LHS AP STATISTICS



AP Statistics Unit 4.1 Day 1Name: ____________________Notes: 4.1 Sampling DesignDate: ____________ Per: ____Surveys, Opinion polls, interviews, studies, experimentsHow do we gather data?CensusPopulation__________________ - the entire group of individuals that we want information about__________________ - a complete count of the populationList of everySampling frameSampling framemethodSampling designgeneralizeSampleNot very accurateHow good is a census? Frog Fairy TaleNot accurate, very expensive, perhaps impossible, if using destructive sampling,you would destroy populationWhy would we not use a census all the time?_________________ – A part of the population that we actually examine in order to gather information. We use a sample to _________________________ about the population.___________________ – refers to the ______________ used to choose the sample from the population.___________________ – a _______________________individual in the populationJelly Blubber ActivityWe have recently discovered a colony of jelly blubbers, a new marine species, and that our task is to try to determine the average length (measured horizontally) of a blubber. Since we cannot measure all jelly blubbers (the population), we will sample from the population of jelly blubbers.Horizontal lengthThe set of jelly blubbers that we actually examineJelly Blubber ColonyPopulation:Sample:Parameter of Interest:How shall we sample? Which sampling method is best? Let’s investigate the following sampling techniques. You will record the class results from each sampling technique here.Convenience Sample – First we will select jelly blubbers that are convenient to sample. Select 5 Jelly Blubbers that are convenient to sample. Record the blubbers you selected in the chart below under Blubber #. Record the lengths of your five Blubbers.Calculate the mean of your 5 samples, and record the mean in the table below and on the class dot plot. Sketch the class results on p3.Blubber #Lengthx=________Just pick out 100 students that are close to you and easy to get info fromExample: How can we choose 100 LHS students from the entire school (the population) using convenience sampling?(2) Simple Random Sample – Next we will randomly select 10 jelly blubbers from the population. Use the calculator (directions below) to find five random numbers between 1 & 100. Record the random numbers in the chart below under Blubber #. Locate the corresponding Jelly Blubbers in the Appendix and record their lengths.Calculate the mean of your 5 samples, and record the mean in the table below and on the class dot plot. Sketch the class results on p3.Using the calculator to find 5 random numbers: (1) Reseed the random number generator in the calculator: type <6 digit bday> STO> MATH PRB 1:RAND ENTER(2) Generate a random integer between 1 and 10: MATH PRB 5:RANDINT RANDINT(1,100) ENTERBlubber #Length (3) Repeat by pressing ENTER, until you get 10 random numbers – no repeats allowed.x=________Simple Random Sample (SRS)- consists of n individuals from the population chosen in such a way that every individual has an equal chance of being selected and every set of n individuals has an equal chance of being selectedAssign consecutive numbers from 1 to n(population number). Use the random number generator on calculator randintnorepeat(1, n) and write down the first 100 numbers and correlated names.Example: How can we choose 100 LHS students from the entire school (the population) using simple random sampling?Probably notpossible Every set every____________ student has the same chance to be selected AND _____________________________ of 100 students has the same chance to be selected! Therefore, it has to be ________________ for all 100 students to be seniors in order for it to be an SRS! Is that good?*Note that “names in a hat” is a College Board accepted way to describe taking an SRS!*(3) Stratified Random Sample – Now let’s try a different sampling technique where we first divide the Jelly Blubbers into 5 strata based upon their size. Use the calculator (directions below) to find 2 random numbers for each strata.Record these random numbers in the chart below under Blubber # for strata. Locate the corresponding Jelly Blubbers from the Appendix and record their lengths.Calculate the mean over all 5 jelly blubbers, and record the mean in the table below and on the class dot plot. Sketch the class results on p3.Using the calculator to find 2 random numbers within each strata: (1) No need to reseed the calculator (only needs to be done when the calculator is reset). (2) Generate a random integer between 1 and 19 for the first strata: RANDINT(1,19) (3) Repeat by pressing ENTER, until you get 1 random numbers – no repeats allowed.Strata12345Blubber #Length (4) Do this for each strata using RANDINT(1,<ending number>).x=________Stratified random sample - population is divided into homogeneous groups called strata, then SRS’s are pulled from each strata.Homogeneous groups are groups that are ______________ based upon some characteristic of the group members.Divide the population into freshman, sophomores, jrs and srs, then random sample 25 from each class.Example: How can we choose 100 LHS students from the entire school (the population) using stratified random sampling?