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 𝑥 ̅: E(𝑥 ̅) = u
Standard Deviation of 𝑥 ̅ :
Finite Population: 𝜎𝑥 ̅ =√𝑁−𝑛/(𝑁−1)) (𝜎/√𝑛)
Infinite Population: 𝜎𝑥 ̅ =𝜎/√𝑛
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
Z-value at the lower endpoint of the interval=smallest value-u/𝜎𝑥 ̅
Area under the curve to the left of the lower endpoint=smallest 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.
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 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.
𝑥 ̅ 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
𝑥 ̅=(∑𝑥𝑖 )/n
Sampling Distribution of
Expected value of 𝑝 ̅=E(𝑝 ̅)=𝑝
Standard Deviation of 𝑝 ̅;
Finite Population: 𝜎𝑝 ̅ =√𝑁−𝑛/(𝑁−1))( √𝑝(1−𝑝/𝑛)
Infinite Population: 𝜎𝑝 ̅ =√𝑝(1−𝑝/𝑛
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 ̅
Z-value at the lower endpoint of the interval=smallest value-p/ 𝜎𝑝 ̅
Area under the curve to the left of the lower endpoint=z=value of mallest value-p/ 𝜎𝑝 ̅
Probability=area under curve to left of upper endpoint-area under curve to left of lower endpoin
Help Us Go Positive!
We offset our carbon usage with Ecologi. Click the link below to help us!