Introduction. Interval estimation

Chapter 6

Interval estimation

Introduction

The problem of statistical inference arises when we wish to make generalization about a population when only a sample will be available. Once a sample is observed, its main features can be determined by the methods of descriptive summary discussed in previous chapters. Our principal concern is with not just the particular data set, but what can be said about the population based on the information extracted from analyzing the sample data.

Statistical inference deals with drawing conclusions about population parameters from an analysis of the sample data.

The value(s) assigned to a population parameters based on the value of a sample statistic is called an estimate of the population parameters.

For example, suppose the manager selects a sample of 50 new employees and finds that the mean time taken to learn the job for these employees is 10 hours. If manager assigns this value to the population mean, then 10 hours will be called an estimate of . Thus, the sample mean is an estimator of the population mean , and the sample proportion is an estimator of the population proportion p.

An estimate may be a point estimate or an interval estimate.

Definition:

The value of a sample statistic that is used to estimate population parameters is called a point estimate.

Each sample taken from a population is expected to yield a different value of the sample statistics. Thus, the value assigned to a population parameter based on the point estimate depends on which of the sample is drawn. Consequently, the point estimate assigns a value to a population parameters almost always differs from the true value of the population parameters.

In the case of interval estimation, instead of assigning a simple value to a population parameter, an interval is constructed around the point estimate and then a probability statement that this interval contains the corresponding population parameter is made.

Definition:

In interval estimation, an interval is constructed around the point estimate, and it is stated that this interval likely to contain the corresponding population parameter.

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