## MATH1725 Introduction to Statistics

### 10 creditsClass Size: 300

Module manager: Dr A. Baczkowski
Email: sta6ajb@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2008/09

### Pre-requisite qualifications

A-level in Mathematics, including some Statistics.

### Pre-requisites

 MATH1715 Introduction to Probability

This module is approved as an Elective

### Module summary

This module builds on the ideas introduced in MATH1715 by focusing on relationships between variables, including techniques for handling data arising from both related and independent samples. Inferential methods are used to compare the means of two populations, e.g. 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 course 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) carry out appropriate hypothesis tests on the means of one or two populations; (b) understand and carry out simple least squares linear regression; (c) carry out inference on proportions; (d) carry out chi-squared tests; (e) have knowledge of descriptive statistics; (f) understand simple inference.

### Syllabus

1. Populations and samples. Frequency distributions. Histograms.
2. Measures of location. Measures of spread. Interpreting the standard deviation.
3. Statistical Inference. Iid random variables. Point estimation. Sampling distribution of the sample mean. Central limit theorem. Interval estimation. Confidence intervals for mean (variance known and unknown).
4. Hypothesis testing for means. p-values. Tests concerning means. z-test. t-test.
5. Inference for two populations. Two independent samples. Paired samples.
6. Several random variables. Sample covariance and correlation. Continuous bivariate distributions. Properties of expectations, population covariance, correlation. Linear combinations of random variables.
7. Regression. Least squares regression. Inference concerning slope. Computer package for regression.
8. Attribute data. Hypothesis tests for a population proportion. Large sample confidence interval for a population proportion. Comparing two proportions.
9. Chi-squared tests. Single sample classified into two or more groups. Fitting distributions, for example binomial, Poisson, normal. Goodness of fit tests. Contingency tables.

### 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 20 1.00 20.00 Practical 2 1.00 2.00 Tutorial 5 1.00 5.00 Private study hours 73.00 Total Contact hours 27.00 Total hours (100hr per 10 credits) 100.00

### 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 . 20.00 Total percentage (Assessment Coursework) 20.00

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

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 80.00 Total percentage (Assessment Exams) 80.00

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