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Course Outline
School of Health Sciences
Program: Biological Sciences Technology
Option:
Service provided by: School of Computing and Academic Studies, Mathematics Dept.
Start Date:
Total Hours:
Hours/Week:
End Date:
100 Total Weeks:
Lecture:
5
20
3
Prerequisites
Course No.
Course Name
MATH 1441
Technical Mathematics for
Biological Sciences
or consent of the instructor

MATH 2441
Statistics
Lab:
2
Term/Level:
Shop:
2
Course Credits:
Seminar:
6.5
Other:
MATH 2441 is a Prerequisite for:
Course No. Course Name
MATH 3441 Microcomputer Applications for
Food Technology
FOOD 3030 Quality Control 1
Course Description
The course covers the organization and graphical representation of data, frequency distributions, measures of
central tendency, variation and other measures; probability theory and laws, random variables, discrete and
continuous probability distributions; sampling, estimation and hypothesis testing with both large and small samples;
application to population means, proportions, difference of population means, paired differences; method of least
squares, liner regression and correlation, goodness-of-fit tests and a brief introduction to analysis of variance.

Detailed Course Description
The goal of this course is to aid the student in the development of a comprehension of



descriptive statistics
elementary probability including both discrete and continuous distributions
statistical estimation and hypothesis testing, for large and small samples, including linear regression and
correlation, goodness-of-fit tests and an introduction to ANOVA,
sufficient to apply appropriate basic statistical methods to problems arising in biological sciences technology.

Evaluation
Final Examination
Term Tests (4)
Quizzes (many)
TOTAL
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40%
40%
20%
100%
Comments: Minimum passing grade for this course is 50%.
Page 1 of 9
Course Outline
MATH 2441 Statistics

(cont’d.)
Course Learning Outcomes/Competencies
Upon successful completion, the student will be able to:
1.
construct class frequency and relative class frequency tables, and produce histograms based on these tables.
2.
design and construct stem-and-leaf displays, interpret such displays, and demonstrate how to regenerate the
original data from such a display.
3.
demonstrate use of summation notation.
4.
compute several measures of central tendency (mean, median, mode, etc.), explain the advantages and
disadvantages of each, and give examples of situations in which each would be used.
5.
describe and compute various measures of dispersion (variance, standard deviation, range, coefficient of
variation), and explain the advantages and disadvantages of each.
6.
compute proportions associated with categorical data.
7.
compute and interpret measures of relative standing (percentile); compute the five-number summary for a set
of data, and construct a boxplot; also construct and interpret side-by-side boxplots for two sets of data.
8.
describe some simple approaches to detecting or dealing with outliers in a set of observations, and explain why
the issue of outliers is a sensitive one in statistics.
9.
state the relative frequency interpretation of probability and distinguish it from the notion of a subjective
probability.
10. state the basic properties of probabilities, and justify them in terms of the characteristics of an actual random
experiment.
11. compute empirical probabilities from observational data and for simple models (coin flips, random draw, etc.)
where the possible outcomes (sample space) can be expressed in terms of a set of equally-likely elementary
events.
12. demonstrate the use of simple counting techniques (combinations and permutations) to compute probabilities
of selection of samples with certain characteristics from a population of known characteristics (and use this
skill to comment on simple claims made about the population. For example, if 9 out of 10 randomly selected
packages of a food are found to be underweight, what can we say about the claim that a certain proportion of
all of these packages have the appropriate weight?)
13. explain the concept of a conditional probability.
14. demonstrate the application of the so-called “total probability formula” and Bayes’ formula to a variety of
situations arising in biological sciences (e.g., dealing with the false positive problem when testing for the
presence of a rare disease, rare contaminant, etc.).
15. explain what is meant by a random variable, a probability distribution and a cumulative probability
distribution, demonstrate how to use cumulative probability tables to compute probabilities; explain what is
meant by the mean and standard deviation of a random variable; distinguish between discrete and continuous
random variables.
16. describe the characteristics of a binomial experiment; justify the use of the binomial probability distribution in
appropriate circumstances; demonstrate the determination of binomial probabilities from formula, probability
tables and cumulative probability tables.
17. apply the binomial distribution to solve problems involving lot-acceptance sampling.
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Course Outline
MATH 2441 Statistics

