Size and CI’s for  Suppose we do not have any information about the standard deviation of the cholesterol levels of individuals in this population. Suppose we do not have any information about the standard deviation of the cholesterol levels of individuals in this population. We could use the Range/4 or Range/6 as crude approximations to the standard deviation. We could use the Range/4 or Range/6 as crude approximations to the standard deviation. What is the smallest serum cholesterol level we would expect to see? 100 mg/dl (my guess) What is the smallest serum cholesterol level we would expect to see? 100 mg/dl (my guess) What is the largest? 300 mg/dl (my guess again) What is the largest? 300 mg/dl (my guess again) SD approximation = 200/4 = 50 mg/dl SD approximation = 200/4 = 50 mg/dl or or SD approximation = 200/6 = mg/dl SD approximation = 200/6 = mg/dl

Sample Size and CI’s for  Using this crude estimate for the standard deviation we find the following sample size requirements Using this crude estimate for the standard deviation we find the following sample size requirements or or

Sample Size and CI’s for p Suppose we wish to estimate p using a 95% CI and have a margin of error of 3%. What sample size do we need to use? Suppose we wish to estimate p using a 95% CI and have a margin of error of 3%. What sample size do we need to use? Recall the CI for p is given by: Recall the CI for p is given by: MARGIN OF ERROR (E)

Sample Size and CI’s for p Here for a 95% CI we want E =.03 or 3% Here for a 95% CI we want E =.03 or 3% After some wonderful algebraic manipulation After some wonderful algebraic manipulation Oh, oh! We don’t know p-hat !! 1.“Guesstimate” 2.Use p-hat from pilot or prior study. 3.Largest n we would ever need comes when p-hat =.50.

Sample Size and CI’s for p 1. Informed approach 2. Conservative approach (i.e. worst case scenario) Standard normal values 90% = % = % = 2.578

Sample Size and CI’s for p Original Question: Suppose we wish to estimate p using a 95% CI and have a margin of error of 3%. What sample size do we need to use? Original Question: Suppose we wish to estimate p using a 95% CI and have a margin of error of 3%. What sample size do we need to use? Assume that we estimate the 5 yr. survival rate for a new kidney cancer therapy, and we know historical that it this survival rate is around 20%. Assume that we estimate the 5 yr. survival rate for a new kidney cancer therapy, and we know historical that it this survival rate is around 20%. Using informed approach Using informed approach

Sample Size and CI’s for p Original Question: Suppose we wish to estimate p using a 95% CI and have a margin of error of 3%. What sample size do we need to use? Original Question: Suppose we wish to estimate p using a 95% CI and have a margin of error of 3%. What sample size do we need to use? Assume that we estimate the 5 yr. survival rate for a new kidney cancer therapy, and we know historical that it this survival rate is around 20%. Assume that we estimate the 5 yr. survival rate for a new kidney cancer therapy, and we know historical that it this survival rate is around 20%. Using conservative approach Using conservative approach This is why in media polls you they usually report a sampling error of + 3% and that the poll was based on a sample of n = 1000 individuals.