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Probability and Statistics Math 542 Spring 2014 Syllabus Instructor: Office: Li Zhang 310 Thompson Hall Class Schedule: Phone: Email: 843-953-5033 [email protected] 5:30 – 8:15 pm Thursday, 317 Thompson Hall Instructor’s Office Hours: 12:30 – 3:00 PM Tuesday and 3:00 – 5:20 PM Thursday or by appointment Course Description: Topics will include probability, random variables, important probability distributions, sampling distributions, point and interval estimation, hypothesis testing, regression, correlation, and analysis of variance. Emphasis will be given to applications in the fields of biology, business, agriculture, political science, and education. Course Website: http://macs.citadel.edu/zhangli/courses/math542/index.htm. Course syllabus, assignments and course resources (such as PowerPoint slides and video clips) are posted on this course website. Texts: Essentials of Mathematical Statistics, Brian Albright, Jones & Bartlett Learning Chance (News, Videos, Course, and Teaching Aids), Dartmouth College, http://www.dartmouth.edu/~chance/ Addenda Series: Data Analysis and Statistics, NCTM, 1992 Addenda Series: Dealing with Data and Chance, NCTM, 1991 Grading: Exams (2): Projects: Presentation: Paper: Homework and Quizzes: Final (comprehensive) 40% 10% 5% 10% 10% 25% Exams: There will be two in-class exams which account for 40% of the final course grade. The dates for these exams are to be announced in class. No make-up exams will be offered under any circumstances. Technology Project: You will be assigned several technology projects that will combine the knowledge of statistics and probability with technology tools such as spreadsheets and statistical software such as Excel, SPSS, “R” or others that you are familiar with. A grading rubric for each project will be provided to the student. The topics for the projects will be discussed in class. Also, you are required to present your last project near the end of the semester. Late project will not be accepted. Writing Assignment: A paper/essay about a mathematician or development of mathematics is required for this class. The broad topic will be the historical development of statistics and probability including contributions from diverse cultures. You can choose a specific topic which must be approved by me, and it should have a connection to secondary mathematics. Papers should be approximately 5 pages of text, double-spaced, 12-font, 1” margins, with a minimum of three sources. A grading rubric for the paper will be provided to the student. Late paper will not be accepted. Homework/Quizzes: Homework problems will be assigned for each class and some selective homework problems will be graded. Quizzes may be given from time to time based on these problems. Final Exam: Final exam is scheduled for Thursday, May 1. Final exam is comprehensive and it accounts for 25% of your course grade. Exam Policies: All exams are close-book and close-notes exams. You may, however, refer to the formula and table attachments in your textbook. Always bring your calculator. Extra Credit: You can earn extra credit for this course by doing Problem of the Week. For each one you get right, I will add 1 point (on a 100 scale) to your final exam. Important Dates: The following dates are subject to change. Reflection Instrument Mathematical Problem Solving due date: February 27th Technology project 1 due date: March 6th Last day to withdraw with a “W”: March 10th Exam 1: March 7th - March 13th Exam 2: March 14th – April 3rd Spring break (no class): March 27th Writing assignment due date: April 10th Technology project 2 due date: April 17th Project presentations: April 24th Final Exam: May 1st in classroom You will not be allowed to take the final exam at an earlier date under any circumstances. Academic Misconduct: All work submitted for an individual grade, including paper and projects, should be the work of that single individual, and not their friends, nor their tutor. You can discuss homework problems with others but you must write in your own wordings. I will mention in the class if something like project is a group work. It is your responsibility to be familiar with the policies mentioned in The Honor Manual of The Citadel. Ignorance of these policies is not an excuse for violating them. Disability: Any student in this course who has a disability that may prevent him or her from fully demonstrating his or her abilities should contact the instructor personally as soon as possible so that necessary accommodations can be made to ensure full participation and facilitate educational opportunities. Objectives: The goal of this course is to introduce teachers to the concepts of elementary probability and statistics, allow them to generate and manipulate data sets by hand and with technology, and introduce ideas for integrating statistics into the middle and secondary curriculum. The course will require that: 1. The student will study the history of statistics and learn how statistics can be both used and abused. The student will: a. b. c. d. define statistics recognize some uses and abuses know how the study of statistics began read statistical analysis articles from educational journals and apply to classroom instruction 2. The student, using descriptive statistical techniques, will summarize, analyze, describe using measures of central tendency and variation, and graph statistical data using a variety of graphics. The student will: a. construct a frequency distribution for a set of data b. construct a pie chart, histogram, frequency polygon, ogive, and stem-and-leaf plot c. define the different types of averages or measures of central tendency: mean, median and mode for grouped and ungrouped