Undergraduate Programme and Module Handbook 2023-2024

# Module MATH1617: Statistics I

## Department: Mathematical Sciences

### MATH1617: Statistics I

Type | Open | Level | 1 | Credits | 10 | Availability | Available in 2023/24 | Module Cap | None. | Location | Durham |
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#### Prerequisites

- Normally, A level Mathematics at grade A or better, or equivalent

#### Corequisites

- Calculus I (Maths Hons) (MATH1081) or Calculus I (MATH1061) and Probablity I (MATH1597)

#### Excluded Combination of Modules

- Mathematics for Engineers and Scientists (MATH1551), Single Mathematics A (MATH1561), Single Mathematics B (MATH1571) may not be taken with or after this module.

#### Aims

- To introduce the principles and procedures of frequentist and Bayesian statistics, and illustrate them with canonical examples. This lays the foundations for all subsequent study of statistics.
- To present frequentist and Bayesian principles as alternative approaches to doing statistics; to compare frequentist and Bayesian procedures and results.
- To demonstrate the relevance of these principles and procedures to real problems.

#### Content

- Introduction: applications; the nature of statistics; two schools of thought: frequentist and Bayesian.
- Frequentist inference: principles and procedures of frequentist statistics; statistics and sampling distributions, confidence intervals, hypothesis testing; examples.
- Bayesian inference: principles and procedures of Bayesian statistics; posterior distributions, credible intervals, decisions; examples.
- Comparison between frequentist and Bayesian inference.
- Demonstration of how the principles and procedures apply to real problems.

#### Learning Outcomes

Subject-specific Knowledge:

- Knowledge of the principles and procedures of both frequentist and Bayesian inference as approaches to doing statistics.
- Understanding of how to apply these principles and procedures, both in general, and in canonical examples.
- Knowledge of the strengths and weaknesses of each approach.
- Knowledge of the similarities and differences between the two approaches.
- Understanding of the relevance of these principles and procedures to real problems.

Subject-specific Skills:

- Ability to solve in principle and in practice a range of both routine and more challenging problems in statistics.

Key Skills:

- Students will have basic mathematical skills in the following areas: problem solving, modelling, computation.

#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

- Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
- Tutorials provide the practice and support in applying the methods to relevant situations as well as active engagement and feedback to the learning process.
- Problem classes show how to solve example problems in an ideal way, revealing also the thought processes behind such solutions.
- Weekly homework problems provide formative assessment to guide students in the correct development of their knowledge and skills. They are also an aid in developing students' awareness of standards required.
- The examination provides a final assessment of the achievement of the student.

#### Teaching Methods and Learning Hours

Activity | Number | Frequency | Duration | Total/Hours | |
---|---|---|---|---|---|

Lectures | 27 | 3 pw in wks 11,12,13,15,17,19; 2 pw in wks 14, 16, 18, 20; (alternating with Problems Classes), 1 revision in wk 21 | 1 Hour | 27 | |

Tutorials | 6 | 1 pw in wks 12, 14, 16, 18, 20; 1 revision in wk 21 | 1 Hour | 6 | ■ |

Problem classes | 4 | 1 pw in wks 14, 16, 18, 20 | 1 Hour | 4 | |

Preparation and Reading | 63 | ||||

Total | 100 |

#### Summative Assessment

Component: Examination | Component Weighting: 90% | ||
---|---|---|---|

Element | Length / duration | Element Weighting | Resit Opportunity |

Written examination | 2 hours | 100% | Yes |

Component: Continuous Assessment | Component Weighting: 10% | ||

Element | Length / duration | Element Weighting | Resit Opportunity |

Weekly written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students. Students will have about one week to complete each assignment. Students will have about one week to complete each assignment. | 100% | Yes |

#### Formative Assessment:

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University