Download Math 542 - Department of Mathematics and Computer Science

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