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- 1. Introduction to Probability and Statistics STAT 101 Introduction What is Statistics? By: Robert J. Beaver • Barbara M. Beaver • William Mendenhall 14th edition (2013)
- 2. 2 Course assessment References and learning resources • Required Textbook: Mendenhall, Beaver, and Beaver (2013). Introduction to Probability and Statistics, 14th edition. Brooks/Cole, CENGAGE Learning • Suggested Additional Resources: • Introductory Statistics, By Neil Weiss, 9th edition, 2012, Pearson Education Inc. • Introduction to Statistics. By R. D. Deaux and P. F. Velleman, 3rd edition, 2008, Adison Welesy. • http:// www.statsci.org Assessment tool Grade Weight Day, Date and Time First Exam 20% Will be posted on Blackboard. Second Exam 20% Will be posted on Blackboard. Quizzes 15% Best three. Lab work 5% Will be posted on Blackboard. Final Exam: 40% ( COMPREHENSIVE EXAM), TBA
- 3. WEEKS CLASS TOPICS READINGs 1 What is Statistics?: Population and Sample, Descriptive and inferential Statistics, Achieving the objective of Inferential Statistics PAGE 1-6 2 Describing data with Graphics: Variables and Data, type of variables, graphs for Categorical Data 1.1, 1.2, 1.3 3 Graphs for Quantitative Data: Pie chart and Bar chart, Line chart, Dot Plot, Stem and Leaf Plots, Interpreting Graphs with critical eyes, Relative frequency histograms: 1.4, 1.5 (Quiz 1) 4 Describing data with numerical measures: Describing a set of data with numerical measures, Measures of centres (mean, median, mode), measures of variability 2.1, 2.2, 2.3 5 On the practical Significance of the standard deviation, A check on the calculation of S, measures of Relative Standing, five-number summary, Boxplot 2.4, 2.5, 2.6, 2.7 (Quiz 2) 6 Probability and probability distribution: The role of probability in Statistics, Events and Sample space, Calculating probability using simple events, Useful counting rules( Rule, permutation and combination) 4.1, 4.2, 4.3, 4.4 7 Event Relations and Probability Rules (Calculating probabilities for unions and complements), Independence, conditional probability and Multiplication Rule. 4.6, 4.7 8 Discrete random variables and several useful discrete distributions: Random variables, probability distribution, mean and standard deviation for a discrete random variables, The Bernoulli, Binomial, and Poisson distributions. 5.2, 5.3 9 Spring Break (no class) 10 The Normal probability distribution: probability distributions for continuous random variables, The normal probability distribution, Tabulated areas of normal probability distribution(Areas under standard normal and general normal distributions), Assessing normality(Using Minitab software) 6.1,6.2, 6.3,6.4(Quiz 3) 11 Sampling Distributions: Sampling Plans and experimental designs, Statistics and Sampling distributions, the sampling distributions of the sample mean and sample proportions 7.1, 7.2, 7.3, 7.4, 7.5, 7.6 12 Large-Sample estimation: Where have we been? Where are we going (Statistical Inference), types of estimators, Point estimation, Interval estimation (constructing confidence interval, large-sample confidence interval for population mean, interpreting confidence interval, Large- sample confidence interval for population proportion), one-sided confidence bounds. 8.1, 8.2, 8.3, 8.4, 8.5, 8.8, 8.9 13 Large-sample tests of hypotheses: Testing hypotheses about population parameters, A statistical test of a hypothesis, Large sample test about a population mean (The essentials of the test, Calculating the P-values, two types of errors) 9.1, 9.2, 9.3(Quiz 4) 14 Large-sample tests of hypotheses: Large sample test about a population proportion (The essentials of the test, Calculating the P-values, two types of errors) 9.5 15 Inference from small samples: Introduction, Students t distribution, t-tables, small-sample inference concerning a population mean 10.1, 10.3 16 REVISION FOR THE FINAL EXAM 17 Final Exam Period
- 4. Statistics is a science dealing with the collection, analysis, interpretation, organization, presentation of data. Collect Data Statistical Analysis Information Statistic = Estimator (Unknown parameter in a population can be estimated by a known statistic (estimator) obtained from a representative sample).
