## MATH1712 Probability and Statistics II

### 10 creditsClass Size: 455

Module manager: Dr Jochen Voss
Email: J.Voss@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2020/21

### Pre-requisite qualifications

MATH1710 or equivalent.

### This module is mutually exclusive with

 LUBS1240 Maths&Stats For Bus&Ec 1

Module replaces

MATH1725

This module is approved as a discovery module

### Module summary

This module extends the ideas introduced in MATH1710, using approximating distributions to estimate quantities of interest in the population using a frequentist approach. We model relationships between variables, including data arising from both related and independent samples. Inferential methods are used to compare the means of two populations, eg to compare the average wages of males and females doing similar occupations. Where two variables are related, the nature and strength of the relationship can be examined by regression procedures. The module also includes techniques relevant to the analysis of count data and tests concerning proportions.

### Objectives

On completion of this module, students should be able to:
(a) describe properties of key distributions and understand simple inference
(b) with the aid of a statistical package, carry out appropriate hypothesis tests on the means of one or two populations
(c) understand and carry out simple least squares linear regression
(d) carry out inference on proportions
(e) carry out chi-squared tests

### Syllabus

1. Sampling distributions and central limit theorem.
2. Frequentist statistical inference. Iid random variables. Point estimation and interval estimation. Confidence intervals for mean (variance known and unknown).
3. Hypothesis testing for means. p-values. Tests concerning means. z-test. T-test.
4. Inference for two populations. Two independent samples. Paired samples.
5. Several random variables. Sample covariance and correlation. Continuous bivariate distributions. Properties of expectations, population covariance, correlation. Linear combinations of random variables.
6. Regression. Least squares regression. Inference concerning slope.
7. Binary data. Hypothesis tests for a population proportion. Large sample confidence interval for a population proportion. Comparing two proportions.
8. Chi-squared tests. Single sample classified into two or more groups. Fitting distributions, for example binomial, geometric, Poisson, normal. Goodness of fit tests. Contingency tables and test of independence.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

 Delivery type Number Length hours Student hours Lecture 11 1.00 11.00 Practical 2 1.00 2.00 Tutorial 5 1.00 5.00 Independent online learning hours 10.00 Private study hours 72.00 Total Contact hours 18.00 Total hours (100hr per 10 credits) 100.00

### Private study

This will include tutorial exercise sheets, lecture preparation, studying course material, using R for data analysis, revision for exams, preparing for tutorials.

### Opportunities for Formative Feedback

Fortnightly tutorials and homework sheets.

!!! In order to pass the module, students must pass the examination. !!!

### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 30.00 Total percentage (Assessment Coursework) 30.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams
 Exam type Exam duration % of formal assessment Online Time-Limited assessment 2 hr 70.00 Total percentage (Assessment Exams) 70.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated