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Math 308 Instructor: Dr. Richard Rubin Office Hours: MTWTh 1-3PM TTh 9-10AM or by appointment Statistics Office: Phone: email: Spring 2001 Science 103C 901-321-3457 rrubin@cbu.edu Catalog Data: The course considers statistical methods with applications to engineering and science. Topics are selected from: an introduction to probability, descriptive statistics, sampling methods, design of statistical experiments, concepts of hypothesis testing and confidence intervals, correlation, linear regression and analysis of variance. Prerequisite: Math 232. You must have skills in problem solving, differential and integral calculus, and differential equations. Textbook: Lawrence Lapin, Modern Engineering Statistics, Duxbury Press, 1997. Tentative Course Schedule Topics Chapter ---------------------------------------------------------------------------------------Chapter 1: What's It All About?? Introduction : 1.1-6 The Meaning and Role of Statistics 1.1 Statistical Data 1.2 The Population and the Sample 1.3 The Need for Samples 1.4 Selecting the Sample 1.5 Applications 1.6 Chapter 2: How Do We View All of This?? Describing, Displaying & Exploring Data 2.1-4 The Frequency Distribution 2.1 Summary Statistical Measures: Location 2.2 Summary Statistical Measures: Variability 2.3 Summary Statistical Measures: Proportion 2.4 Chapter 3: Do We Have Any Control?? Statistical Process Control 3.1-4 The Control Chart 3.1 Control Charts for Quantitative Data 3.2 Control Charts for Qualitative Data 3.3 Further Issues in Statistical Quality Control 3.4 Chapter 4: How Do We Analyze the Data Making Predictions: Regression Analysis Linear Regression using Least Squares Correlation Regression Analysis Multiple Regression Analysis Classes 2 2 2 4.1-3 4.1 4.2 4.3 3 Math 308 Statistics Spring 2001 Chapter 5: Models are the Way! Statistical Analysis in Model Building Nonlinear Regression Curvilinear Regression Polynomial Regression Multiple Regression with Indicator Variables Chapter 6: What's the Chance of..? Probability Fundamental Concepts of Probability Probability for Compound Events Conditional Probability The Multiplication Law, Trees & Sampling Prediction Reliability of Systems Chapter 7: What's the Chance, pt 2! Random Variables & Probability Distributions Random Variables & Probability Distributions Expected Value and Variance The Binomial Distribution The Normal Distribution 5.1-4 5.1 5.2 5.3 5.4 3 6.1-5 6.1 6.2 6.3 6.4 6.5 4 7.1-4 7.1 7.2 7.3 7.4 4 Chapter 8: There is Probability and then there is Probability! Important Probability Distributions 8.1-5 Poisson Distribution 8.1 Exponential Distribution 8.2 Gamma Distribution 8.3 Failure Time Distributions: Weibull 8.4 Hypergeometric Distribution 8.5 Chapter 9: Take a Sample! Sampling Distributions 9.1-9.6 Sampling Distribution of the Mean 9.1 Sampling Distribution of X , Normal Distribution 9.2 Sampling Distribution of X , General Distribution 9.3 Student t Distribution 9.4 Sampling Distribution of the Proportion 9.5 Sampling Distribution of the Variance 9.6 Chapter 10: Make Your Best Guess! Statistical Estimation 10.1-10.6 Estimators and Estimates 10.1 Interval Estimates of the Mean 10.2 Interval Estimates of Proportion 10.3 Interval Estimates of Variance 10.4 Confidence Intervals for Diff between Means 10.5 Bootstrapping Estimation 10.6 2 5 5 Math 308 Statistics Spring 2001 Chapter 11: Test Your Guess! Statistical Testing Basic Concepts of Hypothesis Testing Procedures for Testing the Mean Testing the Proportion Hypothesis Testing Comparing 2 Means More Ideas for Making Your Best Guess! Theory and Inferences in Regression Analysis Assumptions & Properties of Linear Regression Analysis Assessing the Quality of the Regression Statistical Inferences Using the Regression Line Inferences in Multiple Regression Analysis Design an Experiment! What Fun! Experimental Design Issues in Experimental Design The 2 Level Factorial Design Other Approaches to Experimental Design Tests Total 11.1-4 11.1 11.2 11.3 11.4 2 Chapter 12: 12.1-4 12.1 12.2 12.3 12.4 2 Chapter 14: 14.1-14.3 14.1 14.2 14.3 3 3 42 Math 308 Statistics Course Objectives Spring 2001 This course provides a foundation in applied statistics that will allow the student to solve applied statistical problems in engineering and science. Topics are selected from: 1) descriptive statistics, 2) inferential statistics, and 3) experimental design. Descriptive statistics includes methods for summarizing data. Inferential statistics includes fundamental probability, discrete random variables and their probability distributions, continuous random variables and their probability distributions, sampling distributions and the Central Limit Theorem, estimation of parameters, and hypothesis testing. Experimental design includes an introduction to the design of experiments. For each of these topics, at the end of the course, you will be able to: a) b) c) d) e) f) define each important concept; apply the rules and techniques of statistics to routine exercises; transform among the geometric, numeric and algebraic representations of the concepts; solve applied problems in engineering and science, in specific contexts, by using appropriate techniques of statistics; judge the relevance of the results obtained from the problems; use computer software to illustrate numerically, graphically and symbolically appropriate important concepts. Specific learning objectives follow. They appear in three groups: 1. 2. 3. basic knowledge objectives, meaningful integrated objectives and critical thinking objectives. Tests and quizzes will focus on (but are not limited to) the basic knowledge objectives. Assignments will focus on the basic knowledge and non-rote objectives. In order to earn a grade of at least a C in the course, you must achieve most of the basic knowledge objectives. In order to earn a grade of B, you must achieve most of the basic knowledge and meaningful integrated objectives. To earn an A, you must achieve most objectives. Basic Knowledge or Rote Objectives Chapter 1 1. 