# Chapter 7: Sampling and Sampling Distributions Cheat Sheet by allyrae97

### 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: ππ₯Β Μ =βπβπ/­(πβ1)) (π/βπ) Infinite Popula­tion: ππ₯Β Μ =π/βπ Z-value at the upper endpoint of interv­al=­largest value-­u/ππ₯Β Μ Area under the curve to the left of the upper endpoi­nt=­largest value-­u/ππ₯Β Μ on the z table Z-value at the lower endpoint of the interv­al=­sma­llest value-­u/ππ₯Β Μ Area under the curve to the left of the lower endpoi­nt=­sma­llest value-­u/ππ₯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 πΒ Μ is the point estimator of the population proportion π₯Β Μ=(βπ₯π )/n π =ββ(π₯­π-π₯­Β Μ)­^2/n-1 πΒ Μ=x/n

### Sampling Distri­bution of

 Expected value of πΒ Μ=E(­πΒ Μ)=π Standard Deviation of πΒ Μ; Finite Popula­tion: ππΒ Μ =βπβπ/­(πβ1))( βπ(1βπ/π) Infinite Popula­tion: ππΒ Μ =βπ(1βπ/π Z-value at the upper endpoint of the interv­al=­largest value-p/ ππΒ Μ Area under the curve to the left of the upper endpoint equals z value of largest value-p/ ππΒ Μ Z-value at the lower endpoint of the interv­al=­sma­llest value-p/ ππΒ Μ Area under the curve to the left of the lower endpoi­nt=­z=value of mallest value-p/ ππΒ Μ Probab­Β­il­iΒ­t­y=area under curve to left of upper endpoi­Β­nt­-area under curve to left of lower endpoin

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