### Introduction

When you are dealing with large populations, for example populations created by the manufacturing processes, it is impossible, or very difficult indeed, to deal with the whole population and know the parameters of that population. Items such as car components, electronic components, aircraft components or ordinary everyday items such as light bulbs, cycle tyres and cutlery effectively form infinite populations. Hence we have to deal with samples taken from a population and estimate those population parameters that we need. This Workbook will show you how to calculate single number estimates of parameters - called point estimates - and interval estimates of parameters - called interval estimates or confidence intervals. In the latter case you will be able to calculate a range of values and state the confidence that the true value of the parameter you are estimating lies in the range you have found.

#### Prerequisites

• understand and be able to calculate means and variances
• be familiar with the results and concepts met in the study of probability
• be familiar with the normal distribution

#### Learning Outcomes

• understand what is meant by the terms sample and sampling distribution
• explain the importance of sampling in the application of statistics
• explain the terms point estimate and the term interval estimate
• calculate point estimates of means and variances
• find interval estimates of population parameters for given levels of confidence

1.1 Why sample?