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Chapter One

Chapter One. What is Statistics?. FYI – Past Grades in This Statistics Course. FYI – Past Grades in This Statistics Course. FYI – Past Grades in This Statistics Course. In today’s world…. …we are constantly being bombarded with statistics and statistical information. For example:

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Chapter One

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  1. Chapter One What is Statistics?

  2. FYI – Past Grades in This Statistics Course

  3. FYI – Past Grades in This Statistics Course

  4. FYI – Past Grades in This Statistics Course

  5. In today’s world… • …we are constantly being bombarded with statistics and statistical information. For example: • Customer Surveys Medical News • Political Polls Economic Predictions • Marketing Information Scanner Data • How can we make sense out of all this data? • How do we differentiate valid from flawed claims? • Three types of liars!

  6. What is Statistics? Where does this Data come from? • “Statistics is a way to get information from data” Statistics Data Information Data:Facts, especially numerical facts, collected together for reference or information. Information:Knowledge communicated concerning some particular fact. Statistics is a tool for creating new understanding from a set of numbers. Definitions: Oxford English Dictionary

  7. Key Statistical Concepts… • Population • — a population is the group of all items of interest to a statistics practitioner. • — frequently very large; sometimes infinite. • E.g. All 5 million Florida voters who voted in today’s election. • Sample • — A sample is a set of data drawn from the population. [Part of a population] • — Potentially very large, but less than the population. • E.g. a sample of 1000 voters exit polled on election day.

  8. Key Statistical Concepts… • Parameter • — A descriptive measure of a population. • - the true percent of Florida Voters who will vote for Mary Poppins • Statistic • — A descriptive measure of a sample. • - Of the 1000 exit voters polled, 550 indicated that they voted for Mary Poppins or 550/1000 = 0.55 or 55%

  9. Key Statistical Concepts… Population • Populations have Parameters, • Samples have Statistics. Sample Subset Statistic Parameter

  10. Descriptive Statistics… • …are methods of organizing, summarizing, and presenting data in a convenient and informative way. These methods include: • Graphical Techniques (Chapter 2), and • Numerical Techniques (Chapter 4). • The actual method used depends on what information we would like to extract. Are we interested in… • • Your weight each Monday when you are on a 6 month diet. • • The amount of medication in blood pressure pills. • The starting salaries for business students from TCU, SMU, and UTA. • Others… • Descriptive Statistics helps to answer these questions…

  11. Inferential Statistics… • Descriptive Statistics describe the data set that’s being analyzed, but doesn’t allow us to draw any conclusions or make any interferences about the data, other than visual “It looks like …..” type statements. Hence we need another branch of statistics: inferential statistics. • Inferential statistics is also a set of methods, but it is used to draw conclusions or inferences about characteristics of populations based on data from a sample.

  12. Statistical Inference… • Statistical inference is the process of making an estimate, prediction, or decision about a population based on a sample. Population Sample Inference Statistic Parameter What can we infer about a Population’s Parameters based on a Sample’s Statistics?

  13. Rationale: • Large populations make investigating each member impractical and expensive + it’s been shown that observing 100% of a population is not perfect. • Easier and cheaper to take a sample and make inferences about the population from the sample. However: Such conclusions and estimates are not always going to be correct. For this reason, we build into the statistical inference “measures of reliability”, namely confidence level and significance level. Statistical Inference…

  14. Confidence & Significance Levels… • The confidence level is the proportion of times that an interval estimate for a population parameter will be correct. • E.g. a confidence level of 95% means that, interval estimates based on this form of statistical inference will be correct 95% of the time. • I am 95% confident that the “TRUE” mean IQ of female business students at UTA is between 120 and 122. • When the purpose of the statistical inference is to test a claim about a population parameter, the significance level measures how frequently a “true claim” is accidently rejected. • E.g. a 5% significance level means that, in the long run, a true claim will be rejected 5% of the time. • Coin flips should result in 50% heads, on average. A 5% significance level implies that we run a 5% risk of concluding that heads do not occur 50% of the time, on average [even though everyone in this room most likely believes that heads do occur 50% of the time].

  15. Confidence & Significance Levels… • We use  (Greek letter “alpha”) to represent the significance level when testing a claim about a population parameter , • and • 1– to represent the confidence level when we wish to estimate a population parameter.

  16. Statistical Applications in Business… • Statistical analysis plays an important role in virtually all aspects of business and economics. • Throughout this course, we will see applications of statistics in accounting, economics, finance, human resources management, marketing, operations management, and my favorite, “Quality Issues”,associated with manufacturing and service processes.

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