056. Estimation/ Introduction

Populations are generally too large to study in their entirety. Their size requires that samples should be selected. If a manager of a retail store wished to know tie mean expenditure by her customers last year, she would find it difficult to calculate the average of the hundreds or perhaps thousands of customers who shopped in to store. It would prove much easier to use an estimate of the population mean b; calculating the mean of a representative sample.

There are at least Two types of estimators commonly used for this purpose:

1) a point estimate,

2) and an interval estimate.

A Point estimate uses a statistic to estimate tie parameter at a Single value or point. The store manager may select a sample of n 500 customers and find . This value serves as the point estimate for tie population mean.

An Interval estimate specifies a Range within which the unknown parameter may lie. The manager may decide the population mean lies somewhere between $35 and $38. Such an interval is often accompanied by a statement as to the level of confidence that can be placed in its accuracy. It is therefore called a Confidence interval.

Actually there are Three levels of confidence commonly associated with confidence intervals: 99, 95, and 90 Percent. There is nothing magical about these three values. It’s easy to calculate an 82 percent confidence interval if it’s so desirable. These three levels of confidence, called Confidence coefficients, are simply conventional. The manager referred to above might, for example, be 95 percent confident that tie population mean is between $35 and $38.

Interval estimates enjoy certain advantages over point estimates. Due to sampling error, will likely not equal . However, there is no way of knowing how large the sampling error is. Intervals are therefore used to account for this unknown discrepancy.

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