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MATH 550 Applied Probability & Statistics Instructor: Bill Blubaugh, Ph.D. Email: [email protected] Summer Semester, 2002 Phone: 970 - 667 - 8793 Math office: 351 - 2820 Textbook: Elementary Statistics: A Step by Step Approach, A Brief Edition (Second Edition), written by Allan Bluman, and published by McGraw Hill, 2002. Course Objectives: • To develop proficiency in the use of statistics to structure understanding of and investigate questions in the world around us. • To develop proficiency in treating statistical content at the appropriate level. • Demonstrate competence in the use of numerical, graphical, and algebraic representations. • Demonstrate proficiency in the use of statistics to formulate and solve problems. • Demonstrate the ability to interpret data, analyze graphical information, and communicate solutions in written and oral form. • Demonstrate proficiency in the use of computer and calculator technology in supporting the use of statistics. • To learn and connect topics of probability and statistics in a context for use in secondary mathematics. Course Content: • The Nature of Probability and Statistic a. Descriptive and Inferential Statistics b. Variables and Types of Data c. Data Collection and Sampling Techniques • • Frequency Distributions and Graphs a. Organizing Data c. Other Types of Graphs Data Description a. Measures of Central Tendency c. Measures of Positions b. Histograms, Frequency Polygons, and Ogives b. Measures of Variation d. Exploratory Data Analysis • Probability a. Sample Spaces and Probability b. The Addition Rules for Probability c. The Multiplication Rules and Conditional Probability • Probability Distributions a. Probability Distributions c. The Binomial Distribution b. Mean, Variance, and Expectation • The Normal Distribution (ND) a. Properties of the ND b. The Standard ND c. Applications of the ND d. The Central Limit Theorem e. The Normal Approximation to the Binomial Distribution • Confidence Intervals (CI) and Sample Size (SS) a. CI and SS with a Known Mean b. CI and SS with an Unknown Mean c. CI and SS for Proportions d. CI for Variances and Standard Deviations (SD) • Hypothesis Testing a. Steps in Hypothesis Testing c. Small Sample Mean Test e. Variance or SD Test b. Large Sample Mean Test d. Proportion Test f. CI and Hypothesis Testing • Testing the Difference among Means, Variance, and Proportions a. Testing the Difference between Two Means: Large Samples b. Testing the Difference between Two Variances c. Testing the Difference between Two Means: Small Independent Samples d. Testing the Difference between Two Means: Small Dependent Samples e. Testing the Difference between Proportions • Correlations and Regressions a. Scatter Plots c. Regressions • b. Correlations d. Coefficient of Determination and Standard Error of Estimate Chi-Squared and Analysis of Variance (ANOVA) a. Test for Goodness of Fit b. Tests Using Contingency Tables c. Analysis of Variance (ANOVA) Attendance: Attendance to class is expected and required. Material and methods may be covered in class which are not in your textbook. If you absolutely cannot be in class for a test or lab, you must contact me in advance if you wish to make it up; there will be no exceptions. Disabilities: Students with disabilities who believe they may need accommodations in this class are encouraged to contact the Disability Access Center (970) 351-2289 as soon as possible to better ensure that accommodations are implemented in a timely fashion. Homework: Assignments will be made for each class period, but not collected. You will