(4) Systematic Sample – Now let’s try a 4th sampling technique, where this time we will use a system to select the sample. Use the calculator to find just one random number between 1&20. Record this number in the chart below as your first Blubber #. Then add 20 to each previous number to find the other four Blubber #’s and record these Blubber #’s in the chart below.Locate the corresponding Jelly Blubbers from the Appendix and record their lengths.Calculate the mean over all 5 jelly blubbers, and record the mean in the table below and on the class dot plot. Sketch the class results on p3.Blubber #Lengthx=________Systematic random sample- select sample by following a systematic approach (e.g. every 50th), after randomly selecting where to beginExample: How can we choose 100 LHS students from the entire school (the population) using systematic random sampling?We could assign consecutive numbers to every student, then take population # divided by 5. Use calculator to get random integer from 1 to the number calculated, then add the calculated to the random number and then continue to add this number so that you have all of numbers for the sample(5) Cluster Sample - The population of jelly blubbers exist in 20 different families (clusters) with 5 members in each family. We will choose 1 family to represent the population. Use the calculator to find just one random number between 1&20. This number will represent the family we will use. Record this Cluster #’s in the chart below.From the Appendix, locate the five Jelly Blubbers for each family, record the Blubber #’s, and record their lengths.Calculate the mean over all 5 jelly blubbers, and record the mean in the table below and on the class dot plot. Sketch the class results on p3.Cluster #Blubber #Lengthx=________Cluster sample - based upon location; randomly pick a location, then sample ALL in that locationExample: How can we choose 100 LHS students from the entire school (the population) using cluster sampling?And now for the real answer… what was the actual mean size for Jelly Blubber colony (the population mean)? ____________Now go back to page 3. Mark the population mean on the dotplots. What can you conclude? Mean Length of Jelly Blubbers (n=10) for Different Sampling TechniquesConvenience-6540597699SRS-32385267335Stratified15240267970Systematic52705244475Cluster-26035271780Randomization reduces bias and that stratification reduces variation.Identify the sampling designIn each survey, answer the following questions: What is the sampling design being used?What is the population of interest in this survey?What is the sample in this survey?What is the parameter of interest in this survey?1) The Educational Testing Service (ETS) needed a sample of colleges. ETS first divided all colleges into groups of similar types (small public, small private, etc.) Then they randomly selected 3 colleges from each group.a)b)c)d)2) A county commissioner wants to survey people in her district to determine their opinions on a particular law up for adoption. She decides to randomly select blocks in her district and then survey all who live on those blocks.a)b)c)d)3) A local restaurant manager wants to survey customers about the service they receive. Each night the manager randomly chooses a number between 1 & 10. He then gives a survey to that customer and to every 10th customer after that, to fill out before they leave.a)b)c)d)Finding random numbers without a calculator_______________________ – each entry is equally likely to be any of the 10 digits; digits are independent of each other.The following table is part of the random digit table. 14518 05137 12015 5801570389 93435 06305 13712Numbers can be read across - the random numbers generated would be:Numbers can be read down - the random numbers generated would be:Numbers can be read diagonally - the random numbers generated would be:This is similar to using the calculator to generate random numbers. You must know how to use TABLES to generate random numbers for the AP Test!!!!Aidan11) KathyBob12) LouChico13) MatthewDoug14) NanEdward15) OpusFred16) PaulGloria17) ShawnieHannah18) TracyIsrael19) Uncle SamJung20) VernonRandom Digit Activity - Suppose your population consisted of these 20 people:Use the following random digits to select a sample of five from these people.45180 51371 01558 0157089934 35063 06305 13712Define procedure:My final sample is: AdvantagesDisadvantagesSimple Random Sample (SRS)unbiasedeasy large variancemay not be representativemust have sampling frame (list of population), i.e. must know populationStratified random samplemore precise unbiased estimator than SRSless variabilitycost reduced if strata already existsdifficult to do if you must divide stratumformulas for SD & confidence intervals are more complicatedneed sampling frame, i.e. must know populationSystematic random sampleunbiaseddon’t need sampling frame, i.e. don’t need to know populationensures that the sample is spread across populationmore efficient, cheaper, etc.large variancecan be confounded by trend or cycleformulas are complicatedCluster sample unbiasedcost is reducedsampling frame may not be available (not needed, i.e. don’t need to know population) clusters may not be representative of populationformulas are complicated ................
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