Applied Statistics and Probability for Engineers, 6th Edition

Point Estimation of Parameters and Sampling Distributions

Chapter Outline

7-1 Point Estimation

7-2 Sampling Distributions and the Central Limit Theorem

7-3 General Concepts of Point Estimation

7-3.1 Unbiased Estimators

7-3.2 Variance of a Point Estimator

7-3.3 Standard Error: Reporting a Point Estimate

7-3.4 Bootstrap Standard Error

7-3.5 Mean Squared Error of an Estimator

7-4 Methods of Point Estimation

7-4.1 Method of Moments

7-4.2 Method of Maximum Likelihood

7-4.3 Bayesian Estimation of Parameters

Introduction

Statistical methods are used to make decisions and draw conclusions about populations. This aspect of statistics is generally called statistical inference. These techniques utilize the information in a sample for drawing conclusions. This chapter begins our study of the statistical methods used in decision making.

Statistical inference may be divided into two major areas: parameter estimation and hypothesis testing. As an example of a parameter estimation problem, suppose that an engineer is analyzing the tensile strength of a component used in an air frame. This is an important part of assessing the overall structural integrity of the airplane. Variability is naturally present in the individual components because of differences in the batches of raw material used to ...