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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 84097062305/17 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. 84097062305/17 Page 2 of 9 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). 84097062305/17 Page 3 of 9 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. 84097062305/17 Page 4 of 9 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. 84097062305/17 Page 5 of 9 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. 84097062305/17 Page 6 of 9 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 84097062305/17 Page 7 of 9 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 84097062305/17 Page 8 of 9 Course Outline MATH 2441 Statistics Weeks 1 84097062305/17 (cont’d.) Topics Reference/ Reading Comprehensive Final Examination Page 9 of 9