(cont’d.)
Course Learning Outcomes/Competencies
18. describe the characteristics of the Poisson experiment; justify the use of the Poisson probability distribution in
appropriate circumstances; and apply the Poisson distribution to solve problems involving the likelihood of a
given number of occurrences of some event within a specified interval (e.g., number of service calls within a
specified time interval, number of organisms within a specific region of a surface).
19. describe the general characteristics of the normal distribution; describe the relationship between the standard
normal distribution and all other normal distributions; demonstrate the computation of normal probabilities
using a table of standard normal probabilities; demonstrate the computation of percentiles for both standard
and general normal distributions; construct and interpret normal probability plots for sets of observations.
20. demonstrate the computation of approximations to binomial probabilities using the standard normal probability
table.
21. demonstrate the computation of approximation binomial probabilities from using a cumulative Poisson
probability table, and state the conditions under which this and the previous approximation are considered
valid.
22. explain what is meant by a sampling distribution, and explain how the characteristics of a sampling
distribution are related to those of the sampled population.
23. distinguish between a point estimate and an interval estimate, and state the advantages of interval estimates.
24. illustrate the development of confidence interval estimates for the mean of a single population under various
circumstances ( is known,  unknown but large sample available,  unknown and small sample available),
describing typical contexts in which each type of situation is likely to arise.
25. demonstrate the use of the student t-distribution tables; explain how the t-distribution differs from the standard
normal distribution.
26. explain what is meant by the standard symbols z and t, and how to determine values for these quantities
given specific values of .
27. illustrate the development of confidence interval estimates for the population proportion in the large sample
case.
28. illustrate the development of confidence interval estimates for the variance/standard deviation of a single
population, using the 2-distribution and the normal distribution.
29. illustrate the development of a confidence interval estimate of the difference of two population means
(variances known, variances unknown but large samples available, variances unknown but assumed to be
equal).
30. illustrate the development of a confidence interval estimate of the difference of two population proportions
(large samples available).
31. describe the basic procedures for setting up a test of hypotheses; define, explain, illustrate basic concepts such
as hypothesis, type 1 and 2 errors, level of significance, test statistic, rejection region, one-tailed and two-tailed
tests, etc.
32. describe and carry out the test of hypotheses involving a population mean (large and small sample case), and
of hypotheses involving a population proportion (large sample case).
33. describe and carry out the test of hypotheses involving the difference of two population means (or the
difference of two population proportions).
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Course Outline
MATH 2441 Statistics

(cont’d.)
Course Learning Outcomes/Competencies
34. describe and carry out the test of hypotheses involving differences of paired observations from
two populations (paired difference test); explain the difference between independent and dependent samples
from two populations; and describe the advantage of using a paired-difference test when applicable.
35. describe the major features of the basic single-independent variable linear regression model; and be able to
compute the slope and intercept of the least-squares best-fit line through a scatterplot of points.
36. interpret the value of the coefficient of determination and the appearance of a plot of residuals to assess the
effectiveness and validity of a linear regression model in a specific instance.
37. carry out tests of hypotheses involving the slope of the regression line (t-test); construct and interpret
estimation and prediction intervals for the dependent variable.
38. compute the correlation coefficient; interpret the result using the conventional rule of thumb; and perform tests
of the hypothesis that the correlation coefficient has the value zero.
39. discuss and distinguish between issues of regression, correlation and causality.
40. carry out the 2-test for goodness-of-fit of observational data to a given discrete distribution.
41. carry out the 2-test to test for independence of homogeneity in the distribution of observations.
42. explain why the 2-test is not ideal for testing goodness-of-fit for continuous distributions.
43. carry out the steps of the Kolmogorov-Smirnoff test for normality, and describe the conditions under which the
test is valid.
44. explain the basic principle behind single-factor ANOVA; set up the standard ANOVA table; carry out the
F-test and interpret the results.

Verification
I verify that the content of this course outline is current.
Authoring Instructor
Date
I verify that this course outline has been reviewed.
Program Head/Chief Instructor (Math)
Date
Program Head/Chief Instructor (Technology)
Date
I verify that this course outline complies with BCIT policy.
Dean/Associate Dean (Math)
Date
Note: Should changes be required to the content of this course outline, students will be given reasonable notice.
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Course Outline
MATH 2441 Statistics

Instructor(s)
David W. Sabo

(cont’d.)
Office Location: SW2–231
Office Hrs.:
TBA
Office Phone:
604-432-8698
E-mail Address: [email protected]
Office Fax:
604-432-9173
Learning Resources
Text(s) and Equipment:
Required:
There is no required textbook for the course.
Recommended:
A list of suggested reference texts will be given in class. The course will continue to be presented at a level
compatible with such standard textbooks as Introduction to Probability and Statistics by Mendenhall and Beaver
(9th edition, Duxbury Press).
A hand-held calculator with statistical functions is desirable (two-variable statistical functions are an asset).
Internet access is a definite asset. All BCIT students now have Internet access through any Institute microcomputer
attached to an internal network. Access to supplemental course materials is available through the website
apples.soe.bcit.ca.

Information for Students
(Information below can be adapted and supplemented as necessary.)
Assignments: Late assignments, lab reports or projects will not be accepted for marking. Assignments must be done on an
individual basis unless otherwise specified by the instructor.
Makeup Tests, Exams or Quizzes: There will be no makeup tests, exams or quizzes. If you miss a test, exam or quiz, you will
receive zero marks. Exceptions may be made for documented medical reasons or extenuating circumstances. In such a case, it
is the responsibility of the student to inform the instructor immediately.
Ethics: BCIT assumes that all students attending the Institute will follow a high standard of ethics. Incidents of cheating or
plagiarism may, therefore, result in a grade of zero for the assignment, quiz, test, exam or project for all parties involved and/or
expulsion from the course.
Attendance: The attendance policy as outlined in the current BCIT Calendar will be enforced. Attendance will be taken at the
beginning of each session. Students not present at that time will be recorded as absent.
Illness: A doctor’s note is required for any illness causing you to miss assignments, quizzes, tests, projects or exam. At the
discretion of the instructor, you may complete the work missed or have the work prorated.
Attempts: Students must successfully complete a course within a maximum of three attempts at the course. Students with two
attempts in a single course will be allowed to repeat the course only upon special written permission from the Associate Dean.
Students who have not successfully completed a course within three attempts will not be eligible to graduate from the
appropriate program.
Course Outline Changes: The material or schedule specified in this course outline may be changed by the instructor. If
changes are required, they will be announced in class.
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Course Outline
MATH 2441 Statistics

