# BSc Actuarial Science and Mathematics

Year of entry: 2022

## Course unit details:Introduction to Statistics

Unit code MATH10282 10 Level 1 Semester 2 Department of Mathematics No

### Overview

The course gives a general introduction to statistics and is a prerequisite for all future statistics courses.

### Pre/co-requisites

Unit title Unit code Requirement type Description
Probability 1 MATH10141 Pre-Requisite Compulsory

### Aims

The aims of this course unit are to help students

develop a knowledge of basic statistical concepts and methodology which build on the ideas in probability studied in MATH10141;

develop practical statistical skills.

### Learning outcomes

On successful completion of this course unit students will be able to:

• define elementary statistical concepts and terminology such as sampling distribution, unbiasedness, confidence intervals and hypothesis tests,
• analyse and compare statistical properties of simple estimators and tests,
• conduct exploratory data analysis and statistical inferences, including confidence intervals and hypothesis tests, in simple one and two-sample situations,
• interpret the results of such analyses,
• use the statistical computing software R to carry out simple data analysis, including presentation of graphical and numerical summaries, and simulations.

### Syllabus

Populations and samples, random sampling. 

Representing sample data the histogram, boxplot, numerical summary measures. 

Probability models for data. 

Sampling distributions of sample statistics - the sample mean and its distribution under Normality, using the Central Limit Theorem, the sample proportion, the sample variance, the chi-squared distribution. 

Point estimation the bias and variance of an estimator, choosing between competing estimators. 

The likelihood function and maximum likelihood estimators for discrete variables. 

Confidence intervals. Single sample procedures for a Normal mean and variance, the population proportion. Two sample procedures for the difference between two Normal means and the difference between two population proportions. 

Hypothesis testing introductory ideas and concepts. 

Tests based on a single sample the Normal mean (variance known and unknown), the Normal variance, a non-Normal mean parameter, the Binomial probability parameter. Relationship between CIs and hypothesis testing. 

Calculation of the probability of rejecting the null for a given value of the population parameter. 

Tests based on two independent samples for differences between two Normal means, two non-Normal means, two population proportions. [2

### Assessment methods

Method Weight
Other 20%
Written exam 80%

Two coursework assignments (20%) plus end of semester examination (80%).

### Feedback methods

Feedback supervision will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

G M Clarke and D Cooke, A Basic Course in Statistics (Fourth Edition) Oxford University Press, 1998;

Robert V Hogg, Introduction to Mathematical Statistics (Sixth Edition) Prentice Hall, 2005;

Sheldon M Ross, Introduction to Probability and Statistics for Engineers and Scientists (Third edition) Elsevier Science, 2004;

Michael J Crawley, Statistics: An Introduction Using R. John Wiley & Sons Ltd, 2007

### Study hours

Scheduled activity hours
Lectures 22
Tutorials 11
Independent study hours
Independent study 67

### Teaching staff

Staff member Role