1 2016 Cengage Learning. All Rights Reserved. 2016 Cengage Learning. All Rights Reserved. A A population population is the set of all the elements o is the set of all the elements o A A sample sample is a subset of the population. is a subset of the population. An An element element is the entity on which data are co is the entity on which data are co The reason we select a sample is to collect d The reason we select a sample is to collect d answer a research question about a population answer a research question about a population A A frame frame is a list of the elements that the sa is a list of the elements that the sa be selected from. be selected from. Chapter 7 - Sampling Chapter 7 - Sampling
A A populationpopulation is the set of all the elements of interest. is the set of all the elements of interest. A A populationpopulation is the set of all the elements of interest. is the set of all the elements of interest.
A A samplesample is a subset of the population. is a subset of the population. A A samplesample is a subset of the population. is a subset of the population.
An An elementelement is the entity on which data are collected. is the entity on which data are collected. An An elementelement is the entity on which data are collected. is the entity on which data are collected.
The reason we select a sample is to collect data toThe reason we select a sample is to collect data to answer a research question about a population.answer a research question about a population. The reason we select a sample is to collect data toThe reason we select a sample is to collect data to answer a research question about a population.answer a research question about a population.
A A frameframe is a list of the elements that the sample will is a list of the elements that the sample will be selected from.be selected from. A A frameframe is a list of the elements that the sample will is a list of the elements that the sample will be selected from.be selected from.
The sample results provide only The sample results provide only estimatesestimates of the of the values of the population characteristics.values of the population characteristics. The sample results provide only The sample results provide only estimatesestimates of the of the values of the population characteristics.values of the population characteristics.
With With proper sampling methodsproper sampling methods, the sample results, the sample results can provide “good” estimates of the populationcan provide “good” estimates of the population characteristics.characteristics.
With With proper sampling methodsproper sampling methods, the sample results, the sample results can provide “good” estimates of the populationcan provide “good” estimates of the population characteristics.characteristics.
IntroductionIntroduction
The reason is simply that the sample contains only aThe reason is simply that the sample contains only a portion of the population.portion of the population. The reason is simply that the sample contains only aThe reason is simply that the sample contains only a portion of the population.portion of the population.
This chapter provides the basis for determining howThis chapter provides the basis for determining how large the estimation error might be.large the estimation error might be. This chapter provides the basis for determining howThis chapter provides the basis for determining how large the estimation error might be.large the estimation error might be.
In large sampling projects, computer-generated In large sampling projects, computer-generated random random numbersnumbers are often used to automate the sample selection process. are often used to automate the sample selection process.
Sampling without replacementSampling without replacement is the procedure used most often is the procedure used most often..
Replacing each sampled element before selecting subsequent Replacing each sampled element before selecting subsequent elements is called elements is called sampling withsampling with replacementreplacement..
Sampling from a Finite PopulationSampling from a Finite Population Finite populationsFinite populations are often defined by lists such as: are often defined by lists such as:
A A simple random sample of size simple random sample of size nn from a finite from a finite population of size population of size NN is a sample selected such that each possible sample of size is a sample selected such that each possible sample of size nn has has the same probability of being selected.the same probability of being selected.
The random numbers generated by Excel’s The random numbers generated by Excel’s RANDRAND function follow a uniform probability function follow a uniform probability distribution between 0 and 1.distribution between 0 and 1.
The random numbers generated by Excel’s The random numbers generated by Excel’s RANDRAND function follow a uniform probability function follow a uniform probability distribution between 0 and 1.distribution between 0 and 1.
Step 1:Step 1: Assign a random number to each of the 900 Assign a random number to each of the 900 applicants.applicants.
Step 2:Step 2: Select the 30 applicants corresponding to the Select the 30 applicants corresponding to the 30 smallest random numbers.30 smallest random numbers.
Sampling from a Finite Population Using Sampling from a Finite Population Using ExcelExcel
Example: St. Andrew’s CollegeExample: St. Andrew’s College
St. Andrew’s College received 900 applications for St. Andrew’s College received 900 applications for admission in the upcoming year from prospective admission in the upcoming year from prospective students. The applicants were numbered, from 1 to students. The applicants were numbered, from 1 to 900, as their applications arrived. The Director of 900, as their applications arrived. The Director of Admissions would like to select a simple random Admissions would like to select a simple random sample of 30 applicants.sample of 30 applicants.
Put Random Numbers in Ascending OrderPut Random Numbers in Ascending Order Set calculation option to manualSet calculation option to manual
Step 4Step 4 Choose Choose Sort Smallest to LargestSort Smallest to LargestStep 3Step 3 In the In the EditingEditing group, click group, click Sort & FilterSort & FilterStep 2Step 2 Click the Click the HomeHome tab on the Ribbon tab on the Ribbon
Step 1Step 1 Select any cell in the range B2:B901Select any cell in the range B2:B901
Sampling from a Finite Population Using Sampling from a Finite Population Using ExcelExcel
A B
1Applicant Number
23456789
Random Number0.000270.001920.003030.004810.005380.005830.006490.00667
Populations are often defined by an Populations are often defined by an ongoing ongoing processprocess whereby the elements of the population whereby the elements of the population consist of items generated as though the consist of items generated as though the process would operate indefinitely.process would operate indefinitely.
Sampling from a ProcessSampling from a Process
Some examples of on-going processes, with infiniteSome examples of on-going processes, with infinite populations, are:populations, are:
• parts being manufactured on a production lineparts being manufactured on a production line• transactions occurring at a banktransactions occurring at a bank• telephone calls arriving at a technical help desktelephone calls arriving at a technical help desk• customers entering a storecustomers entering a store
The sampled population is such that a frame cannotThe sampled population is such that a frame cannot be constructed.be constructed.
In the case of infinite populations, it is impossible toIn the case of infinite populations, it is impossible to obtain a list of all elements in the population.obtain a list of all elements in the population.
The random number selection procedure cannot beThe random number selection procedure cannot be used for infinite populations.used for infinite populations.
A A random sample from an infinite populationrandom sample from an infinite population is a is a sample selected such that the following conditionssample selected such that the following conditions are satisfied.are satisfied.
• Each of the sampled elements is independent.Each of the sampled elements is independent.
• Each of the sampled elements follows the same probability Each of the sampled elements follows the same probability distribution as the elements in the population.distribution as the elements in the population.
