MTH345: Statistics for Scientists and Engineers. Spring 2016

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1 MTH345: Statistics for Scientists and Engineers Instructor: Songfeng (Andy) Zheng Spring Phone: Room and Time: Cheek 207, 12:30 pm - 1:45 pm, TR Office and Hours: Cheek 22M, 2:00pm 3:30pm, Tuesday and Thursday; or by appointment. Office hours are offered for individual help and getting to know how you understand the material, so please use them. Textbook: William Navidi, Statistics for Engineers and Scientists, 4th Edition, McGraw Hill. This is a good textbook, providing a lot of examples in science and engineering. I strongly suggest you read the textbook regularly. Course webpage: will provide homework assignments, announcements, the topics covered each lecture, the suggested reading materials, and other learning materials. Objectives & Prerequisites: Statistical theory and methodology are needed in almost all disciplines. The course MTH345 is a beginning course in probability and statistics emphasizing applications in science and engineering. This course deals with various statistical tools and ideas to collect, analyze, and draw inference from data arising from both observational and experimental studies in science and engineering. The students will receive training in descriptive statistics, probability, and statistics inference. Theoretical concepts needed for the study of statistical inference will be introduced. The prerequisite for this course is MTH280 or MTH288 or equivalent. The knowledge of differentiation, integration and summation of infinite series will be needed in the course. We will use the software Microsoft Excel to perform certain calculations. Outcomes: Understand and create graphical summaries of data, and compute various descriptive measures of data. Work with introductory probability, discrete and continuous probability distributions and their simulations. Work with sampling distributions, and the Central Limit Theorem. Construct confidence intervals for population means, proportions, and difference between mean values. Conduct tests of hypotheses for population means, proportions and difference between mean values. Do simple linear regression analysis and analysis of variance by using Excel.

2 Materials to be covered: Descriptive statistics, Graphical Summary. Events, basic properties of probability, conditional probability, discrete and continuous random variables and their distributions, expectation and variance. Commonly used distributions, central limit theorem. Confidence intervals for population means and population proportions, confidence intervals for the difference of the means and proportions. Hypothesis testing about the population mean and population proportions. Hypothesis testing about the difference between two population means and population proportions. Introduction to distribution free tests, Chi-square tests. Simple linear regression models, linear correlations. The appended is a copy of the schedule of tentative topics. Grading Policy and Studying Suggestions: Homework: 20% Two In-class Tests: 40% Final Exam: 40% Grading policy: A (>90%), B ( %), C ( %), D (60 70%), F(<60%) Final exam date: 11: :00, May 12, Thursday. It is important that you read the text book and lecture notes regularly (I will list the suggested reading materials online for each week), understand the problems worked out in the text and practice by doing the problems. Doing the homework problems is absolutely essential to get a better grade in this course. You are allowed to discuss the homework problems among yourselves or with me. However the final work handed in must be completely your own. Anyone who receives or gives an unauthorized aid on a homework or test is considered to be cheating. Late Homework will not be accepted! There will be two midterm exams: Midterm 1 will cover chapters 1 and 2, and midterm 2 will cover chapters 4 and 5. The final exam will be comprehensive! No make-up test or exam will be given under ordinary conditions. The only acceptable excuse for missing a test is an extreme emergency. However, you must obtain a written explanation from a physician, etc. The exam date will be announced in class (and on the course webpage) about two weeks ahead. If you cannot take the test on the scheduled day, you must contact me at least three days before the test date. ing format: is an important means to communication in everyday life as well as in this course. Due to the large amount of s sent to me every day, and due to different courses I am teaching, I suggest you clearly write a subject in the , and in the

