Chapter 5: Confidence Interval Estimation and Hypothesis Testing PDF

# Chapter 5: Confidence Interval Estimation and Elements of Hypothesis Testing ## Learning Outcome - 5 - Examine confidence interval estimation and the elements of hypothesis testing. ## Chapter 5 - Outline - Estimation - Introduction - Notations of Population and Sample - Types of Estimates - P...

# Chapter 5: Confidence Interval Estimation and Elements of Hypothesis Testing ## Learning Outcome - 5 - Examine confidence interval estimation and the elements of hypothesis testing. ## Chapter 5 - Outline - Estimation - Introduction - Notations of Population and Sample - Types of Estimates - Point and Interval Estimates - Hypothesis - Hypothesis Testing - Types of Statistical Hypotheses - Parametric and Nonparametric Test - Errors in Hypothesis Testing ## Estimation - Introduction - One aspect of inferential statistics is estimation, which is the process of estimating the value of a parameter from information obtained from a sample. - For example: - "One out of 4 Americans is currently dieting." (Calorie Control Council) - "Seventy-two percent of Americans have flown on commercial airlines." - "The average kindergarten student has seen more than 5000 hours of television." ## Estimation Process A graphic image showing a population with an unknown mean. A person is drawing a random sample from the population. The person states: "I am 95% confident that m is between 40 & 60." ## Statistical INFERENCE ## Types of Estimates - Inferential statistics enable you to estimate unknown population characteristics such as a population mean or a population proportion. - Two types of estimates are used to estimate population parameters: - Point estimates - Interval estimates ## Point and Interval Estimates - A point estimate is a single number. - A confidence interval provides additional information about the variability of the estimate. A graphic image showing a confidence interval. ## How Good is a Point Estimate? - How much uncertainty is associated with a point estimate of a population parameter? - The answer is that there is no way of knowing how close a particular point estimate is to the population mean. - This answer places some doubt on the accuracy of point estimates. For this reason, statisticians prefer another type of estimate, called an interval estimate. ## Confidence Intervals - An interval estimate provides more information about a population characteristic than does a point estimate. - Such interval estimates are called confidence intervals. ## Confidence Interval Contd... - An interval estimate of a parameter is an interval or a range of values used to estimate the parameter: - Takes into consideration variation in sample statistics from sample to sample - Based on observations from 1 sample - Gives information about closeness to unknown population parameters - stated in terms of probability (level of confidence) - e.g. 95% confident, 99% confident - Never 100% Sure ## HYPOTHESIS - A hypothesis is an assumption that is made based on some evidence. - It includes components like variables, population, and the relation between the variables. - A research hypothesis is a hypothesis that is used to test the relationship between two or more variables. - A statistical hypothesis is a conjecture (assumption) about a population parameter. This conjecture may or may not be true. ## Hypothesis Testing - Is also called significance testing - Hypothesis testing is a decision-making process for evaluating claims about a population. - Hypothesis-testing situation begins with the statement of a hypothesis ## Types of Statistical Hypotheses - There are two types of statistical hypotheses for each situation: - Null hypothesis - Alternative hypothesis ## Null Hypothesis - The null hypothesis symbolized by Ho, is a statistical hypothesis that states that there is no difference between a parameter and a specific value, or there is no difference between two parameters. ## Alternative Hypothesis - The alternative hypothesis symbolized by H₁, is a statistical hypothesis that states the existence of a difference between a parameter and a specific value, or states that there is a difference between two parameters. ## Parametric and Nonparametric Test - Parametric tests are those that make assumptions about the parameters of the population distribution from which the sample is drawn. This is often the assumption that the population data are normally distributed. - Non-parametric tests do not require that samples come from populations (researchers have no idea bout the population) with normal distributions or have any other particular distributions. Consequently, nonparametric tests are called distribution-free tests ## Errors in Hypothesis Testing - Two types of error are possible - A type I error occurs if you reject the null hypothesis when it is true. - A type II error occurs if you do not reject the null hypothesis when it is false. A table showing possible decisions in hypothesis testing: | | $H_0$ true | $H_0$ false | |---|---|---| | Reject $H_0$ | Error Type I | Correct decision| | Do not reject $H_0$ | Correct decision | Error Type II| ## References - Bluman, A. G. (2011). *Elementary statistics: A step by step approach*(8th ed). New York: McGraw-Hill Higher Education, pp.356-425. Retrieved from: https://ugess3.files.wordpress.com/2016/01/bluman-step-by-step-statistics-8th-edition.pdf - Levine, D. M., Stephan, D. F., Krehbiel, T. C., & Berenson, M. L. (2008). *Statistics for Managers Using Microsoft® Excel.* (5th ed), Chapter 8& 9, Pearson Education, Inc. Published by Prentice Hall. Retrieved from: www.pdfdrive.net - Holmes, A., ILLOWSKY, B., Dean, S., (2018). *Introductory Business Statistics*. OpenStax, Rice University. Retrieved from: http://cnx.org/content/col11776/1.33 ## Contact Information Dr. S. Porkodi Office: BS032, Business Department Email: [email protected] ## Version History | Version No | Date Approved | Changes incorporated | |---|---|---| | New Outcome Version: 01 | Sem. (1) 2022/2023 | |