2. 3. 4. 5. 6. 7. What's It All About?? Explain statistics in your own words. Describe the role of statistics in engineering and science. Classify a data set as quantitative or qualitative. Classify a quantitative data set as nominal, ordinal, interval, or ratio. Explain a statistical population in your own words. Explain a statistical sample in your own words. Distinguish among a data set, a sample and a population. Math 308 8. 9. 10. 11. 12. Statistics Spring 2001 Distinguish between deductive and inductive statistics. Explain the practical need for a sample from a population. List several advantages of a sample over a census. Describe a good technique to select a sample. List several practical applications of statistics. How Do We View All of This?? Chapter 2 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. Explain a sample frequency distribution in you own words. Draw a relative frequency histogram for a small data set by "hand". Draw a cumulative frequency histogram for a small data set by "hand". Draw a stem and leaf plot for a small data set. Draw a boxplot for a small data set. Draw a scatter diagram for a small data set. Describe some common frequency distributions. Describe some common statistical measures of location. Describe some common statistical measures of variability. Compute a descriptive measure of a small data set using your calculator. A descriptive measure is one of: a) mean b) median c) mode d) percentile proportion, e) range f) interquartile range g) variance h) standard deviation. Explain the meaning of each of the descriptive measures. Use computer software to draw a histogram for a data set. Use computer software to draw a boxplot for a data set. Calculate descriptive numerical measures for a data set with computer software. Use computer software to draw a scattergram for a data set. Give an empirical rule describing a data set in terms of its mean and standard deviation. Statistical Process Control Chapter 3 29. 30. 31. 32. 33. 34. 35. 36. 37. Describe a control chart for the mean of a process. Justify theoretically the use of control charts in the statistical process control of the mean. Justify practically the use of control charts in the statistical process control of the mean. State when to use control charts based on the sample mean and when to use control charts based on the sample range. Explain a false alarm for a control chart. Explain a missed call for a control chart. Determine several different types of control charts. Draw a control chart for a small data set by "hand". Use computer software to draw a control chart for a large data set. Regression Chapter 4 38. 39. 40. Describe the method of least squares in linear regression in your own words. Discuss the mathematical basis for the method of least squares. Determine the normal linear regression equations for a small data set by "hand". Math 308 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. Statistics Spring 2001 Solve the normal equations for linear regression for a small data set. Explain the standard error of the estimate about the regression line in your own words. Distinguish between observed and predicted values in regression. Explain total variability of the dependent variable. Use computer software for linear regression analysis of a data set. Explain correlation in your own words. List several types of correlation. Compute the correlation coefficient of a small data set by "hand". Explain the role of correlation in regression. Explain the connection between a scattergram and correlation. Explain multiple regression in your own words. Use computer software for multiple regression analysis of a data set. Explain the advantage multiple regression can have over linear regression. Explain residual in your own words. Explain the standard error of the estimate for multiple regression in your own words. Statistical analysis in model building Chapter 5 56. 57. 58. 59. 60. 61. 62. Explain how to use regression analysis for non linear relations. Explain the role of a scatter diagram in model building. List several common transformations of a non linear relation into a linear relation. Explain curvilinear regression in your own words. Explain polynomial regression in your own words. Explain multiple regression with indicator variables in your own words. Use computer software to build models for regression analysis of a data set. Probability Chapter 6 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. Explain the concept of sample space in your own words. Determine whether two events are independent. Use the addition law to find the probability of events in a sample space. Define statistical independence. Use the multiplication law to find the probability of two events. Explain the concept of conditional probability in your own words. Use probability trees to determine probability of dependent events. Find the probability that one of two events occurs. Find the probability that both of two events occur. Find the probability of an event similar to one discussed in class. Use probability to determine system reliability. Random Variables and Probability Distributions Chapter 7 74. 75. 76. Explain the concept of a random variable in your own words. Identify a random variable as continuous or not. Identify a random variable as discrete or not. Math 308 77. 78. 79. 80. Statistics Spring 2001 81. 82. 83. 84. 85. 86. 87. 