3 subject, clearly tell which course you are from. For example, a good subject would be like Subject: MTH 345: Q about #4 in HW2 Thus, I can quickly locate your problem and will reply quickly. s which don t have a clear subject may be simple ignored! Miscellaneous Notes: Attendance policy: The University expects instructors to be reasonable in accommodating students whose absence from class resulted from: (1) participation in University-sanctioned activities and programs; (2) personal illness; or (3) family and/or other compelling circumstances. Instructors have the right to request documentation verifying the basis of any absences resulting from the above factors. Please see The University s attendance policy can be found in the Undergraduate Catalog at Academic integrity: Missouri State University is a community of scholars committed to developing educated persons who accept the responsibility to practice personal and academic integrity. You are responsible for knowing and following the university s Student Academic Integrity Policies and Procedures, available at You are also responsible for understanding and following any additional academic integrity policies specific to this class (as outlined by the instructor). Any student participating in any form of academic dishonesty will be subject to sanctions as described in this policy. If you are accused of violating this policy and are in the appeals process, you should continue participating in the class. Nondiscrimination: Missouri State University is an equal opportunity/affirmative action institution, and maintains a grievance procedure available to any person who believes he or she has been discriminated against. At all times, it is your right to address inquiries or concerns about possible discrimination to the Office for Equity and Diversity, Park Central Office Building, 117 Park Central Square, Suite 111, (417) Other types of concerns (i.e., concerns of an academic nature) should be discussed directly with your instructor and can also be brought to the attention of your instructor s Department Head. Please visit the OED website at Disability Accommodation: To request academic accommodations for a disability, contact the Director of the Disability Resource Center, Plaster Student Union, Suite 405, (417) or (417) (TTY), Students are required to provide documentation of disability to the Disability Resource Center prior to receiving accommodations.

4 The Disability Resource Center refers some types of accommodation requests to the Learning Diagnostic Clinic, which also provides diagnostic testing for learning and psychological disabilities. For information about testing, contact the Director of the Learning Diagnostic Clinic, (417) , Cell phone policy: As a member of the learning community, each student has a responsibility to other students who are members of the community. When cell phones or pagers ring and students respond in class or leave class to respond, it disrupts the class. Therefore, the Office of the Provost prohibits the use by students of cell phones, pagers, PDAs, or similar communication devices during scheduled classes. All such devices must be turned off or put in a silent (vibrate) mode and ordinarily should not be taken out during class. Given the fact that these same communication devices are an integral part of the University s emergency notification system, an exception to this policy would occur when numerous devices activate simultaneously. When this occurs, students may consult their devices to determine if a university emergency exists. If that is not the case, the devices should be immediately returned to silent mode and put away. Other exceptions to this policy may be granted at the discretion of the instructor. Emergency Response policy: Students who require assistance during an emergency evacuation must discuss their needs with their professors and Disability Services. If you have emergency medical information to share with me, or if you need special arrangements in case the building must be evacuated, please make an appointment with me as soon as possible. For additional information students should contact the Disability Resource Center, (PSU 405), or Larry Combs, Interim Assistant Director of Public Safety and Transportation at For further information on Missouri State University s Emergency Response Plan, please refer to the following web site: Dropping a Class: It is your responsibility to understand the University s procedure for dropping a class. If you stop attending this class but do not follow proper procedure for dropping the class, you will receive a failing grade and will also be financially obligated to pay for the class. For information about dropping a class or withdrawing from the university, contact the Office of the Registrar at

