Laying fiber optic cable is expensive cable companies want...

Laying fiber-optic cable is expensive. Cable companies want to make sure that, if they extend their lines out to less dense suburban or rural areas, there will be sufficient demand and the work will be cost-effective. They decide to conduct a survey to determine the proportion of households in a rural subdivision that would buy the service. They select a sample of 5 blocks in the subdivision and survey each family that lives on those blocks. (a) What is the name for this kind of sampling method? (b) Suppose there are 65 blocks in the subdivision. Use technology or Table D to select 5 blocks to be sampled. Explain your method clearly.

Transcript

00:01 All right, statisticians and training.

00:03 It's time to conduct a survey.

00:06 Let's say we're interested in surveying households in a rural subdivision.

00:10 And that subdivision has 65 blocks, and imagine 10 houses are on each block, and we'd like to get 50 houses to survey to see if they would be interested in purchasing a new service.

00:21 That new service might be pest control or a lawn service or a cable company service.

00:27 So rural subdivisions, when being developed, it might be important for a developer to know what the homeowners would be willing to pay for.

00:39 So how should we go about sampling? well, you could do a simple random sample.

00:43 In a simple random sample, let's see, 65 times 10, there's 650 houses.

00:49 So you'd have to randomly sample 50 the houses by choosing 50 random numbers from 1 to 650.

00:55 Well, you can imagine that that would be kind of challenging to go to 50 different houses across 65 different blocks.

01:06 So i think simple random samples is a little bit too complicated.

01:11 So in a stratified sample, you could perhaps say, well, there's 65 blocks.

01:16 So i could just take the numbers 1 to 65 and pick 10 of them out at random.

01:24 And once i have 10 blocks picked out, i could randomly sample houses on those blocks.

01:32 So still, even though i've reduced myself to a handful of blocks, i still have to randomly go to the selected houses on those randomly selected blocks.

01:42 So stratification, i think, still is somewhat complicated.

01:46 Well, now, cluster sampling.

01:48 Because these 65 blocks don't have a whole heck of a lot of difference in them, and the 10 houses, you know in a subdivision per block they're not they're not very different so to simplify matters we could simply number the blocks from one to 65 choose five blocks at random from the 65 blocks and survey all ten houses on each block so that makes the sampling process for this survey relatively straightforward to carry out.

02:39 So the difference between stratification and clustering is in stratification, you still kind of feel there's a block -to -block difference.

02:47 So you want to randomly sample the blocks.

02:50 And once you have the blocks randomly sample, you still want to randomly sample the houses on each block.

02:57 So you've created the blocks and then randomly sampled the houses.

03:02 Well in cluster sampling, because we believe the blocks are fairly uniform, we'd rather just choose the blocks at random and go to every house on the block...

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