Description
This is the second in a series of books written to support the Statistics modules in MEI Structured Mathematics, but you may also use them for an independent course in the subject. Throughout the course the emphasis is on understanding, interpretation and modelling, rather than on mere routine calculations. This is the third edition of this book.
There are four chapters in this book. The Poisson distribution is covered in the first chapter and this is followed by the Normal distribution in Chapter 2. Chapter 3 is about samples and hypothesis testing. The book ends with a chapter on bivariate data, covering correlation and regression lines; you meet two correlation coefficients (Pearson’s product moment and Spearman’s rank) and use them as statistics for suitable hypothesis tests.
Several examples are taken from the pages of a fictional local newspaper, The Avonford Star. Much of the information that you receive from the media is of a broadly statistical nature. In these books you are encouraged to recognise this and shown how to evaluate what you are told.
Contents
1 The Poisson distribution 1
The Poisson distribution 3
Modelling with a Poisson distribution 7
The sum of two or more Poisson distributions 12
The Poisson approximation to the binomial distribution 18
2 The Normal distribution 32
Using Normal distribution tables 34
The Normal curve 39
Modelling discrete situations 49
Approximating the binomial distribution so
Approximating the Poisson distribution 52
3 Samples and hypothesis testing es
Interpreting sample data using the Normal distribution 68
Contingency tables 81
The \2 test for independence in a contingency table 87
4 Bivariate data 104
Describing variables 106
Interpreting scatter diagrams 107
Product moment correlation 110
Rank correlation 132
The least squares regression line 142
Appendices 159
1. Mean and variance of the Poisson distribution 159
2. The sum of two independent Poisson distributions 160
3. The equivalence of Spearman’s rank correlation
coefficient and Pearson’s product moment correlation
coefficient 161
4. The least squares regression line 162
Answers ies
Chapter 1 165
Chapter 2 167
Chapter 3 171
Chapter 4 173