be tested "directly" over some of the assigned problems on the tests. You should feel free and are encouraged to work with other class members, and become interested in each other's achievements. Your success in mathematics is not only important to you, but also to the hundreds of students you influence in your future classrooms. Labs: There will be four labs assigned and collected. The software program Excel will be used. Each lab write-up will be due shortly after the lab is conducted in class. The lab assignment will be worth 25 points each. You are encouraged to work in groups of two (three maximum or individually if preferred) for the lab work. Each lab will be a group project and the lab partner will receive the same grade for each assignment. You can change partners for each lab project if you like. Tests: There will be three tests of approximately 60 minutes each, over the course material. If you absolutely cannot be in class for a test or lab, you must contact me in advance if you wish to make it up; there will be no exceptions. The written tests will be returned, with a key, the class period immediately following the examination date (if possible). Each test will consist of problems which require knowledge of the techniques covered in class and on homework problems assigned. Evaluation: There will be three tests and four laboratory write-ups. Each test will be worth 100 points and each lab write-up is worth 25 points. You will be allowed to bring a 3 by 5 (or 4 by 6) note card for each test and will be allowed the use of your calculator. Letter grades will be based on 90%, 80%, 70% and 60% of total 400 points possible. Tentative Schedule Class Day Sections Problems Due July 1 July 2 July 3 July 4 Introduction, 2.2, 2.3, 2.5 3.1 - 3.3 3.4, 3.5, Lab #1 No Class None 2.2, 2.3, 2.5 3.2, 3.3 July 8 July 9 July 10 July 11 5.1-5.4 6.1-6.3 6.4, (Lab #1 Due), Review, Lab #2 Test #1 (Chapters 2, 3, 5, 6) 3.4, 3.5 5.2, 5.3, 5.4 6.2, 6.3 6.4 July 15 July 16 July 17 July 18 7.1 - 7.4 7.5, 7.6, (Lab #2 Due) 8.1, 8.2, 8.3 8.4, 8.5, Lab #3 none 7.3, 7.4 7.5, 7.6 8.2, 8.3 July 22 July 23 July 24 July 25 9.1, 9.2, 9.3 9.4, 9.5 9.6, Review for Test Test #2, (Chapters 7, 8, 9) 8.4, 8.5 9.2, 9.3 9.4, 9.5 9.6 July 29 July 30 July 31 Aug. 1 10.1,10.2, 10.4 (Lab #3 Due) 10.5, 10.6 11.1, 11.2 11.3, 11.4, Lab #4 None 10.2, 10.4 10.5, 10.6 11.2 Aug. 5 Aug. 6 Aug. 7 12.2, 12.3 Review for Test, (Lab #4 Due) Test #3, (Chapters 10, 11, 12) 11. 11.4 12.2, 12.3 None Problems Per Section Section 2.2 2.3 2.5 3.2 3.3 3.4 3.5 5.2 5.3 5.4 6.2 6.3 6.4 7.3 7.4 7.5 7.6 8.2 8.3 8.4 8.5 9.2 9.3 9.4 9.5 9.6 10.2 10.3 10.4 10.5 10.6 11.2 11.3 11.4 12.2 12.3 12.4 Page 41 54 79 106 123 136 150 194 201 214 228 236 243 270 280 293 300 318 326 333 339 359 369 380 387 397 418 430 441 454 463 486 494 506 523 535 548 Problems 5, 8, 10, 13 19, 23, 28 59, 61, 65 1, 3, 5, 6, 7, 30, 31 43, 45, 46, 48, 49, 51, 55, 70, 72 96, 100, 101, 110, 112 120, 122, 129 3, 4, 5, 9, 10, 11, 12, 13, 15, 17, 21, 27, 34 41, 43, 49, 61 70 71, 73, 74, 84, 85, 94-101, 110, 113, 118 6-18, 20, 22, 25, 27 37, 39, 48, 50, 54 64, 65, 66, 73, 77, 82 7, 11, 15, 19, 25, 29, 33, 35, 37, 39, 41, 43, 46 55, 57, 61, 65, 71, 77 101, 105, 111, 114, 117 125, 127, 129, 130 11, 13, 16, 18, 20, 24 31, 33, 34, 37, 39, 45 49, 50, 54, 57, 60 70, 71, 73, 75 1, 2, 4, 5, 9, 12, 13(a-g) 15, 17, 22, 23, 25, 27, 31, 33 47, 49, 50, 55, 58, 59 66, 69, 70, 73, 75 81, 82, 84, 87 6, 7, 9, 11, 15 29, 30, 32, 33 43, 44, 45, 47, 49 56, 57, 59, 61, 64 68, 69, 71, 73, 76, 80 13, 15, 17, 22, 23, 27 41, 43, 45, 50, 55, 57 76, 77, 81, 83 6, 7, 9, 14, 17 28, 30, 34, 42 64, 65, 66, 69