MATH1725 Introduction to Statistics

MATH1725 Introduction to StatisticsLecturer: Andrew J. Baczkowski – room 6.13 E.C.Stoner – email: sta6ajb@leeds.ac.ukRegularly updated information about the module is available on the internet at:http://www.maths.leeds.ac.uk/∼sta6ajb/math1725/math1725.htmlModule Objective: To provide an introduction to statistics; to consider hypothesis tests andthe relationships between variables and to analyse count data.Provisional Detailed Syllabus:1. Populations and samples. Frequency distributions. Histograms. Measures of location andspread.2. Statistical inference. Point estimation. Sampling distribution of the sample mean. Centrallimit theorem. Interval estimation. Confidence interval for mean.3. Hypothesis testing for mean; p-values. Inference for two populations: two independent samplesand paired samples.4. Several random variables: sample covariance and correlation, discrete and continuous variables,properties of expectations and population covariance, linear combinations of random variables.5. Least squares regression.6. Attribute data: hypothesis test for a population proportion, large sample confidence intervalfor a population proportion, comparing two populations.7. Chi-squared tests: single sample classified into groups, tests of goodness-of-fit for fitting distributionsto data, contingency tables.Booklist: Any of the books suggested for MATH1715 will be useful.1. “Essential Statistics” by D.G. Rees, published by Chapman and Hall, 2001, price ≈ £44. Areasonable mix of examples and theory. Some errors!2. “Mathematical Statistics and Data Analysis (3rd edition)” by J.A. Rice, published by DuxburyPress, 2007, price ≈ £50. Quite advanced but interesting if you have done Statistics before.3. “A Basic Course in Statistics (4th edition)” by G.M. Clarke and D. Cooke, published byEdward Arnold, 2004, price ≈ £40. A book widely used at A-level.4. “Elementary Statistics (8th edition)” by N.A. Weiss, published by Pearson, 2012, price ≈ £40.A nice book.5. “Stats: Data and Models” by R.D. de Veaux, P.F. Velleman, and D.E. Bock, published byPearson/Addison-Wesley, 2005, price ≈ £43. Another simple textbook. Lots of real examples andminimal mathematics. Internet on-line examples.Attendance: Attendance sheets will be circulated in each lecture for you to sign.Assessment:80% of marks for two hour examination at end of semester.20% of marks for continuous assessment (Practical work and the exercises).Examination Paper: The examination paper will be in two parts, each worth 50% of the examinationmark. Part A will consist of twenty questions. Half will be multiple choice questions andhalf will require a short answer with each question being worth two marks. Part B will have fourlonger questions, taking perhaps 30 minutes each. You have to answer all questions from part Aand two questions from part B.1

Exercise Sheets for MATH1725: A new exercise sheet will be commenced every two weeks orso. You will have a fortnight to discuss each in your tutorials before having them marked. One ofthe exercises will be marked by a fellow student and some by your tutor!Arrange with your tutor how you are to hand-in your completed work.Solution sheets will generally be given out in lectures about a week after the due completiondate. If you cannot understand the solutions, ask your tutor!The exercise start and completion dates are given in terms of lecture number; exercises arestarted after the relevant work has been examined in lectures. Week 1 (lectures 1 and 2) of themodule is the first week after the January examinations, week commencing Monday 26th January2015. (The University designates this as week 14 in the Module Timetable!)Marking of Exercise Sheets – information for students: Exercises I, III, IV and V will bemarked by your tutor who will give you a mark out of FIVE for each piece of work.Exercise II will be marked by a fellow student. Get someone from your tutorial group to markyour work. For each question award one mark for a completely correct answer, half a mark if “halfright”, and no marks if the question is not done or is completely wrong. Your total mark for theseexercises will be out of FIVE. Tell your TUTOR your mark.At the end of the semester, your tutor will give me the mark out of 20 for the four exerciseshe has marked, together with the mark out of 5 for the exercise your fellow student has marked.Yes, it is easy to cheat, but recall Wainwright’s Pennine Way Companion,If you start, don’t give up, or you will be giving up at difficulties all your life.To re-express this,If you mark, don’t cheat, or you will be cheating all your life.And what for? One mark? Even Sir Richard Rich perjured (cheated) himself for more than that!As Sir Thomas More remarked on seeing Rich had been appointed Attorney-General for Wales inRobert Bolt’s A Man for all Seasons,For Wales? Why, Richard, it profits a man nothing to give his soul for the whole world...But for Wales —!Marking of Exercise Sheets – information for tutors: Exercises I, III, IV and V will bemarked by the tutor who will give a mark out of FIVE for each piece of work and return themarked work to the student. The standard School of Mathematics 0-5 coursework marking schemeused by tutors is as follows:5 – “Excellent” Substantially correct with only minor errors and well explained.4 – “Good” Very few significant errors, or all correct but not well explained.3 – “Satisfactory” Good enough to pass but with significant errors, or with some significant questionsnot answered.2 – “Unsatisfactory” Some correct answers, but lots of errors, or many questions not answered.1 – “Very Unsatisfactory” More or less all wrong, or almost all questions not answered.0 – “No Work Submitted” No work handed in, or handed in after the deadline.For exercise II the students will mark one another’s work. Each question receives one markfor a completely correct answer, half a mark if “half right”, and no marks if the question is notdone or is completely wrong. This exercise will be marked out of FIVE by a fellow student. Thestudents should tell you their mark. If you wish, you can ask your tutees to hand in their markedwork for you to check.At the end of the semester, please give me the mark out of 20 for the FOUR exercises you havemarked, together with the mark out of 5 for the ONE exercise the students have marked.Lecture 12