data d. compute the mean, median, mode, midrange, and weighted mean of the data e. for a specific set of data determine which measure is most helpful f. define the measures of variation: range, variance, and standard deviation for a set of data g. compute the range, variance, and standard deviation of a set of data h. determine the effects of data transformations on the measures of central tendency and variability i. determine the standard score or z-score for a data value 3. The student will identify and apply counting principles, combinations and permutations and be able to determine the probability of an event. The student will: a. b. c. d. e. f. g. h. i. j. k. define probability terminology and the fundamental counting principle define a sample space find the probability that an event will occur find the probability one event or another will occur identify mutually exclusive events and find the probability of their occurrence apply the multiplication rule for dependent and independent events find the probability of the complement of an event define and identify conditional probability events apply Bayes’ theorem convert probability to odds and odds to probability apply the fundamental counting principle l. define permutations and find the permutations of a group of elements m. define combinations and find the number of ways in which combinations of elements can be found n. design and use simulations to determine experimental probability, emphasizing the difference in experimental and theoretical probability 4. The student will complete binomial experiments, calculate the mean and standard deviation of the binomial distribution, and determine distribution shapes. The student will: a. determine and identify random variables and probability distributions b. apply the formula for mean, variance, and expected value for a population to problem solving c. define and identify binomial experiments and compute probabilities using the formula for binomial experiments d. compute the mean of standard deviation for a binomial distribution e. identify distribution shapes and use the uniform distribution shape to find the probability of an event f. construct a box-and-whiskers plot and identify the median, minimum, maximum, upper and lower quartiles, inter-quartile range and outliers 5. The student will study applications of the standard and nonstandard normal distribution, the probability of an event, the percentile rank of a score, and the score given the percentile rank. The student will: a. b. c. d. e. define the standard normal distribution and identify its shape use the standard normal distribution to determine probabilities of events find percentages and probabilities for nonstandard normal distributions find scores when given probabilities define the Central Limit Theorem, standard error of the mean, and population correction factor and determine probabilities applying this information 6. The student will form and test a claim using a null hypothesis or alternative hypothesis to determine whether it meets the criteria of the appropriate test at a specific level of significance and will determine by means of a t-test whether there is a significant change after some type of intervention. The student will: a. define and identify a null hypothesis b. use the null hypothesis relating to a mean, proportion, or variance to determine validity and state the alternative hypothesis c. apply the t-test and P-value to test claims in which the distribution is not necessarily normal d. test a hypothesis made about a population proportion or percentage e. find the confidence interval of the population and the population mean given a sample mean f. test both dependent and independent sample means to determine if the means are statistically the same or whether there is a significant change after some type of intervention 7. The student will calculate the correlation coefficient for a set of data and then find the equation of the line of best fit (regression) to be used to make predictions when two variables are determined to be significantly related. The student will: a. b. c. d. plot ordered pairs to determine whether the variables appear to be related find the equation of the median-median line of fit calculate the correlation coefficient find the slope of the line of best fit if the correlation between the variables is strong e. determine the equation of the regression line f. use the equation of the line to make predictions 8. The student will design experiments, collect sample data, analyze the data and draw conclusions in order to present the final report. The student will: a. describe the different types of sampling b. apply the techniques of sampling and collecting data to write and test a claim using the methods previously studied to test claims c. evaluate the results of the testing d. write a report of the results drawing inferences or making conclusions e. present the results of the study to the class Suggested Outline of Topics: The following schedules are subject to change. Week 1: Orientation, introduction, and basics of probability Week 2: Probability and discrete random variables Week 3: Discrete probability distributions and continuous random variables Week 4: Normal and other probability distributions and applications Week 5: The Central Limit theorem and basics of statistics Week 6: Basic graphical descriptive techniques and numerical descriptive techniques Week 7: Confidence intervals Week 8: Confidence intervals and hypothesis testing Week 9: Hypothesis testing Week 10: The analysis of variance Week 11: Spring break Week 12: Simple regression Week 13: Regression and nonparametric statistics Week 14: Catch up and review Week 15: Project presentations Week 16: Final exam