Department of

Mathematics and Statistics

Stat 2507: Introduction to Statistical Modelling

Summer 2016

Instructor: Mr. Fares Said Lecture: Mon. & Wed. 18:05-19:25

Email: fares.said@carleton.ca Place: Azreili Theatre room 102

O�ce: TBD O�ce Hours:16:30-18:30 on Mondays

or by appointment

Course Pages:

1. https://www.carleton.ca/culearn/

2. https://students.carleton.ca/

Objectives: This course is primarily designed for undergraduate students. It covers introductionto probability theory, random variables, discrete and continuous distributions, contingency tables,sampling distributions, distribution of sample mean, Central Limit Theorem, interval estimation andhypothesis testing. The statistical software Minitab will be used.

Precludes: BIT 2000, BIT 2100, BIT 2300, ECON 2200, ECON 2201, GEOG 2006, STAT 2606

Textbook: Introduction to Probability and Statistics, Third Canadian Edition, by Menden-hall,

Beaver, and Ahmed. Publisher: Nelson.

Reference: Student Solutions Manual for Use with Introduction to Probability and Statistics, 3rdCanadian Edition, by Mendenhall, Adamic, Gillis, and Caron.

Labs: Herzberg building (HP) room 3393. One-hour compulsory computer lab per week.

Assignments: There will be 5 assignments with speci�c due dates to be announced in class. Allassignments must be submitted; however, only the top four will count toward the term mark. Lateassignments will not be accepted.

Midterm: There will be a 90-minute closed-book midterm held on Wednesday, June 22, 18:00-19:30.The place TBA in class and on cuLearn.

Final: 3-hour �nal exam is a closed-book exam of the whole course covered during the term, tobe held during the exam period (August 19-25). Ensure that you DO NOT schedule �ights or otherdepartures during the exam period. The format includes both multiple-choice and non-multiple-choicequestions.

Grade Distribution:

Assignments 25%Midterm Exam 25%Final Exam 50%

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Stat 2507 Introduction to Statistical Modelling Monday 18th April, 2016

� If you miss the midterm test you will receive a zero unless you provide your instructor with aproper documented reason (e.g., medical), in which case the weight of the midterm test will beshifted to the �nal exam. The same rule applies to each assignment.

� Students wishing to see their �nal examination papers must make an appointment within oneweek of the examination to do this. Please note that we do not change your grade on the basisof your needs (such as scholarships, etc).

� Selected exercises, mainly from the text, will be assigned for your practice. These exercises arenot to be handed in and will not be graded. However, to succeed in the course it is absolutelyessential that you do the exercises on a regular basis.

� Students who miss the examination may be eligible for a deferred exam. Application for adeferral exam must be made, with appropriate documentation, to the Registration O�ce within�ve working days after the examination. Please note that the deferred exam for this course willbe the �nal exam for the Summer term course and will be written in September.

Calculator: You may use non-programmable, non-graphing calculators for the tests and the �nalexam. I reserve the right to disallow any calculator.

Important Dates:

May 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . First classMay 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Statutory holidayJune 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exam accommodation requestJune 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Last day of early summer classesJune 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MidtermJuly 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Statutory holidayJuly 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Late summer classes beginAugust 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Statutory holidayAugust 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Last day of classesTBD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Final Exam

Academic Accommodations: You may need special arrangements to meet your academic obliga-tions during the term. For an accommodation request the processes are as follows:

Pregnancy obligation: write to me with any requests for academic accommodation during the �rst twoweeks of class, or as soon as possible after the need for accommodation is known to exist. For moredetails visit the Equity Services website http://www2.carleton.ca/equity/accommodation/

Religious obligation: write to me with any requests for academic accommodation during the �rst twoweeks of class, or as soon as possible after the need for accommodation is known to exist. For moredetails visit the Equity Services website http://www2.carleton.ca/equity/accommodation/

Academic Accommodations for Students with Disabilities: The Paul Menton Centre for Students withDisabilities (PMC) provides services to students with Learning Disabilities (LD), psychiatric/mentalhealth disabilities, Attention De�cit Hyperactivity Disorder (ADHD), Autism Spectrum Disorders(ASD), chronic medical conditions, and impairments in mobility, hearing, and vision. If you have adisability requiring academic accommodations in this course, please contact PMC at +1613-520-6608or pmc@carleton.ca for a formal evaluation. If you are already registered with the PMC, contactyour PMC coordinator to send me your Letter of Accommodation at the beginning of the term, andno later than two weeks before the �rst in-class scheduled test or exam requiring accommodation (ifapplicable). After requesting accommodation from PMC, meet with me to ensure accommodationarrangements are made. Please consult the PMC website for the deadline to request accommodationsfor the formally-scheduled exam (if applicable).

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Stat 2507 Introduction to Statistical Modelling Monday 18th April, 2016

Tentative Course Outline: The weekly coverage might change as it depends on the progress ofthe class. However, you must keep up with the reading assignments.

Week Content Chapter

Week 1May 2,4

� What is Statistics? Population and sample. Elements of Statistical problems.� Data sets, describing data sets by graphs, histograms, stem and leaf plots

1

Week 2May 9,11

� Mathematical notation. Mean, median, mode. Standard deviation , variance� Tchebyshe�'s theorem, empirical rule. Percentiles, quartiles, z-scores. Box plots, Bivariate

data

2-3

Week 3May 16,18

� Events, sample space, combination of events, probability of an event� Addition rule, multiplicative rule. Conditional probability and independence

4

Week 4May 25,30

� Bayes' rule. Probability distribution of a discrete random variable� Expectation and variance de�nitions

4

Week 5Jun 1,6

� Binomial, hypergeometric, and Poisson distributions� Poission approximation to the binomial

5

Week 6Jun 8,13

� Continuous distributions, normal distribution.� Normal approximation to the binomial.

6

Week 7Jul 4,6

� Random sampling. Sampling distributions. Central Limit Theorem.� Sample mean and sample proportion. Sum and di�erence of independent random variables

7

Week 8Jul 11,13

� Large Sample Estimation. Population Mean.� Large sample con�dence intervals for the population mean

8

Week 9Jul 18,20

� Con�dence intervals for parameter of a binomial.Choosing sample size.� Di�erence between two means. Di�erence between two binomial populations

8

Week 10Jul 25,27

� Test of hypothesis: Large sample. Rejection region. Acceptance region. Test Statistic.� Test of hypothesis for the mean. Test of hypothesis for a binomial proportion

9

Week 11Aug 3,8

� Test of hypothesis, large and small sample tests.� p-values. Type-I & II errors.

9

Week 12Aug 10,15

� Small-sample inference for di�erence between two means.� Di�erence between two proportions. Inference for population variance.

10

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