Statistics – Ch 4.1A Notes Name: _________________ Sampling and Surveys

Practice Problem Identify the population and the sample in each of the following settings.

1. A furniture maker buys hardwood in large batches. The supplier is supposed to dry the wood before shipping (wood that isn’t dry wont holds its size and shape). The furniture maker chooses five pieces of wood from each batch and tests their moisture content. If any piece exceeds 12% moisture content, the entire batch is sent back.

2. Each week, the Gallup Poll questions a sample of about 1500 adults U.S. residents to determine national opinion on a wide variety of issues.

The Idea of a Sample Survey

How to Sample Badly

Suppose we want to know how long students at Lipscomb University spent during homework last week. We go to the Library and ask the first 30 students we see about their homework time.

x Choosing individuals from the population who are easy to reach results in a

_______________________

x The design of a statistical study shows bias if it would consistently ______________________ or

consistently _________________________ the value you want to know.

x Bias is not just bad luck in one sample. It’s the result of a bad study that will consistently miss

the truth about the ________________________.

__________________ in a statistical study is the entire group of individuals we want information about.

A _________________ collects data from every individual in the population.

A __________________ is a subset of individuals in the population from which we actually collect data.

Step 1: Define the _______________________ we want to describe.

Step 2: Say exactly what we want to _________________________________.

A “sample survey” is a study that uses an organized plan to choose a sample that represents some specific

population.

Step 3: Decide how to choose a ________________________ from the population.

Choosing a Sample

KeyPopulationCensusSample

Population Allpiecesofhardwoodin abatchsample 5piecesofwoodthatareselectedfromthat

batch

andtested

Population All VSResidentsSample The1500adultswhoactually respondtothesurveyquestions

populationmeasure

Sample

ConvenienceSampleunderestimate

overestimate

population

Statistics – Ch 4.1A Notes Name: _________________ Sampling and Surveys

Tips for Determining Bias (2 things needed to describe bias)

1. Identify the problem with the ________________________________.

2. Explain how this problem would lead to an ___________________________________________.

Example: Explain how using your statistics class as a sample to estimate the proportion of all high school students who own a graphing calculator could result in bias.

How to Sample Badly

Practice Problem Former CNN commentator Lou Dobbs doesn’t like illegal immigration. One of his shows was largely devoted to attacking a proposal to offer driver’s licenses to illegal immigrants. During the show, Mr. Dobbs invited his viewers to go to loudobbs.com to vote on the question: “Would you be more or less likely to vote for a presidential candidate who supports giving driver’s licenses to illegal aliens?” The results: 97% of the 7350 people who voted who voted by the end of the show said “Less likely”. What type of sample did Mr. Dobbs use in his poll? Explain how this sampling method could lead to bias in the poll results. How to Sample Well: Simple Random Sampling x A sample chosen by chance rules out both favoritism by the sampler and self-selection by

respondents. x Random sampling involves using a chance process to determine which members of a population are

included in the sample.

A _____________________________ sample consists of people who choose themselves by responding

to a general invitation.

Voluntary response samples show bias because people with strong ______________________ (often in

the same direction) are most likely to respond.

A simple random sample (SRS) of size n is chosen in such a way that every group of n individuals in the

population has an equal _____________________ to be selected as the sample.

designunderestimate or overestimate

This is a conveniencesample thatwouldoverestimate theproportionofstudentswithgraphingcalculators because a calculatorisrequiredforthisclass

Voluntary Response

Opinions

VoluntaryResponseSample Thosewhovoted wereviewers ofMr Dobbs

programwhichmeansHneyare likelyto supporthis viewsThe 97 pollresultis probablyanextremeoverestimate

Chance

Statistics – Ch 4.1A Notes Name: _________________ Sampling and Surveys

Generating Random Numbers on the Calculator: ____________ Æ _____________ ÆRandInt( Practice Problem: Use Table D at line 130 to choose an SRS of 4 hotels.

Table D line 130: 69051 64817 87174 09517 84534 06489 87201 97245

Now find a new SRS by generating random numbers on your calculator.

Independent Practice: Each year, the state Department of Education randomly selects three schools from each district to conduct a detailed audit of their attendance records.

Amphitheater High Cross Middle Keeling Elementary Prince Elementary Amphitheater Middle Donaldson Elementary La Cima Middle Rio Vista Elementary Canyon del Oro High Harelson Elementary Mesa Verde Elementary Walker Elementary

Copper Creek Elementary Holaway Elementary Nash Elementary Wilson K-8 Coronado K-8 School Ironwood Ridge High Painted Sky Elementary

a) Describe how to use a table of random digits to select an SRS of three schools from this list of 19 schools.

b) Use the random digits here to choose the sample 62081 64816 87374 09517 84534 06489 87201 97245

Step 1: ____________. Give each individual in the population a distinct numerical label from 1 to N.

Step 2: ________________. Use a random number generator to obtain n different integers from 1 to N.

Choosing an SRS With Technology

01 Aloha Kai 08 Captiva 15 Palm Tree 22 Sea Shell 02 Anchor Down 09 Casa del Mar 16 Radisson 23 Silver Beach 03 Banana Bay 10 Coconuts 17 Ramada 24 Sunset Beach 04 Banyan Tree 11 Diplomat 18 Sandpiper 25 Tradewinds 05 Beach Castle 12 Holiday Inn 19 Sea Castle 26 Tropical Breeze 06 Best Western 13 Lime Tree 20 Sea Club 27 Tropical Shores 07 Cabana 14 Outrigger 21 Sea Grape 28 Veranda

LabelRandomize

MATH PRB smallestLargest ofintegers

I l I l I I l l l l l l l l l l l I Itoolarge skiprepeats

oursrsofaHotelsfortheeditorstocontactis1BeachcastleaRaddison3Ramada4seaclub

Randint 1 284 6n 22 Allsamplesmaydiffer

01 06 11 1602 07 12 1703 08 13 is04 09 14 1905 co 15

LabelHeschoolsfromolto19inalphabeticalorderMovealong a lineof randomdigitsfromleft torightreadingtwodigitsatatimeuntilthreedifferentnumbersfroma cahavebeenselectedSkiprepeatsandnumbersoutsidetherangefrom01 19

I l I l I l l l l l l l I l I l l I IHarlesonElementary PrinceElementary RioVistaElementary