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Chapter 7: Sampling and Sampling Distributions Cheat Sheet by

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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 π‘₯Β Μ…: E(π‘₯Β Μ…) = u
Standard Deviation of π‘₯Β Μ… :
Finite Popula­tion: 𝜎π‘₯Β Μ… =βˆšπ‘βˆ’π‘›/­(π‘βˆ’1)) (𝜎/βˆšπ‘›)
Infinite Popula­tion: 𝜎π‘₯Β Μ… =𝜎/βˆšπ‘›
Z-value at the upper endpoint of interv­al=­largest value-­u/𝜎π‘₯Β Μ…
Area under the curve to the left of the upper endpoi­nt=­largest value-­u/𝜎π‘₯Β Μ… on the z table
Z-value at the lower endpoint of the interv­al=­sma­llest value-­u/𝜎π‘₯Β Μ…
Area under the curve to the left of the lower endpoi­nt=­sma­llest value-­u/𝜎π‘₯Β Μ… 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.
π‘₯Β Μ… is the point estimator of the population mean
s is the point estimator of the population standard deviation
𝑝 ̅ is the point estimator of the population proportion
π‘₯Β Μ…=(βˆ‘π‘₯𝑖 )/n
𝑠=βˆšβˆ‘(π‘₯­π‘–-π‘₯­Β Μ…)­^2/n-1
𝑝 ̅=x/n

Sampling Distri­bution of

Expected value of 𝑝 ̅=E(­π‘Β Μ…)=𝑝
Standard Deviation of 𝑝 ̅;
Finite Popula­tion: πœŽπ‘Β Μ… =βˆšπ‘βˆ’π‘›/­(π‘βˆ’1))( βˆšπ‘(1βˆ’π‘/𝑛)
Infinite Popula­tion: πœŽπ‘Β Μ… =βˆšπ‘(1βˆ’π‘/𝑛
Z-value at the upper endpoint of the interv­al=­largest value-p/ πœŽπ‘Β Μ…
Area under the curve to the left of the upper endpoint equals z value of largest value-p/ πœŽπ‘Β Μ…
Z-value at the lower endpoint of the interv­al=­sma­llest value-p/ πœŽπ‘Β Μ…
Area under the curve to the left of the lower endpoi­nt=­z=value of mallest value-p/ πœŽπ‘Β Μ…
Probab­Β­il­iΒ­t­y=area under curve to left of upper endpoi­Β­nt­-area under curve to left of lower endpoin

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