(cont’d.)
Information for Students (cont’d.)
Course Credit: Applications for course credit or course exemption on the basis of previously completed mathematics courses
are assessed on a case-by-case basis by the BCIT Mathematics Dept. taking into account all of the following:
 the correspondence between topics, content and level
 recency (generally no more than 3–5 years)
 the grade (generally at least a C+ or 65%)
 the context (course taken as part of a university or college science or engineering program, rather than, for example, an arts
or social science program).
Course Makeup — Equivalents: In most cases, students who fail a math course or withdraw from a math course may make
up the course by taking makeup courses. These courses may be BCIT evening or correspondence courses, or equivalent courses
from another institution. In some cases, students may be required to take more than one course or several distance education
modules to gain credit. In some cases, students may be required to achieve a mark of greater than 50% in the makeup course in
order to achieve credit for the failed course. If a student fails a course, a makeup letter signed by the mathematics program head
will be sent to the student, the technology program head, and to Student Records. Any course substitutions would require prior
written approval of the mathematics program head.
Learning Disabilities: BCIT is committed to providing opportunities for students with disabilities to meet their educational,
career, and personal goals within the context of the Institute’s training mandate. For further information, contact the Disability
Resource Centre.
I.D. Required in Examination Centres: In order to write exams, students will be required to produce photo identification at
examination centres. Photo I.D. must be placed on the desk and must remain in view on the desk while writing the exam, for
inspection by invigilators. Students should bring a BCIT OneCard or alternatively two pieces of identification, one of which
must be government photo I.D. such as a driver’s licence. Please see BCIT Policy #5300, Formal Invigilation Procedures.

Assignment Details
There are no assignments in the course to be submitted for grading. However, practice problem sets will be
distributed weekly, and students are expected to work on these for their own benefit during tutorial sessions each
week. It is impossible for most students to achieve a working knowledge of the basic course material without
spending at least the two hours in the tutorial sessions working through practice problems.
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Course Outline
MATH 2441 Statistics
(cont’d.)
Schedule
Time allocations for various topics are as indicated below. The precise order in which the topics will be covered
may differ from the schedule below, and details will be provided in class. Information regarding the
Reference/Reading column will be provided in class and/or via the course website.
Weeks
2
Topics
Reference/
Reading
Organization of Data – Pictorial Summaries
 stem-and-leaf displays
 frequency distributions
 graphs and charts, histograms
Organization of Data – Numerical Summaries
 summation notation
 measures of central tendency
 categorical data, proportions
 measures of dispersion
 measures of relative standing
 five-number summaries and boxplots, treatment of outliers
Use of Model Distributions
5
Elementary Probability
 what is probability?
 calculating elementary probabilities
 counting techniques (combinations and permutations, branching
diagrams)
 conditional probability formula and Bayes’ formula, with applications to
biological sciences
Midterm Test #1
Probability Distributions
 random variables
 discrete random variables
 binomial distribution
 Poisson distribution
 continuous random variables
 exponential distribution
 normal and standard normal distribution
 approximations
 normal approximation to the binominal distribution
 Poisson approximation to the binominal distribution
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Course Outline
MATH 2441 Statistics
Weeks
(cont’d.)
Topics
Reference/
Reading
Sampling Distributions
 distribution of sample means
Midterm Test #2
6
Estimation – One Population
 point estimation
 confidence interval for  when  is known
 confidence interval for  when  is unknown
 large sample case
 small sample case (t-distribution)
 confidence interval for the population proportion (large sample case)
 confidence interval for the population variance (2 and large sample
case)
Estimation – Two Populations
 difference of population means
 variances known
 variances unknown/assumed equal
 difference of two population proportions
 exponentia
Midterm Test #3
Tests of Hypotheses
 terminology, general formalism, concepts
 tests of hypotheses: single populations
 tests of hypotheses: two populations
 paired differences tests
2
Linear Regression and Linear Correlation
 computation of the regression line
 inferences based on the regression line
 correlation analysis
 discussion of regression, correlation and causality
Midterm Test #4
2
Analysis of Categorical Data
 2-test for goodness-of-fit (discrete distributions)
 2-test for independence
 2-test for homogeneity
 Kolmogorov-Smirnoff test for normality
2
Introduction to ANOVA
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Course Outline
MATH 2441 Statistics
Weeks
1
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(cont’d.)
Topics
Reference/
Reading
Comprehensive Final Examination
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