COURSE SYLLABUS College of William & Mary Elementary Probability and Statistics MATH Spring Semester, 2015

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1 COURSE SYLLABUS College of William & Mary Elementary Probability and Statistics MATH Spring Semester, 015 GENERAL INFORMATION Instructor: Daniel McGibney Class time: 9:00am - 9:50am MWF Semester hours: 3 Class Location: Hugh Jones Hall Room: 301 Office Hours: 1:00pm - :00pm MW Office: Hugh Jones Hall Room: 14 dpmcgibney@wm.edu Website: COURSE DESCRIPTION The following concepts and statistical techniques are included: measures of central tendency and variability; random variables and probability distributions; binomial, normal, and sampling distributions; estimation; tests of hypotheses; chi square tests; linear regression and correlation; and multiple regression. This course fulfills GER 1 requirement. Therefore, the content must meet the following:: Involve numerical calculations; Include mathematical justifications explaining why the approaches and calculations used in the course actually work; Include applications of mathematics to real-world settings or to disciplines other than mathematics. TEXTBOOK Fundamentals of Statistics: Informed Decisions Using Data Michael Sullivan, III, 4 th edition Pearson Prentice Hall GRADING PROCEDURE A. Major Exams: There will be a final exam. The final exam will be cumulative and derived from the material covered in class and in the text. B. Homework: Collection and grading of homework will be used in the evaluation of the student. Additionally students will be assigned regular reading assignments, which they are responsible for. Late Homework will not be accepted. C. Quizzes: There will be eight quizzes. Quizzes will be derived from the material covered in class and related sections covered in the book. The lowest quiz will be dropped. If you anticipate missing class during a quiz day, you should contact your professor one week prior to the quiz date.

2 Make-up quizzes will not be given for any reason. D. Projects: Projects using a statistical software package such as MINITAB, Excel, or R will be used in the evaluation of the student. E. Final Exam: A comprehensive final exam will be given during the assigned time period of final exam week and will be weighted as outlined in below in the evaluation of the final grade. F. Evaluation of the Final Semester Grade: Homework: 15% Projects: 5% Quizzes: 60% Final Exam: 0% The final grade is assigned using the scale: A , A- 90-9, B , B 83-86, B- 80-8, C , C 73-76, C- 70-7, D , D 63-66, D- 60-6, F < 60 ADDITIONAL INFORMATION Regular attendance and class participation are expected. This includes the expectation that the use of computers and cell phones for personal or recreational purposes is not permitted during class time. A calculator is necessary for this course. A graphing calculator is ideal, but not required. TI-83/84 user instructions are included in the textbook. Grades will be posted regularly on Blackboard. Assignments will be posted on the course website. SCHEDULE Monday Wednesday Friday 1 1/1 Introduction 1/3 1/6 1/8 1/30 HW1 due 3 / /4 Quiz 1 /6 4 /9 /11 HW due /13 5 /16 Quiz /18 /0 6 /3 HW3 due /5 /7 Quiz 3 7 3/ ¾ 3/6 HW4 due 8 3/9 No class 3/11 No class 3/13 No class 9 3/16 3/18 Quiz 4 3/0 10 3/3 Project 1 due 3/5 HW5 due 3/7 11 3/30 Quiz 5 4/1 4/3 1 4/6 HW6 due 4/8 4/10 Quiz /13 4/15 4/17 HW7 due 14 4/0 4/ Quiz 7 4/4 15 4/7 Project due 4/9 Quiz 8 5/1 Review 16 5/4 No class 5/6 Final Exam The instructor reserves the right to make any additions, changes, etc. to the syllabus. Any such changes or additions will be announced in class.

3 COURSE OBJECTIVES A. Sampling Techniques The student will be able to: 1. Classify statistical studies as either descriptive or inferential.. Explain what is meant by a representative sample and why samples are used. 3. Use and describe sampling techniques. 4. Identify and explain the characteristics of observational studies and designed experiments. B. Organizing Data The student will be able to: 1. Classify variables and data as either qualitative or quantitative, and if quantitative, as either discrete or continuous.. Group data into a frequency distribution and a relative-frequency distribution. 3. Construct graphical representations of data (histograms, dotplots, stem-andleaf diagrams, etc.). 4. Identify the shape and modality of the distribution of a data set, including whether a unimodal distribution is symmetric, right skewed, or left skewed. 5. Identify and explain misleading graphs. C. Descriptive Measures The student will be able to: 1. Define, calculate and interpret measures of center and variation for a data set, sample, or finite population.. Calculate and interpret percentiles, quartiles, interquartile range, and fivenumber summary of a data set. 3. Explain and apply Chebyshev s rule and the empirical rule. 4. Identify potential outliers numerically and graphically. 5. Construct boxplots and use them to identify the distribution shape for large data sets. 6. Distinguish between a parameter and a statistic and explain how and why statistics are used to estimate parameters. 7. Calculate and interpret z-scores. D. Probability The student will be able to: 1. Compute and interpret theoretical and empirical probabilities.. State and apply the basic properties of probability. 3. Determine and explain whether two or more events are mutually exclusive or independent. 4. State and apply the complementation rule, the special and general addition and multiplication rules, the conditional probability rule, the rule of total probability, and Bayes' rule. 5. State and apply the basic counting rule and the permutations and combinations rules. E. Probability Distributions The student will be able to: 1. Determine the probability distribution of a discrete random variable.

4 . Compute the mean (expected value) and standard deviation of discrete, binomial, and Poisson random variables. 3. State and explain the law of large numbers. 4. Define and apply the concept of Bernoulli trials and assign probabilities to the outcomes. 5. Calculate discrete, binomial, and Poisson probabilities. 6. Use the Poisson and normal distributions to approximate binomial probabilities. 7. Identify the basic properties of and sketch the standard and other normal, t, and distributions and their curves. 8. Find areas under normal curves, t-curves, and -curves. 9. Find the z, t, and values corresponding to a specified area under the respective curves. 10. Solve applied problems using normally distributed variables. 11. Construct a normal probability plot and use it to assess normality and to detect outliers. F. Central Limit Theorem The student will be able to: 1. Define sampling error and explain the need for sampling distributions.. Find the mean and standard deviation of the variable x, given the mean and standard deviation of the population and the sample size. 3. State and apply the central limit theorem. G. Confidence Intervals The student will be able to: 1. Find and interpret confidence intervals for a population mean, a population standard deviation, and a population proportion.. Compute and interpret the margin of error for the estimate of and of p. 3. Explain the relationship between sample size, standard deviation, confidence level, and margin of error for a confidence interval for and for p. 4. Determine the sample size required for a specified confidence level and margin of error for the estimate of and for p. H. Hypothesis Tests The student will be able to: 1. Choose the null and alternative hypotheses in a hypothesis test.. Explain the logic behind hypothesis testing. 3. Identify the test statistic, rejection region, non-rejection region, and critical value(s) for a hypothesis test. 4. Define and apply the concepts of Type I and Type II errors. 5. State and interpret the possible conclusions for a hypothesis test. 6. Perform hypothesis tests for one population mean, one population standard deviation, and one population proportion, using the critical-value and P-value approaches. I. Chi-Square Procedures The student will be able to:

5 1. Perform chi-square goodness-of-fit and chi-square independence tests. J. Linear and Multiple Regression The student will be able to: 1. Obtain and graph the regression equation for a set of data points, interpret the slope of the regression line, and use the regression equation to make predictions.. Identify outliers and influential observations. 3. Explain when it is appropriate to obtain a regression line for a set of data points. 4. Calculate and interpret the coefficient of determination, r, and the linear correlation coefficient, r. 5. Obtain the sample multiple linear regression equation and the standard error of the estimate. 6. Find and interpret the 95% confidence and prediction intervals for new observations.

Probability and Statistics Curriculum Pacing Guide

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