Statistics – Ch 4.1B Notes Name: _________________________ Sampling and Surveys

Stratified Random Sample

x To get a stratified random sample, start by classifying the population into groups of similar

individuals, called _____________________________.

x Then choose a separate __________________ in each stratum and combine these

____________ to form the sample.

Although a stratified random sample can sometimes give more precise information about a population than an SRS, both sampling methods are hard to use when populations are large and spread out over a wide area.

In that situation, we’d prefer a method that selects groups of individuals that are “near” one another. Cluster Sampling

x To get a cluster sample, start by classifying the population into groups of individuals that are

located near each other, called _______________________.

x Then choose an ______________ of the clusters. All individuals in the chosen clusters are

included in the sample.

The difference between strata and clusters:

x We want stratum to contain ______________________ individuals and for there to be large

differences ______________________ strata. (homogenous groups)

x We want each cluster to look like the __________________________, but on a smaller scale.

(heterogeneous groups)

Key

strataSRS

SRS's

clustersS.RS

Similarbetween

population

Statistics – Ch 4.1B Notes Name: _________________________ Sampling and Surveys

Example Problem: The student council wants to conduct a survey about the use of the school library during the first five minutes of an all-school assembly in the auditorium. There are 800 students present at the assembly. Here is a map of the auditorium. Note that the students are seated by grade level and that the seats are numbered from 1 to 800.

a) Describe how to obtain a sample of 80 students using stratified random sampling. Explain your choice of strata and why this method might be preferred to simple random sampling.

b) Describe how to obtain a sample of 80 students using cluster sampling. Explain your choice of clusters and why this method might be preferred to simple random sampling.

Becausestudentslibraryusemightbesimilarwithingradelevelsbutdifferentacrossgradelevelsusethegradelevelsealingasstratafor9thgradegenerate20differentrandomintegersfromaoitosooandgivethesurveytothestudentsinthoseseatsDothesameforsophomoresjuniorsandseniorsusingtheircorrespondingseatnumbersStratificationbygradeshouldresultinmorepreciseestimates ofstudent opinionthanasimplerandomsample ofthesamesize

Eachcolumnofseatsfromthestagetothebackoftheauditoriumcouldbeusedas acluster because itwouldberelativelyeasytohandoutthesurveytoanentirecolumnLabelthecolumnsfrom1 to20startingattheleftsideofthestagegenerate 2differentintegersfrom 1to20 andgivethe surveytothesostudentssittinginthesetwocolumns Clustersampling is muchmoreefficientthanfindingsoseatsscatteredabouttheauditoriumas requiredby a simpleRandomSample

Statistics – Ch 4.1B Notes Name: _________________________ Sampling and Surveys

Independent Practice: A factory runs 24 hours a day, producing wood pencils on three 8-hour shifts – day, evening, and overnight. In the last stage of manufacturing, the pencils are packaged in boxes of 10 pencils each day. Each day a sample of 300 pencils is selected and inspected for quality.

a) Describe how to select a stratified random sample of 300 pencils. Explain your choice of strata

b) Describe how to select a cluster sample of 300 pencils. Explain your choice of clusters.

c) Explain a benefit of using a stratified random sample and a benefit of using a cluster sample in this context.

Inference for Sampling x The process of drawing conclusions about a population on the basis of sample data is called

________________.

Why should we rely on Random Sampling?

1. To avoid ________________ in selecting samples from the list of available individuals.

2. The laws of probability allow trustworthy inference about the population

• Results from random samples come with a __________________________that sets bounds

on the size of the likely error.

• ___________________ random samples give better information about the population than

smaller samples.

BecauseHequalityofpencilsmaybethesamewithineachshift butdifferacrossshiftsuseshiftsas strata Attheendofeach 8 hr shift labelallthepencilsproducedduringthatshiftfrom 1 to N where Nisthetotalnumber ofpencilsproduced on thatshift Generatetoorandomintegersfrom 1 to N oRandintCoolNtoo andselect

7thosepencilsforinspection skiprepeats

Theboxesofpencilscouldbeused as a cluster because it wouldbe relativelyeasytoselectboxes Attheendofthedaylabel allthe boxes ofpencils 1 toN where N is HenumberofboxesproducedthatdayGenerate 30differentrandomintegersfrom 1 toNandinspectallthepencilsinselectedboxesskiprepeats

stratified0Weare guaranteed to inspect 100 pencilsfromeach ofthe 3 shiftsThiswillleadto a more preciseestimateofoverallqualityifqualityis consistentwithineach shiftbutdiffersacrossthe 3 shifts

Cluster SimplifiesthesamplingprocessRatherthanhavingtolabeleverypencilproducedonlytheboxesof io pencilswouldneedtolabeled

inference

bias

Margin of error

Larger

Statistics – Ch 4.1B Notes Name: _________________________ Sampling and Surveys

Sampling Surveys: What Can Go Wrong?

Example Problem: What percent of Americans wash their hands after using the bathroom? It depends on how you collect the data. In a telephone survey of 1006 U.S. adults, 96% said they always wash their hands after using a public restroom. An observational study of 6028 adults in public restrooms told a different story: only 85% of those observed washed their hands after using the restroom. Explain why the results of the two studies are so different. Independent Practice: 1. Each of the following is a possible source of bias in a sample survey. Name the type of bias that

could result. a) The sample is chosen at random from a telephone directory.

b) Some people cannot be contacted in five calls.

c) Interviewers choose people walking by on the sidewalk to interview.

x _____________________________ occurs when some members of the population cannot be chosen in a

sample.

o A sample survey of households will miss not only homeless people but also prison inmates and

students in dormitories.

x _____________________________ occurs when an individual chosen for the sample can’t be contacted or

refuses to participate.

o Nonresponse can occur only after a sample has been selected. In a voluntary response sample,

every individual has opted to take part, so there won’t be any nonresponse.

x A systematic pattern of incorrect responses in a sample survey leads to ______________________________

x The _____________________________________ is the most important influence on the answers given to a

sample survey.

undercoverage

Nonresponse

response biaswording ofthequestion

ThetelephoneSurveyresulted in responsebiasbecausetherespondents

were moreinclined to lie on thephonetoavoidembarrassmentThismost

likelyoverestimates thetrueproportion

Undercoverage

Nonresponse

undercoverage

Statistics – Ch 4.1B Notes Name: _________________________ Sampling and Surveys

2. A survey paid for by makers of disposable diapers found that 84% of the sample opposed banning disposable diapers. Here is the actual question: “It is estimated that disposable diapers account for less than 2% of the trash in today’s landfills. In contrast, beverage containers, third-class mail, and yard wastes are estimated to account for about 21% of the trash in landfills. Given this, in your opinion, would it be fair to ban disposable diapers?” Do you think the estimate of 84% is less than, greater than, or about equal to the percent of all people in the population who oppose banning disposable diapers? Explain your reasoning.

By making it sound as if they are not a problemin thelandfill thisquestionwill resultin fewerpeoplesuggesting thatweshouldban disposablediapers TheProportionwho wouldsay yes toHis surveyquestion is