88. Determine the probability distribution for a discrete random variable in an applied problem similar to one discussed in class. Find the expected value of a random variable in an applied problem similar to one discussed in class. Find the variance of a random variable in an applied problem similar to one discussed in class. Identify characteristics of some common probability distributions. Some of these distributions are: binomial hypergeometric Poisson uniform normal gamma exponential t chi square F Draw the probability histogram of a common random variable for small parameters with your calculator. Draw the probability histogram of a common random variable for non-small parameters with computer software. Explain a binomial experiment in your own words. Explain the role of a binomial distribution in sampling. Find the probability of an event in an applied problem similar to one discussed in class that involves a discrete random variable having a common distribution. Find the probability density function for a continuous random variable in an applied problem similar to one discussed in class. Transform a normal random variable to the standard normal random variable. Find the probability of an event in an applied problem similar to one discussed in class that involves a continuous random variable having a common distribution. Important Probability Distributions Chapter 8 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. Explain a Poisson process in your own words. Identify the expected value and variance of a Poisson process. Determine whether or not a process is Poisson. List several key practical uses of a Poisson process. Explain an exponential distribution in your own words. Identify the expected value, variance and percentile of an exponential distribution. Determine whether or not a random variable is exponential. List several key practical uses of an exponential random variable. Explain a gamma distribution in your own words. Identify the expected value and variance of a gamma distribution. Determine whether or not a random variable is gamma. Describe the relation of a gamma distribution to a Poisson process. Explain a Weibull distribution in your own words. Explain a failure rate function in your own words. Identify the expected value and variance of a Weibull distribution. Determine whether or not a random variable is Weibull. List several key practical uses of a Weibull random variable. Describe how a gamma distribution can serve as a time to failure distribution. Compute the mean time to failure for a series system. Compute the mean time to failure for a parallel system. Explain a hypergeometric distribution in your own words. Math 308 110. 111. 112. 113. Statistics Spring 2001 Identify the expected value and variance of a hypergeometric distribution. Determine whether or not a random variable is hypergeometric. List several key practical uses of a hypergeometric random variable. Explain how to approximate a hypergeometric distribution with a binomial distribution. Sampling Distributions Chapter 9 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. Define a statistic. Find the sampling distribution of the mean. Identify the mean and variance of the sampling distribution of the mean. Identify the standard error of the sample mean. Describe the role of the standard error. Explain the central limit theorem in your own words. Find the sampling distribution of the sample mean for a normal population. Find the sampling distribution of the sample mean for a general population. Solve an applied problem similar to one discussed in class using the central limit theorem. Compute probabilities for the sample mean. Describe the Student t distribution in your own words. Explain the relation between the student t curve and the normal curve. Describe the sampling distribution of the population proportion. Describe the sampling distribution of the variance. Describe the chi square distribution in your own words. Identify the mean and variance of the chi square distribution. Describe the F distribution in your own words. Solve an applied problem involving the binomial distribution with an approximation based on the normal distribution. Statistical Estimation Chapter 10 132. 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. Describe the process of statistical estimation. Identify several key characteristics of a statistic used as an estimator. Explain the role of probability in statistics. Construct a confidence interval for a common parameter. A common parameter is one of: population mean the difference of 2 population means a population proportion the difference of 2 population proportions a population variance the ratio of two population variances. Identify the assumptions underlying the construction of the confidence interval. Find the sample size needed to estimate a population parameter to a certain accuracy. Explain estimation by bootstrapping in your own words. Describe how to estimate the population mean with the technique of resampling. Use computer software to estimate the population mean with the technique of resampling. Interpret the results produced by computer software. Compare and contrast traditional statistics and bootstrapping. Math 308 Chapter 11 143. 144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. Statistical Testing Statistics Spring 2001 Describe the process of statistical testing. Explain the relation between statistical testing and estimation. Describe the structure of a test of hypothesis. Describe a type I error in a statistical test. Describe a type II error in a statistical test. Distinguish among lower, upper and two tail tests. Explain the p value of a test in your own words. Compute the p value of a test. Summarize the key steps of a hypothesis test of a mean. Summarize the key steps of a hypothesis test of a proportion. Summarize the key steps of a hypothesis test for the comparison of two means with independent samples. Describe how to conduct a statistical test with the technique of resampling. Conduct a statistical test with the technique of resampling using computer software. Theory and Inferences in Regression Analysis Chapter 12 156. 