Stats 2035 Chapter 1 Notes

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Statistical Sciences
Statistical Sciences 2035
Histro Sendov

Chapter 1: Introduction to Business Statistics Population and Samples  Population: A set of units (usually people, objects, or events) o Ex. All of last year’s graduates from an MBA program  Variable: A measureable characteristic of a population unit o Quantitative: Variables that are numbers or quantities  Usually consists of ‘how much’ or ‘how many’  Ex. Starting salary of last year’s graduates of an MBA program o Qualitative: Variables that are categorical to which a population unit belongs  Ex. A person’s sex.  Measurement: Process of determining the quantity or extent of the variable for some particular unit of the population. o Ex. Measuring the starting salary of an MBA graduate to the nearest dollar  Value: The specific measurement for a particular unit in the population (result of measurement) o Ex. Starting salary of an MBA graduate to the nearest dollar  Population of measurement (observation): Measurement of the variable of interest for each and every population unit o Census: An examination of the entire population of measurement o Ex. Annual starting salaries of all graduates from last year’s MBA program  Sample: A selected subset of the population o Often, the population is too large, and it is too expensive and time-consuming to conduct a census. o Ex. A selected subset of last year’s MBA graduates  Sample of measurement: Measurement of the variable of interest of the sample. o Ex. Annual starting salaries of selected graduates from last year’s MBA program  Descriptive statistics: The science of describing the important aspects of a set of measurements o If the population is small, a census of the population can be obtained. o If the population is large, a sample needs to be selected, and statistical inference is required. o Ex. For a set of starting salaries of last year’s MBA graduates, wishing to know much is the average  Statistical inference: The science of using a sample of measurements to make generalizations about the important aspects about a population of measurement o Estimating the important aspects of a population of interest. o Ex. Use a sample of starting salaries to estimate the average of population of starting salaries. Sampling a Population of Existing Units  Random sample: A sample selected so that each population has the same chance of being selected as every other unit.  Random number table: Computerized methods of selecting a random sample, in case of enormous population  Selecting a random sample: o Sample with replacement: Replace every sampled unit before picking the next unit  Every unit remains as candidates for every selection.  For some instances, the sample does not contribute new information. o Sample without replacement: Do not replace every sampled unit before picking the next unit  Every unit that has already been selected is not given a chance to be re-selected.  Recommended for most instances, since this gives us the fullest possible look at the population.  Approximately random samples: o Frame: A list that identifies every individual population unit.  For small populations, frames can be created to create a random sample. th o Systematic sample: Randomly enter the population and systematically sample each k unit.  If the population is large, it is not possible to list every individual population unit. th  Ex. intercepting every 100 customer at the mall, and requesting for participation in the survey. o Voluntary response sample: Participants select themselves to be in the survey  Non-scientific, because it is not representative of the population.  Large amount of the sample consists of individuals with strongly sided opinions Sampling a Process  Process: A sequence of operations that take input (labour, material, methods, machine, etc.) and them into outputs (products, services, etc.)  Population: All output produced in the past, present, and future. o Finite population: Population that is fixed, limited in size, and countable  Ex. Every Toyota Corolla that was produced last year. o Infinite population: Population that is unlimited or counting is impossible.  Sampled at equally spaced time points.  Ex. Every Toyota Corolla that will be produced next year.  Statistical control: A process is in statistical control if it does not exhibit any unusual process variations. o Runs-plot (time-series plot): A graph of individual process measurement versus time. o The process usually displays a constant amount of variation, around a constant or horizontal level. o The process is predictable, and allows the researcher to make statistical inferences about the population. o To determine if a process is in control, sample the process often enough to detect unusual var
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