Math 201 Statistics for Business & Economics. Definition of Statistics. Two Processes that define Statistics. Dr. C. L. Ebert

Transcription

1 Math 201 Statistics for Business & Economics Dr. C. L. Ebert Chapter 1 Introduction Definition of Statistics Statistics - the study of the collection, organization, presentation, and characterization of information to assist both data analysis and decision making. Two Processes that define Statistics Statisticians are trained in collecting numerical information in the form of data, evaluating that information and drawing conclusion about it. 1

2 Two Processes that define Statistics Thus, statistics involves two different processes: describing large data sets; drawing conclusions. Two Processes Descriptive Statistics Inferential Statistics Two Processes Descriptive Statistics - those methods that utilize numerical and graphical methods to look for patterns in a data set. The objective is to correctly describe the various features of the data set. 2

3 Two Processes Inferential Statistics - those methods that make possible the estimation of a characteristic of a population based on sample results. Basic Terminology Population - a set of units (people, objects, transactions or events) that are of interest for study. Basic Terminology Examples of Populations All citizens of the U.S. All vehicles produced in 2001 by the Newark assembly line. All sales made by the UD bookstore located in Trabant. Set of all traffic accidents at a certain location. 3

4 Basic Terminology Variable - a characteristic or property of a population unit. Measurement - process we use to assign numbers to variables of individual population units. Basic Terminology Census - collecting information from every member of the population. Sample - the subset or portion of the population selected for analysis. Example 1 We refer to the Cola Wars as the popular term for the intense competition between Coca Cola and Pepsi. 4

5 Example 1 If 1000 cola consumers are given a blind taste test and asked for a preference, describe the following: Population and sample Variable of Interest and inference Four Elements of Descriptive Statistical Problems Population or sample of interest; One or more variables to be investigated; Tables, graphs, or numerical summary tools; Conclusions about the data based on the patterns revealed. Five Elements of Inferential Statistical Problems Population of interest; One or more variables that are to be investigated; Sample of population units; 5

6 Five Elements of Inferential Statistical Problems The inference about the population based on information contained in the sample; A measure of reliability for the inference. Sampling Terminology Representative Sample - exhibits characteristics typical of those possessed by the population of interest. Sampling Terminology Simple Random Sample - sample selected in such a way that both every sample and every member of the population has an equally likely chance of being selected. 6

7 Sampling Terminology Measure of Reliability - statement of the degree of uncertainty (statistical inference). Types of Data Categorical (Qualitative) Variables - yield categorical responses such as gender, party affiliation, color, or yes/no responses. Types of Data Numerical (Quantitative) Variables - yield numerical responses such as # of siblings, height, # of cars your family has owned. Discrete - responses that arise from counting; (# of siblings, # of cars) Continuous - responses that arise from measuring. (height) 7

8 Levels of Measurement The resulting data may be described in accordance with the level of measurement attained. In the broadest sense, all data is measured, even discrete data is measured through counting. Levels of Measurement The 4 widely recognized levels of measurement - from weakest to strongest are: Nominal and Ordinal Interval and Ratio Categorical Measurement Scales Nominal Scales - no order is implied. Examples: All yes/no responses, gender & political party affiliation. Ordinal Scales - order is implied but differences between data values are either meaningless or cannot be determined. 8

9 Categorical Measurement Scales Examples: Ranking of teams in sports, rankings in restaurants, movies, hotels, etc., Class rank upon graduation. Numerical Measurement Scales Interval Scale - ordered scale in which differences between measurements are meaningful. However, there is no intrinsic zero or starting point. (temp. and time on calendar) Numerical Measurement Scales Ratio Scale - ordered scale in which differences and ratios are meaningful. A true zero or starting point exists. (length of fish in Yellowstone river) 9

10 Example 2 - Instruction Classify each of the following as categorical or numerical. If numerical, classify as discrete or continuous. Finally, indicate the measurement scale as nominal, ordinal, interval, or ratio. Example 2 Hiker s Log of Favorite Hikes Destination: Mirror Lake (Categorical, nominal) Distance: 6.5 miles (Numerical, continuous, ratio) Difficulty Level: Moderate (Categorical, ordinal) Example 2 Hiker s Log of Favorite Hikes Change in elevation: 3000 ft. (Numerical, continuous, ratio) Time to Hike (one way): 3 hours (Numerical, continuous, ratio) Last Year Hiked: 1997 (Numerical, discrete, interval) 10

11 Collecting Data Published source Designed Experiment Survey Observational Study Example 3 The county sheriff wants to know the proportion of drivers who make an illegal left turn as they leave the post office parking lot. A sample of 200 cars is observed. What is the implied population and sample? Example 3 The county sheriff wants to know the proportion of drivers who make an illegal left turn as they leave the post office parking lot. A sample of 200 cars is observed. How was the data obtained? 11

12 Example 3 The county sheriff wants to know the proportion of drivers who make an illegal left turn as they leave the post office parking lot. A sample of 200 cars is observed. What is the inference? 12