Chapter 7: Sampling and Sampling Distributions Cheat Sheet by allyrae97
math business statistics probability modern
DefinitionsElement: The entity on which data are collected  Population: A collection of all the elements of interest   Sample: A subset of the population  Sampled population: The population from which the sample is collected  Frame: a list of elements that the sample will be collected from 
Sampling from an Infinite PopulationPopulations generated by an ongoing process are referred to as Infinite Populations: parts being manufactured, transactions occurring at a bank, calls at a technical help desk, customers entering a store  Each element selected must come from the population of interest, Each element is selected independently. 
Sampling Distribution ofExpected value of ๐ฅย ฬ
: E(๐ฅย ฬ
) = u  Standard Deviation of ๐ฅย ฬ
:  Finite Population: ๐๐ฅย ฬ
=โ๐โ๐/(๐โ1)) (๐/โ๐)  Infinite Population: ๐๐ฅย ฬ
=๐/โ๐  Zvalue at the upper endpoint of interval=largest valueu/๐๐ฅย ฬ
 Area under the curve to the left of the upper endpoint=largest valueu/๐๐ฅย ฬ
on the z table  Zvalue at the lower endpoint of the interval=smallest valueu/๐๐ฅย ฬ
 Area under the curve to the left of the lower endpoint=smallest valueu/๐๐ฅย ฬ
on the z table  Probability=area under curve to left of upper endpointarea under curve to left of lower endpoint  When selecting a different sample number, expected value remains the same. When the sample size is increased the standard error is decreased. 
  Sampling from a Finite PopulationFinite Populations are often defined by lists: Organization Member Roster, Credit Card Account Numbers, Inventory Product Numbers  A simple random sample of size n from a finite population of size N: a sample selected such that each possible sample of size n has the same probability of being selected 
Point EstimationPoint Estimation is a form of statistical inference.  We use the data from the sample to compute a value of a sample statistic that serves as an estimate of a population parameter.  ๐ฅย ฬ
is the point estimator of the population mean  s is the point estimator of the population standard deviation  ๐ย ฬ
is the point estimator of the population proportion  ๐ฅย ฬ
=(โ๐ฅ๐ )/n  ๐ =โโ(๐ฅ๐๐ฅย ฬ
)^2/n1  ๐ย ฬ
=x/n 
Sampling Distribution ofExpected value of ๐ย ฬ
=E(๐ย ฬ
)=๐  Standard Deviation of ๐ย ฬ
;  Finite Population: ๐๐ย ฬ
=โ๐โ๐/(๐โ1))( โ๐(1โ๐/๐)  Infinite Population: ๐๐ย ฬ
=โ๐(1โ๐/๐  Zvalue at the upper endpoint of the interval=largest valuep/ ๐๐ย ฬ
 Area under the curve to the left of the upper endpoint equals z value of largest valuep/ ๐๐ย ฬ
 Zvalue at the lower endpoint of the interval=smallest valuep/ ๐๐ย ฬ
 Area under the curve to the left of the lower endpoint=z=value of mallest valuep/ ๐๐ย ฬ
 Probabยญiliยญty=area under curve to left of upper endpoiยญntarea under curve to left of lower endpoin 

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