Quantitative Methods

for Business, Management and Finance

Louise Swift, Sally Piff

• Publisher: Red Globe Press
• Year: 2014
• Print ISBN: 9781137376558
• eBook ISBN: 9781137337948
• Edition: 4
• Topic: Business
• Subtopic: Business Mathematics
• Index: Business

Quantitative Methods is a comprehensive guide to the techniques any student of business or finance is likely to need. The authors' coaching, learning-by-doing approach coupled with the text's clear structural outline makes this title ideal for those less confident with maths. With Swift, the acquisition of essential mathematical skills is achievable and even enjoyable.

STATISTICS

Nationally, 91.9% of 17 year-olds in full-time education attend schools or colleges in the state sector – BIS, SFR12/2012 (Table 2)

There were 2.56 million unemployed people, up 70,000 from September to November 2012 – ons.gov.uk, 13 June 2013

There are approximately 600 million cars, passenger vans, SUVs and light trucks in the world today. Of those about 240 million are found in the United States – wiki.answers.com, 24 June 2013

The overall level of police recorded crime decreased by 8% in the year ending December 2012 compared with the previous year, with the number of recorded offences (3.7 million) now lower than at any time since the introduction of the new recording practices in 2002 – ons.gov.uk, 24 June 2013

The survey, carried out of course, by text message, also found that more than a third of the 16300 respondents would prefer to decline invitations by text – Times, January 2004

We often read statements like these in newspapers and websites or hear them on television. They are all examples of statistics. In everyday language a statistic just means a numerical fact, but the subject or science of Statistics means much more. It splits into two broad areas: descriptive statistics, which you met in Describing Data, and inferential statistics, which forms the major-ity of the subject and which is our interest in this part of the book.

Descriptive Statistics covers the way a set of data is described by using graphs and pictures or by calculating summary measures like the average.

Inferential Statistics is used whenever it is too expensive or impractical to collect all the data of interest, called the population, and only a sample of the data is available. It is the process by which information from the sample is used to infer information about the population.

Whilst we have complete knowledge of the sample of data, we do not usually know about the population exactly, and so any statements we make about the population will be uncertain and have to be expressed using probabilities. For this reason you will need to have covered Probability as well as Describing Data before you start this part of the book. Everything we said about using a computer in the introduction to Describing Data continues to apply.

1 ESTIMATION

By a small sample, we may judge of the whole piece.

Miguel de Cervantes, Don Quixote

Contexts

What is this chapter about?

This chapter explains how to select a sample of data and use it to make valid inferences about the wider set of data or population it came from.

Why is it useful?

Businesses and organisations frequently collect just a sample of the data of interest because it is too costly or impractical to obtain all the information, for instance, in surveys, product testing, quality control, auditing and market research.

Where does it fit in?

The subject of Statistics broadly divides into two parts: Descriptive Statistics, which we considered in Describing Data, is about summarising a set of data, whereas Inferential Statistics, which we consider in this part of the book, Statistics, is concerned with using a sample of data to make wider inferences. Two key ideas underpin Inferential Statistics: estimation and testing. In this chapter we introduce estimation, and in the next chapter, testing.

What do I need to know?

You will need to cope with a few formulae and be able to rearrange some simple equations (Essential Maths), have a basic idea of probability and random variables, including the normal distribution (Probability) and be able to calculate sample means and variances (Describing Data).

Objectives

After your work on this chapter you should:

• understand the concept of a simple random sample and know how to select one;

• be able to estimate the population mean and variance;

• understand what a sampling distribution is;

• know about the sampling distribution of the sample mean;

• know about the t distribution;

• be able to calculate and interpret confidence intervals for the mean.

We gave you a taste of Statistics in Describing Data. However, as we said in the introduction, most of the techniques of Statistics are about using a...

Table of contents

• Cover
• Title page
• Copyright
• Summary Of Contents
• Contents
• Preface to the fourth edition
• To the lecturer
• To lecturers who used the last edition
• Pathways through this book
• To the student please read this first
• Acknowledgements
• Tour of the book
• Companion website
• Essential Maths
• More Maths
• Describing Data
• Probability
• Statistics
• Business Modelling
• Statistical tables
• Index