- 5. 1.5 Key Statistical Concepts Populations have Parameters (usually unknown) Parameter Population Sample Statistic Subset Samples have Statistics (always known)
- 6. Parameter Parameter A numerical value summarizing all the data of an entire population. A parameter is a value that describes the entire population. Often a Greek letter is used to symbolize the name of a parameter. The “average” age at time of admission for all students who have ever attended our college and the “proportion” of students who were older than 21 years of age when they entered college are examples of two population parameters.
- 7. Statistic For every parameter there is a corresponding sample statistic. The statistic describes the sample the same way the parameter describes the population. Statistic A numerical value (Estimator) summarizing the sample data. The “average” height, found by using the set of 25 heights, is an example of a sample statistic. A statistic is a value that describes a sample.
- 8. Parameters and Statistics Population Sample Size 𝑁 𝑛 Mean 𝜇 ҧ 𝑥 Variance 𝜎2 𝑆2 Standard Deviation 𝜎 𝑆 Coefficient of Variation 𝐶𝑉 𝑐𝑣 Covariance 𝜎 𝑥𝑦 𝑆 𝑥𝑦 Coefficient of Correlation 𝜌 𝑟
- 9. Job of a Statistician • Collecting (gathering) numbers or relevant data regarding the problem need to be studied, • Systematically organizing or arranging the data, • Analyzing the data, extracting relevant information to provide a complete numerical description, • Providing inferences and conclusions (results) about the problem using this numerical description, • Making sure that inferences and conclusions can reasonably extend from the sample to the population as a whole. To obtain accurate information from data, statistician can help in:
- 10. Uses of Statistics • Statistics is a theoretical discipline in its own right. • Statistics is a tool for researchers in other fields. • Used to draw general conclusions in a large variety of applications.
- 11. If the election for mayor of Los Angeles were held today, who would you be more likely to vote for? James Hahn 32% Magic Johnson 36% Someone else 11% No opinion yet 21% Politics and Opinion Polls • Forecasting and predicting winners of elections • Where to concentrate campaign advertising
- 12. • To market product • Interested in the average length of life of a light bulb • Cannot test all the bulbs Industry
- 13. Common Problem Decision or prediction about a large body of measurements (population) which cannot be totally enumerated. Examples • Light bulbs (to enumerate population is destructive) • Forecasting the winner of an election (population too big; people change their minds) Population: The set of all measurements of interest to the experimenter.
- 14. Solution Collect a smaller set of measurements that will (hopefully) be representative of the larger set. Sample: A subset of measurements selected from the population of interest.
- 15. Experimental Units and Sample Distinguish between set of objects on which we take measurements and the measurements themselves. Experimental Units The items or objects on which measurements are taken. Sample (or Population) The set of measurements taken on the experimental units.
- 16. The field of statistics can be roughly subdivided into two areas: 1. Descriptive statistics. 2. Inferential statistics. Sometimes (but rarely) we can enumerate the whole population (if so, we need only use Descriptive statistics) • Descriptive statistics: Procedures used to summarize and describe the set of measurements. When we cannot enumerate the whole population, we use Inferential statistics Inferential statistics: Procedures used to draw conclusions or inferences about the population from information contained in the sample.
- 17. Recall statistics is all about data But where then does data come from? How is it gathered? How do we ensure its accurate? Is the data reliable? Is it representative of the population from which it was drawn? 1.18 Descriptive statistics: Graphical or Numerical Descriptive statistics deals with methods of organizing, summarizing, and presenting data in a convenient and informative way.
- 18. 1.19 Statistical Inference Statistical inference is the process of making an estimate, prediction, or decision about a population based on a sample. Parameter Population Sample Statistic Inference What can we infer about a Population’s Parameters based on a Sample’s Statistics?
- 19. But, our conclusions could be incorrect…consider this internet opinion poll. We need a measure of reliability. We’ll PAY CASH For Your Opinions! (as much as $50,000 ) Click Here and sign up FREE! Who makes the best burgers? Votes Percent McDonalds 123 Votes 13% Burger King 384 Votes 39% Wendy’s 304 Votes 31% All three have equally good burgers 72 Votes 7% None of these have good burgers 98 Votes 10%
- 20. The Steps in Inferential Statistics • Define the objective of the experiment and the population of interest. • Determine the design of the experiment and the sampling plan to be used. • Collect and analyze the data. • Make inferences about the population from information in the sample. • Determine the goodness or reliability of the inference.