5 Tentative Lecture Schedule Lecture 1: Course statement. Statistics, Population, Sample, simple random sample. Lecture 2: Tangible population, Conceptual population. Independent sample. Type of data. Mean and median: definition and calculation. Lecture 3: Mean and median: advantages and disadvantages. Range, variance and standard deviation : their definition, explanation, and calculation. outliers, quartile: denifitions. Lecture 4: quartiles: definition and calculation. Percentile, outliers, IQR. trimmed mean value. statistics and parameter. Graphical representations: Pie chart and bar chart for categorical data, Excel examples. Lecture 5: Histogram, excel example. Five number statistics, box plot. Lecture 6: Box-plot. experiments, sample space, events, combination of events. Lecture 7: Example of combining events, DeMorgan's Law. mutually exclusive events. Definition and explanation of Probability, Properties of probability, additive rules, Examples. Factorial, Combination. Lecture 8: Conditional Probability: interpretation and Calculation. Multiplication rule. Independent Events, Examples. Lecture 9: Law of Total probability, understanding, Examples. Bayes' formula, understanding, Example. Lecture 10: Random variables: Motivation, Definition, and Example; discrete random variables, point mass probability function: definition, representation, properties, and example. Cumulative distribution function: definition, calculation. Lecture 11: Cumulative distribution function: definition, calculation, and plot. Example. Mean and variance of discrete random variables. Definition of continuous random variables, probability density function and its properties. Lecture 12: difference between continuous and discrete R.V., cumulative distribution function. Examples. Properties of Cumulative distribution function of continuous R.V., mean and variance of continuous R.V., Examples. Lecture 13: mean and variance of continuous R.V., population percentiles. Examples. Mean of linear combination of random variables. Lecture 14: Independent random variables, variance of linear combination of independent random variables. Mean and variance of simple random sample. Examples.

6 Lecture 15: Bernoulli Random Variable: definition, mean and variance, Examples. Binomial distribution: definition and probability mass function. Lecture 16: Examples for Binomial distribution. Relation between Bernoulli and Binomial, Mean and Variance of Binomial random variable. Examples. Estimating the probability of success and uncertainty. Lecture 17: Persian Princess problem. Poisson distribution as an approximation to Binomial distribution, Examples. Mean and variance of Poisson distribution. Lecture 18: Examples for Poisson distribution. Normal density function: mean and variance, shape of normal curves. Lecture 19: Shape of normal curves. Use of z-table. Finding z value from probability. Examples. Lecture 20: Exam #1 problems. Transform X to Z; Find normal probability from x, find x from probability, Examples. Parameter estimation for normal distribution. Lecture 21: Properties of Normal random variables, Examples. Lecture 22: Central Limit Theorem: Explanation, the theorem. Examples for Central Limit Theorem. Lecture 23: Normal approximation to Binomial distribution, continuity correction. Examples. pp Lecture 24: Example for Normal approximation to Binomial. Motivations for Confidence Intervals; 95% and 68% CI for population mean, General form of CI for mean value. Lecture 25: General form of CI for mean value. Confidence level and width, precision. Probability and confidence, examples. Lecture 26: Probability and confidence, examples. Sample size issue, one-sided confidence interval, various examples. Lecture 27: Examples for Confidence intervals for population mean. Confidence intervals for population proportion: theory and examples. Lecture 28: t-distribution, use of t-table, examples. Small sample confidence interval using t-distribution: derivations. Lecture 29: Small sample confidence interval using t-distribution, Examples. summary of confidence intervals for mean value. Confidence interval for the difference of two mean values.

7 Lecture 30: Confidence interval for the difference of two mean values. Confidence interval for the difference between two population proportions. Lecture 31: Test #2 problems. Motivations for Hypothesis Testing problem, Hypothesis, Null and Alternative Hypotheses. Lecture 32: General steps of Hypothesis Testing, calculating and explanation of p-value. Lecture 33: General steps of Hypothesis Testing, calculating and explanation of p-value. Three types of HT problems and the p-value calculating. Examples. Two types of errors in HT. significant and significant level. Lecture 34: Relation between CI and HT, various examples. Tests for population proportions: an example. Lecture 35: Tests for population proportions, Examples. Small sample test for population mean using t-test: Example. Lecture 36: T-test: Method and Examples. Large sample test for the difference of two mean values: Method and Example. Sec 6.5. Lecture 37: Large sample test for the difference of two mean values: Method and Examples. Large sample test for the difference of two population proportions. Lecture 38: Large sample test for the difference of two population proportions, examples. Paired data and paired t-test: general procedure and example. Lecture 39: Paired data and paired t-test: general procedure and examples.

STA 225: Introductory Statistics (CT)

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