Question 332694: Hello My name is Helen my book is statistical ideals my e-mail is sugar6@aol.com
i really need help with my homework this problem , i tried to figure it out but got it wrong . the question to this problem is concern how to collect a random sample of 800 airline passengers 100 particular flights leaving 200 passengers aboard each flight.
1. decribe how to draw the sample as a stratified random sample using 100 flights as the strats 2. ,,, draw the sample as a cluster randon sample using as the cluster 3. ,,,, draw the sample as a systematic sample from these flights
Answer by jrfrunner(365)   (Show Source):
You can put this solution on YOUR website! Stratified sampling
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You randomly sample from "each" strata (ie 100 flight). Each flight has 200 passenger out of a total of 100*200=20,000 so each strata makes up 200/20,000 =1/100 of the total. Therefore
sample from strata ith = total sample size *(prop strata is of total) = 800*(1/100) = 8 randomly selected from each strata
Keep in mind that if the strats had been different size, the proportions would be different and thus your sample make up from each strata would be different by this proportion
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Cluster sampling
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first randomly select a set of clusters then sample all the elements in the selected samples.
So in your case, since each cluster is made up of 200 passengers, you need 4 random clusters to make your 800 sample.
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Systematic sample
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there are 200*100=20,000 passengers, so you need to select every 20,000/800 =25th passenger.
You need to begin at a random point, so you would select a random number between 1 to 25,
Then proceed sequentially from flight to flight (assume that each passenger in a flight can be identified as passenger 1 to 200), then begin by selecting flight #1, start with the random number you selected between 1 to 25 (say it was 8) select the 8th passenger in flight #1, and sequentially select the next one as passenger 33 (8th + 25) and then passenger 58th (33rd +25) move from flight to flight finding the passengers that match the 8+25*n multiple, from the original random number + 25*n.
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each method has its applications, so some methods are more applicable than others.
Stratified sampling should be used when you suspect that the strata are hetergeneous (ie the "between" strata variation is very different but "within" strata variation is similar).
Cluster sampling should be used when you suspect that cluster are homogeneous
(ie the "between" cluster variation is very similar but "within" cluster variation is very different).
Systematic sampling should be used when you have easily available listings, but is generally not the best type of sampling.
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cost issues and administration complexities also play a role in making a choice of sampling.
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