Chapter 7: Sampling and Sampling Distributions Cheat Sheet by allyrae97

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

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.

Expected value of 𝑥 ̅: E(𝑥 ̅) = u

Standard Deviation of 𝑥 ̅ :

Z-value at the upper endpoint of interv­al=­largest value-­u/𝜎𝑥 ̅

Area under the curve to the left of the upper endpoi­nt=­largest value-­u/𝜎𝑥 ̅ 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.

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 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.

𝑝 ̅ is the point estimator of the population proportion

𝑥 ̅=(∑𝑥𝑖 )/n

Expected value of 𝑝 ̅=E(­𝑝 ̅)=𝑝

Standard Deviation of 𝑝 ̅;

Z-value at the upper endpoint of the interv­al=­largest value-p/ 𝜎𝑝 ̅

Area under the curve to the left of the upper endpoint equals z value of largest value-p/ 𝜎𝑝 ̅

Probab­­il­i­t­y=area under curve to left of upper endpoi­­nt­-area under curve to left of lower endpoin