Statistics I:

QM 1

Lecture N otes

by

Stefan W aner

(5th printing: 2003)

Department of Mathematics, Hofstra University

BUSINESS STATISTCS I: QM 001

(5th printing: 2003)

LECTURE NOTES BY STEFAN WANER

TABLE OF CONTENTS

0. Introduction................................................................................................... 2 1. Describing Data Graphically ...................................................................... 3 2. Measures of Central Tendency and Variability........................................ 8 3. Chebyshev's Rule & The Empirical Rule................................................ 13 4. Introduction to Probability ....................................................................... 15 5. Unions, Intersections, and Complements ................................................ 23 6. Conditional Probability & Independent Events..................................... 28 7. Discrete Random Variables....................................................................... 33 8. Binomial Random Variable ...................................................................... 37 9. The Poisson and Hypergeometric Random Variables............................ 44 10. Continuous Random Variables: Uniform and Normal....................... 46 11. Sampling Distributions and Central Limit Theorem.......................... 55 12. Confidence Interval for a Population Mean .......................................... 61 13. Introduction to Hypothesis Testing ........................................................ 66 14. Observed Significance & Small Samples............................................... 72 15. Confidence Intervals and Hypothesis Testing for the Proportion ...... 75

1

Note: Throughout these notes, all references to the “book” refer to the class text: “Statistics for Business and Economics” 8th Ed.

by Anderson, Sweeney, Williams (South-Western/Thomson Learning, 2002) Topic 0 Introduction

Q: What is statistics?

A: Basically, statistics is the “science of data.” There are three main tasks in statistics: (A) collection and organization, (B) analysis, and (C) interpretation of data. (A) Collection and organization of data: We will see several methods of organizing data: graphically (through the use of charts and graphs) and numerically (through the use of tables of data). The type of organization we do depends on the type of analysis we wish to perform.

Quick Example Let us collect the status (freshman, sophomore, junior, senior) of a group of 20 students in this class. We could then organize the data in any of the above ways. (B) Analysis of data: Once the data is organized, we can go ahead and compute various quantities (called statistics or parameters) associated with the data. Quick Example Assign 0 to freshmen, 1 to sophomores etc. and compute the mean. (C) Interpretation of data: Once we have performed the analysis, we can use the information to make assertions about the real world (e.g. the average student in this class has completed x years of college).

Descriptive and Inferential Statistics

In descriptive statistics, we use our analysis of data in order to describe a the situation from which it is drawn (such as the above example), that is, to summarize the information we have found in a set of data, and to interpret it or present it clearly. In inferential statistics, we are interested in using the analysis of data (the “sample”) in order to make predictions, generalizations, or other inferences about a larger s et o f data (the “population”). For example, we might want to ask how confidently we can infer that the average QM1 student at Hofstra has completed x years of college. In QM1 we begin with descriptive statistics, and then use our knowledge to introduce inferential statistics.

2

Topic 1

Describing Data Graphically

(Based on Sections 2.1, 2.2 in text)

An experiment is an occurrence we observe whose result is uncertain. We observe some...