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Chapter 1 An Introduction to Business Statistics McGraw-Hill/Irwin Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline 1.1 Populations and Samples 1.2 Selecting a Random Sample 1.3 Ratio, Interval, Ordinal, and Nominative Scales of Measurement (Optional) 1.4 An Introduction to Survey Sampling (Optional) 1.5 More About Data Acquisition and Survey Sampling (Optional) 1-2 1.1 Populations and Samples Population: A set of existing units (people, objects or events) Variable: Any characteristic of the population Census: An examination all of the population of measurements Sample: A subset of the units of a population 1-3 Quantitative Versus Qualitative Quantitative: Measurements that represent quantities Annual starting salary Gasoline mileage Qualitative: A descriptive category to which a population unit belongs: a descriptive attribute of a population unit A person’s gender is qualitative Make of automobile 1-4 Population of Measurements Measurement of the variable of interest for each and every population unit Sometimes referred to as an observation For example, annual starting salaries of all graduates from last year’s MBA program Census: The process of collecting the population of all measurements Sample: A subset of population units 1-5 Descriptive Statistics Descriptive Statistics: The science of describing the important aspects of a set of measurements Statistical Inference: The science of describing the important aspects a set of measurements 1-6 1.2 Selecting a Random Sample Random Sample: Selected so that, on each selection from the population, every unit remaining in the population on that selection has the same chance of being chosen Sample with replacement Sample without replacement 1-7 Approximately Random Samples In general, must make a list identifying each and every individual population unit This may not be possible Draw a “systematic” sample Randomly enter the population and systematically sample every kth unit 1-8 Finite and Infinite Populations Finite if it is of fixed and limited size Finite if it can be counted Infinite if it is unlimited Infinite if listing or counting every element is impossible 1-9 Sampling a Process Inputs Process Outputs 1-10 Statistical Control To determine if a process is in control or not, sample the process often enough to detect unusual variations Issue: How often to sample? See Example 1.3, “The Car Mileage Case: Estimating Mileage,” in the textbook 1-11 Runs Plot Figure 1.2 1-12 Out of Control (Level Decreasing) Figure 1.3 1-13 Out of Control (Variation Increasing) Figure 1.4 1-14 1.3 Ratio, Interval, Ordinal, and Nominative Scales of Measurement (Optional) Nominative Ordinal Interval Ratio 1-15 Qualitative Variables Nominative: A qualitative variable for which there is no meaningful ordering, or ranking, of the categories Example: gender, car color Ordinal: A qualitative variable for which there is a meaningful ordering, or ranking, of the categories Example: teaching effectiveness 1-16 Interval Variable All of the characteristics of ordinal plus… Measurements are on a numerical scale with an arbitrary zero point The “zero” is assigned: it is nonphysical and not meaningful Zero does not mean the absence of the quantity that we are trying to measure 1-17 Interval Variable Continued Can only meaningfully compare values by the interval between them Cannot compare values by taking their ratios “Interval” is the arithmetic difference between the values Example: temperature 0 F means “cold,” not “no heat” 60 F is not twice as warm as 30 F 1-18 Ratio Variable All the characteristics of interval plus… Measurements are on a numerical scale with a meaningful zero point Zero means “none” or “nothing” Values can be compared in terms of their interval and ratio $30 is $20 more than $10 $0 means no money 1-19 Ratio Variable Continued In business and finance, most quantitative variables are ratio variables, such as anything to do with money Examples: Earnings, profit, loss, age, distance, height, weight 1-20 1.4 An Introduction to Survey Sampling (Optional) Already know some sampling methods Also called sampling designs, they are: Random sampling Systematic sampling Voluntary response sampling But there are other sample designs Stratified random sampling Multi-stage cluster sampling 1-21 Stratified Random Sample Divide the population into nonoverlapping groups, called strata, of similar units Separately, select a random sample from each and every stratum Combine the random samples from each stratum to make the full sample Appropriate when the population consists of two or more different groups 1-22 Multi-Stage Cluster Sampling Group a population into subpopulations Each cluster is a representative small-scale version of the population Pick a random sample of clusters A simple random sample is chosen from each chosen cluster Combine the random samples from each cluster to make the full sample 1-23 Combination It is sometimes a good idea to combine stratification with multistage cluster sampling For example, we wish to estimate the proportion of all registered voters who favor a presidential candidate Divide United States into regions Use these regions as strata Take a multi-stage cluster sample from each stratum 1-24 Systematic Sampling To systematically select n units without replacement from a frame of N units, divide N by n and round down to a whole number Randomly select one unit within the first N/n interval Select every N/nth unit after that 1-25 1.5 More About Data Acquisition and Survey Sampling (Optional) Web searches… Cheap, fast Limited in type of information we are able to find Data collection agency Cost money Buy subscription or individual reports 1-26 Initiating a Study First, define the variable of interest, called a response variable Next, define other variables that may be related to the variable of interest and will be measured, called independent variables If we manipulate the independent variables, we have an experimental study If unable to control independent variables, the study is observational 1-27 Types of Survey Questions Dichotomous questions ask for a yes/no response Multiple choice questions give the respondent a list of of choices to select from Open-ended questions allow the respondent to answer in their own words 1-28 Errors Occurring in Surveys Random sampling should eliminate bias But even a random sample may not be representative because of: Sampling error Under-coverage Non-response Response bias 1-29