Math 542, Probability and Statistics for Teachers, Spring 2008
Instructor: S. D. Comer
Office Hours: 3:30-4:00 pm Thursday or by appointment.
Phone: 953-5037 (Office), 577-4728 (Home)
Email: steve.comer@citadel.eduCourse Policies: Text, Grading, Homework, projects, and Exams.
Assignments: Consult the Schedule for class topics and Assigments for homework assignments.
Catalog 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.
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
- The student will study the history of statistics and learn how statistics can be both used and abused. The student will:
- 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
- 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:
- construct a frequency distribution for a set of data
- construct a pie chart, histogram, frequency polygon, ogive, and stem-and-leaf plot
- define the different types of averages or measures of central tendency: mean, median and mode for grouped and ungrouped data
- compute the mean, median, mode, midrange, and weighted mean of the data
- for a specific set of data determine which measure is most helpful
- define the measures of variation: range, variance, and standard deviation for a set of data
- compute the range, variance, and standard deviation of a set of data
- determine the effects of data transformations on the measures of central tendency and variability
- determine the standard score or z-score for a data value
- The student will identify and apply counting principles, combinations and permutations and be able to determine the probability of an event. The student will:
- 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
- define permutations and find the permutations of a group of elements
- define combinations and find the number of ways in which combinations of elements can be found
- design and use simulations to determine experimental probability, emphasizing the difference in experimental and theoretical probability
- The student will complete binomial experiments, calculate the mean and standard deviation of the binomial distribution, and determine distribution shapes. The student will:
- determine and identify random variables and probability distributions
- apply the formula for mean, variance, and expected value for a population to problem solving
- define and identify binomial experiments and compute probabilities using the formula for binomial experiments
- compute the mean of standard deviation for a binomial distribution
- identify distribution shapes and use the uniform distribution shape to find the probability of an event
- construct a box-and-whiskers plot and identify the median, minimum, maximum, upper and lower quartiles, interquartile range and outliers
- 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:
- 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
- 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:
- define and identify a null hypothesis
- use the null hypothesis relating to a mean, proportion, or variance to determine validity and state the alternative hypothesis
- apply the t-test and P-value to test claims in which the distribution is not necessarily normal
- test a hypothesis made about a population proportion or percentage
- find the confidence interval of the population and the population mean given a sample mean
- 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
- 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:
- 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
- determine the equation of the regression line
- use the equation of the line to make predictions
- The student will design experiments, collect sample data, analyze the data and draw conclusions in order to present the final report. The student will:
- describe the different types of sampling
- apply the techniques of sampling and collecting data to write and test a claim using the methods previously studied to test claims
- evaluate the results of the testing
- write a report of the results drawing inferences or making conclusions
- present the results of the study to the class
Textbook:
Mario F. Triola, Elementary Statistics (10th edition), Addison Wesley, 2007.
Grading: Your performance will be evaluated by 2 in-class exams (30%), homework, quizzes, and projects (45%), and the final exam (25%). More information on each component is given below.
Homework/Quizzes: Homework problems will be assigned for most class periods. WRITE OUT THE ANSWERS and bring them to class; some will be discussed. Quizzes will occassionally be given based on the material. The homework problems should be kept in a notebook and turned in at the end of the semester. The assignments are posted on the Course Web Page.
Projects: There will be a series of short projects (like homework) and an extensive project where you will design an experiment, collect data, analyze the data, draw conclusions, and present the results.