Cheatography
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Definitions
Element: 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 Population
Populations 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 of
Expected 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 Population
Finite 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 Estimation
Point 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 of
Expected 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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