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Element: The entity on which data are collected
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Population: A collection of all the elements of interest
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Sample: A subset of the population
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Sampled population: The population from which the sample is collected
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Frame: a list of elements that the sample will be collected from
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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
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Each element selected must come from the population of interest, Each element is selected independently.
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Expected value of π₯Β Μ
: E(π₯Β Μ
) = u
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Standard Deviation of π₯Β Μ
:
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Finite Population: ππ₯Β Μ
=βπβπ/(πβ1)) (π/βπ)
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Infinite Population: ππ₯Β Μ
=π/βπ
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Z-value at the upper endpoint of interval=largest value-u/ππ₯Β Μ
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Area under the curve to the left of the upper endpoint=largest value-u/ππ₯Β Μ
on the z table
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Z-value at the lower endpoint of the interval=smallest value-u/ππ₯Β Μ
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Area under the curve to the left of the lower endpoint=smallest value-u/ππ₯Β Μ
on the z table
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Probability=area under curve to left of upper endpoint-area under curve to left of lower endpoint
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When selecting a different sample number, expected value remains the same. When the sample size is increased the standard error is decreased.
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Finite Populations are often defined by lists: Organization Member Roster, Credit Card Account Numbers, Inventory Product Numbers
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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
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Point Estimation is a form of statistical inference.
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We use the data from the sample to compute a value of a sample statistic that serves as an estimate of a population parameter.
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π₯Β Μ
is the point estimator of the population mean
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s is the point estimator of the population standard deviation
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πΒ Μ
is the point estimator of the population proportion
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π₯Β Μ
=(βπ₯π )/n
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π =ββ(π₯π-π₯Β Μ
)^2/n-1
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πΒ Μ
=x/n
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Expected value of πΒ Μ
=E(πΒ Μ
)=π
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Standard Deviation of πΒ Μ
;
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Finite Population: ππΒ Μ
=βπβπ/(πβ1))( βπ(1βπ/π)
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Infinite Population: ππΒ Μ
=βπ(1βπ/π
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Z-value at the upper endpoint of the interval=largest value-p/ ππΒ Μ
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Area under the curve to the left of the upper endpoint equals z value of largest value-p/ ππΒ Μ
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Z-value at the lower endpoint of the interval=smallest value-p/ ππΒ Μ
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Area under the curve to the left of the lower endpoint=z=value of mallest value-p/ ππΒ Μ
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ProbabΒiliΒty=area under curve to left of upper endpoiΒnt-area under curve to left of lower endpoin
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