157. 158. 159. 160. 161. 162. 163. 164. 165. 166. 167. Describe the assumptions of linear regression. Describe the properties of linear regression. Explain the role of the residuals in assessing the validity of the regression model. Explain how to assess the quality of a regression model. Distinguish between explained and unexplained deviation. Explain the coefficient of determination in your own words. Identify the relation between the coefficient of determination and the correlation coefficient. Identify the confidence interval for a conditional mean. Identify the prediction interval for an individual Y given X. Identify the test statistic for the slope of a regression line. Describe how to use bootstrapping to make inferences in regression. Make inferences with bootstrapping using computer software. Chapter 14 Experimental Design 168. Explain how to design a statistical experiment to achieve good results. 169. Explain some elementary experimental designs in your own words. 170. Identify several key issues in experimental design. 171. Explain a factorial design in your own words. 172. Explain a two level factorial design in your own words. 173. Draw a graphical representation of a two level factorial design. 174. Explain the main effect in your own words. 175. Draw a graphical representation of the main effect in a two level factorial design. 176. Explain the interaction effect in your own words. 177. Draw a graphical representation of the interaction effect in a two level factorial design. 178. Explain how to construct a confidence interval of an effect in a two level factorial design. 179. Identify several key approaches to experimental design. Math 308 Statistics B. Meaningful integrated objectives Spring 2001 At the end of the course, you will be able to: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Find the probability of an event dissimilar from one discussed in class. Find the probability distribution for a random variable in an applied problem dissimilar from one discussed in class. Find the expected value of a random variable in an applied problem dissimilar from one discussed in class. Find the variance of a random variable in an applied problem dissimilar from one discussed in class. Find the probability of an event in an applied problem dissimilar from one discussed in class that involves a discrete random variable having a common distribution. Find the probability density function for a continuous random variable in an applied problem dissimilar from one discussed in class. Find the probability of an event in an applied problem dissimilar from one discussed in class that involves a continuous random variable having a common distribution. Find the sampling distribution of a statistic dissimilar from one discussed in class. Solve an applied problem dissimilar from one discussed in class using the central limit theorem. Find a realistic applied problem, either in engineering or science, dissimilar from ones discussed in class, whose solution involves techniques of statistics. A. Critical thinking objectives At the end of the course, you will be able to: 1. Find and solve a realistic applied problem, either in engineering or science, dissimilar from ones discussed in class, whose solution involves techniques of statistics. Math 308 Statistics Spring 2001 Grades: Grades are based on: Tests……………………………………………..75% Assignments……………………………………. 25%. 3 fifty minute tests………………………………50% comprehensive final examination………………..25% Tests: In order to pass the course, the student must earn a passing grade on tests and on homework assignments. There are no make ups for tests or dropped grades. Assignments (General): Assignments include graded written homework, practice homework, and class participation. Each student must submit assignments on time and in a specified format. A graded written homework assignment is due at the start of class. Graded assignments are collected at the beginning of each class. Place them on the teacher’s desk when you enter the room. Practice homework may be submitted at any time and particularly prior to exams over a particular text section. A student must submit his/her own work for assignments. Assignments (Homework) Each student will complete all assigned graded homework and as much of the practice homework as she/he desires. All homework submitted to the instructor is to be formatted as specified in the Homework Guidelines (attached and also available on my WWW home page - www.cbu.edu/~rrubin). Your homework will be graded for quality (how well you follow the homework guidelines) as well as correctness. Late Homework Policy: Homework turned in after the due date will be accepted only for verifiable reasons and no later than 2 class periods after the initial due date. Verifiable reasons include sickness, family emergencies, and absences for university sanctioned events. Attach the reason for lateness to the homework. Only partial credit will be given for late homework. The grading scale in % is: A B C D F 90-100 80-89 65-79 60-65 0-59 Attendance: Students are expected to attend class regularly. See the policy on attendance in the CBU catalog. Other Resources: Tutors will be available in room 104 and Room 151 of the Science Building. Check the web site http://www.cbu.edu/sciences/mathCtr.html for the exact hours. Lecture notes, homework and test assignments, and other interesting things will be posted on my world wide home page: http://www.cbu.edu/~rrubin Math Center: Lecture Notes: