BRONX COMMUNITY COLLEGE OF THE CITY UNIVERSITY OF NEW YORK Department of Mathematics and Computer Science MTH 23 section D04 (18176) Syllabus / Fall 2013 1 Course Learning Objectives On successful completion of this course, students will be able to 1. Sort, analyze, and present numerical data using sample spaces, measures of central tendency, measures of variation, and measures of dispersion. 2. Recognize correlations between data sets using scatter diagrams; express linear correlations using least squares regression; determine the strength of the correlation via the correlation coefficient. 3. Predict experimental outcomes using basic techniques of probability (permutations, combinations, counting techniques). 4. Recognize the features of a binomial experiment and apply the binomial probability distribution. 5. Recognize the features of a normal distribution and compute probabilities using the standard normal distribution. 6. Infer population parameters using sampling distributions and the Central Limit Theorem. 7. Limit the error of estimation by calculating confidence intervals. 8. Accept or reject a hypothesis by establishing a level of significance. This course addresses the following General Education Proficiencies: analysis, interpretation, evaluation, and integration of information to formulate and solve problems; use of mathematical and scientific methods to formulate and solve problems and to understand the physical, natural and social worlds. This course may be used to satisfy Category A (Mathematical and Quantitative Reasoning) of the CUNY Pathways Required Core. 2 Logistics Course Section Credit Prerequisite Co-requisie Text MTH 23: Probability and Statistics D04 3 credits / 3 hours MTH 05 or equivalent ENG 02 and/or RDL 02, if required Understanding Basic Statistics (6 th ed.) by Brase & Brase. Brooks/Cole, Cengage Learning. ISBN 978-1-111-82702-1 Calculator A statistical calculator is useful but any basic scientific one will suffice. Look for these buttons: x 2, x,!. Bring it to class. For tests, your calculator may not be networked (e.g. on your phone). 2.1 Contact Information Instructor Email Class Website Office Office Hours Prof. Antonakos Evangelia.Antonakos@bcc.cuny.edu http://fsw01.bcc.cuny.edu/evangelia.antonakos/file/mth 23 M W Fall 2013.html or go to Antonakos.net, click Teaching tab on top, then click on the image of our textbook. CP (Carl Polowczyk Hall) 308A, (718) 289-5100 x3410 drop-in Mondays 1:30-2:30pm and Tuesdays 10:00-11:00am Please email or see me in class for appointments at other times. Dept. Office CP 315, (718) 289-5411 Dept. Website www.bcc.cuny.edu/mathematicscomputerscience/math cs.htm I expect to be able to contact you at the email account you have listed as preferred on CUNYfirst at the start of the semester. Please inform me if you change it. 1
2.2 Meeting Times Room PH 22 Times Mondays & Wednesdays 10:00-11:15am Due to the BCC calendar, there will be the following changes to our schedule: Mon. Sept. 2 no classes, campus closed (Labor Day) Wed. Sept. 4 no classes (Rosh Hashana) Mon. Oct. 14 no classes, campus closed (Columbus Day) Tue. Oct. 15 Monday schedule Wed. Nov. 27 Friday schedule Other relevant dates: Tue. Sept. 17 deadline to drop a course without receiving a W grade Sun. Nov. 3 Daylight Savings Time ends (set clocks back one hour) Fri. Nov. 8 deadline to withdraw with a W grade Mon. Nov. 26 advisement and registration for Spring 2014 begins Sun. Dec. 15 last day of classes Monday 12/16 through Mon. 12/23: Final Exam period 3 Assignments This is a fast-paced course; we cover one section of material almost every class. Each section has an associated homework assignment due the following Monday. These are listed at the end of this syllabus. If you find the assignments challenging, read the examples in the text and try the odd-numbered exercise as their solutions are given in the back of the text. It is crucial to your understanding and your grade that you are diligent about your homework. Solutions will be posted on the class website within a few days of their due dates. There will be three hour-long tests in class on Wed. 10/2, Wed. 11/6, and Mon. 12/9. The two-hour final will be during finals week, which begins Mon. 12/16. This will be a cumulative exam. 4 Grading Policies 4.1 grade weights Homework assignments will be graded 0, 1, 2, 3, or 4. Assignments are due at the start of the class according to the schedule in 7 below. I will accept homework assignments up to one day late for half-credit. These can be left in my mailbox in CP 315 or emailed to me. Three homework grades will be dropped: the lowest from the material on Test 1 (Chapters 1 5), Test 2 (Ch. 5 7), and Test 3 (Ch. 8 & 9). The lowest of the three test grades will also be dropped. Make-ups will not be given unless arrangements are made beforehand for documented excuses. homework 25% two tests 40% final exam 35% 100% 4.2 attendance Please arrive on time. Arriving late disturbs the class and you miss material. If you have four or more unexcused absences you will be considered excessively absent and may receive a WU as your final grade. However, anyone who takes the final exam must be given an academic grade, though it may be an F. Arriving late three times counts as one absence. 5 Studying Plan to spend three to six hours each week doing homework and studying for this class. In addition to working on homework, reading through the examples in the text, doing the odd-numbered (solved) exercises from each section, and reviewing definitions and theorems are excellent ways to spend your study time. You are always encouraged to see me or email me with questions on material or larger concerns with the course. My office hours are listed above; 2
do drop in, or make an appointment. I encourage you to make friends in the class to study with. Most find this very helpful. The Tutorial Lab is where faculty, staff, and student mentors can help you understand the material and work through examples. (They are not there to do homework help.) It is an excellent resource and is one good place to spend your study time. The Lab, in CP 303, opens every day at 10am and closes at 8pm Monday Thursday, 5pm on Fridays, and 3pm Saturdays and Sundays. The telephone number there is (718) 289-5100 x3029. No appointment is necessary. Both the Tutorial Lab and the Reserve Desk at the Library have copies of the textbook available for short loans of a few hours. Please plan ahead; there are more than 700 students taking MTH 23 this semester so the books may not always be available when you want them. The library may also have older editions of the text which are in their circulating collection which you could borrow to take home. Older editions are just as good to help you learn the material, however, the exercises in older editions are not the same. Be sure to use the 6 th edition for your homework. 6 Responsibilities Respect: You are expected to show respect for the other students, myself, and the learning environment. In particular, behaviors which hinders the learning of other students is not acceptable. Please keep your phone on silent. Besides being a distraction to you, taking calls and texting during class is disrespectful to your fellow students and me, and can be disruptive. If you must take or make an emergency call during class, have the curtesy to quietly step outside. On my part I will support your learning process by making any in-class slides and solved homework sets available on our class page within a couple days of lecture. I will also return assignments within a week. Attendance: If you miss class you it is your job to find out what you missed and you are still responsible any homework assignments. Please do check our class page and the calendar there regularly for notices, updates, slides, etc. Integrity: Academic honesty is expected. No plagiarism or coping is allowed. Cheating on a test will have the minimal consequence of a zero on that test (which will not be dropped) and being reported to the administration, and may result in an F for the course or more serious ramifications. 7 Topics & Schedule chapters sections 1. Getting Started 1.1 What is statistics 1.2 Random Samples 2. Organizing Data 2.1 Frequency Distributions, Histograms, and Related Topics 3. Averages and Variation 3.1 Measures of Central Tendency: Mode, Median, and Mean 3.2 Measures of Variation 4. Correlation and Regression 4.1 Scatter Diagrams and Linear Correlation 4.2 Linear Regression and the Coefficient of Determination 5. Elementary Probability Theory 5.1 What is Probability? 5.2 Some Probability Rules Compound Events 6. The Binomial Probability Distribution 6.1 Introduction to Random Variables and Probability Distributions and Related Topics 6.2 Binomial Probabilities 6.3 Additional Properties of the Binomial Distribution 7. Normal Curves and 7.1 Graphs of Normal Probability Distribution Sampling Distributions 7.2 Standard Units and Areas Under the Standard Normal Distribution 7.3 Areas Under any Normal Curve 7.4 Sampling Distributions 7.5 The Central Limit Theorem 7.6 Normal Approximation to the Binomial Distribution 8. Estimation 8.1 Estimating µ when σ is Known 8.2 Estimating µ when σ is Unknown 8.3 Estimating p in the Binomial Distribution 9. Hypothesis Testing 9.1 Introduction to Statistical Tests 9.2 Testing the Mean µ 9.3 Testing a Proportion 3
UPDATED 10/13 UPDATED Date Topics/Skills Text Section HOMEWORK (due next class) 1 Wed. Aug. 28 Use a random number table to draw a random sample or simulate an experiment. 1.1 1.2 p. 10# 5, 8, 12 p. 18 # 4, 12, 13 2 Mon. Sept. 9 Make a frequency or relative frequency table; display it in a histogram; identify the distribution shape. 2.1 p. 50 # 6, 10, 12 3 Wed. Sept. 11 Find the mean, median and mode; find a trimmed mean; find a weighted average. 3.1 p. 89 # 4, 6, 16, 17, 22, 24 4 Mon. Sept. 16 Find the sample standard deviation; find the coefficient of variation; use Chebyshev s Theorem; distinguish population parameters and sample statistics. 3.2 p. 104 # 5, 6, 12-14, 20 5 Wed. Sept 18 Make a scatter diagram; identify apparent linear correlation; calculate the correlation coefficient; identify possible lurking variables. 4.1 p. 144 # 6, 13, 14, 18 6 Mon. Sept. 23 Find the equation of the least squares line; use the equation to predict values of the response variable. 4.2 p. 160 # 10, 12, 14 7 Wed. Sept. 25 Assign probability to an event; use the complement rule. 5.1 p. 183 # 5, 6, 10, 15, 16, 18 8 Mon. Sept. 30 catch up 9 Wed. Oct. 2 TEST 1: through 5.1 4
UPDATED 10/13 UPDATED Date Topics/Skills Text Section HOMEWORK (due the following Monday) 10 Mon. Oct. 7 Assign conditional probabilities from survey results. 5.2 p. 199 # 4, 6, 8, 10, 16, 18 11 Wed. Oct. 9 Distinguish discrete and continuous random variables; find the expected value and standard deviation of a probability distribution. 6.1 p. 230 # 5, 6, 10, 12 12 Tue. Oct. 15 Recognize a binomial experiment; use the binomial probability distribution table; translate English phrases such as at least, no more than into inequalities. 6.2 p. 243 # 6, 12 18 even 13 Wed. Oct. 16 Make a histogram for a binomial distribution; calculate the mean and standard deviation of a binomial distribution; 6.3 p. 253 # 4, 10, 13, 16 14 Mon. Oct. 21 Recognize the features of a normal curve; apply the empirical rule to estimate the percentage of data lying a specified distance from the mean. 7.1 p. 273 # 5, 6, 9, 10 Convert between raw data and z-scores; 15 Wed. Oct. 23 use the standard normal distribution table; sketch and find areas under the standard normal curve. 7.2 p. 284 # 6, 8, 12, 18-26 even, 36-42 even 16 Mon. Oct. 28 Find the probability that a data value in a normal distribution lies in a specified range; invert the standard normal distribution table to solve, e.g., a guarantee problem. 7.3 p. 296 # 6-12 even, 16, 21, 28, 30 17 Wed. Oct. 30 Obtain sampling distributions; apply the Central Limit Theorem. 7.4 & 7.5 p. 312 # 6, 10, 14, 15 18 Mon. Nov. 4 Use the normal approximation to the binomial distribution (for x and ˆp); make the continuity correction. 7.6 p. 322 # 7, 10, 20, 21 19 Wed. Nov. 6 Test 2: 5.1 7.6 5
UPDATED 10/13 UPDATED Date Topics/Skills Text Section HOMEWORK (due the following Monday) 20 Mon. Nov. 11 Define confidence level and margin of error; compute confidence intervals for an estimate of µ; determine the sample size necessary for estimating µ with a specified confidence level. 8.1 p. 347 # 12-14, 16, 23 21 Wed. Nov. 13 22 Mon. Nov. 18 Use Student s t-distribution when σ is unknown. Compute confidence intervals for an estimate of p in the binomial distribution. 8.2 p. 357 # 2, 4, 11, 12, 14, 16 8.3 p. 370 # 8-10, 16, 19 23 Wed. Nov. 20 Identify the null and alternate hypotheses in a statistical test; identify right, left, and two-tailed tests; determine the P -value of a statistical test; conclude a statistical test using the P - value and a specified level of significance (α). 9.1 24 Mon. Nov. 25 (as above) 9.1, cont. p. 399 # 1-8, 14, 18 25 Mon. Dec. 2 Test µ using normal and Student s t- distributions. 9.2 p. 414 # 8, 10, 11, 16 26 Wed. Dec. 4 Test claims about p in a binomial experiment. 27 Mon. Dec. 9 TEST 3 28 Wed. Dec. 11 Review for Final Exam Week of Dec. 16 FINAL EXAM 9.3 p. 425 # 5, 6, 10, 11 rev. 10/13/13 6