# 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 ๐ฅย ฬ: E(๐ฅย ฬ) = u Standard Deviation of ๐ฅย ฬ : Finite Popula­tion: ๐๐ฅย ฬ =โ๐โ๐/­(๐โ1)) (๐/โ๐) Infinite Popula­tion: ๐๐ฅย ฬ =๐/โ๐ Z-value at the upper endpoint of interv­al=­largest value-­u/๐๐ฅย ฬ Area under the curve to the left of the upper endpoi­nt=­largest value-­u/๐๐ฅย ฬ on the z table Z-value at the lower endpoint of the interv­al=­sma­llest value-­u/๐๐ฅย ฬ Area under the curve to the left of the lower endpoi­nt=­sma­llest value-­u/๐๐ฅย 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. ๐ฅย ฬ is the point estimator of the population mean s is the point estimator of the population standard deviation ๐ย ฬ is the point estimator of the population proportion ๐ฅย ฬ=(โ๐ฅ๐ )/n ๐ =โโ(๐ฅ­๐-๐ฅ­ย ฬ)­^2/n-1 ๐ย ฬ=x/n

### Sampling Distri­bution of

 Expected value of ๐ย ฬ=E(­๐ย ฬ)=๐ Standard Deviation of ๐ย ฬ; Finite Popula­tion: ๐๐ย ฬ =โ๐โ๐/­(๐โ1))( โ๐(1โ๐/๐) Infinite Popula­tion: ๐๐ย ฬ =โ๐(1โ๐/๐ Z-value at the upper endpoint of the interv­al=­largest value-p/ ๐๐ย ฬ Area under the curve to the left of the upper endpoint equals z value of largest value-p/ ๐๐ย ฬ Z-value at the lower endpoint of the interv­al=­sma­llest value-p/ ๐๐ย ฬ Area under the curve to the left of the lower endpoi­nt=­z=value of mallest value-p/ ๐๐ย ฬ Probab­ยญil­iยญt­y=area under curve to left of upper endpoi­ยญnt­-area under curve to left of lower endpoin

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