Cheatography
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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 | Z-value at the upper endpoint of interval=largest value-u/๐๐ฅย ฬ
| Area under the curve to the left of the upper endpoint=largest value-u/๐๐ฅย ฬ
on the z table | Z-value at the lower endpoint of the interval=smallest value-u/๐๐ฅย ฬ
| Area under the curve to the left of the lower endpoint=smallest value-u/๐๐ฅย ฬ
on the z table | Probability=area under curve to left of upper endpoint-area 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(๐ฅ๐-๐ฅย ฬ
)^2/n-1 | 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 | Z-value at the upper endpoint of the interval=largest value-p/ ๐๐ย ฬ
| Area under the curve to the left of the upper endpoint equals z value of largest value-p/ ๐๐ย ฬ
| Z-value at the lower endpoint of the interval=smallest value-p/ ๐๐ย ฬ
| Area under the curve to the left of the lower endpoint=z=value of mallest value-p/ ๐๐ย ฬ
| Probabยญiliยญty=area under curve to left of upper endpoiยญnt-area under curve to left of lower endpoin |
|
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