Answers:
- cluster sampling
- stratified sampling
- simple random sampling
- simple random sampling
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Explanation:
Problem 1
Cluster sampling is where we break a population into non-overlapping subsets. Each sub-group is known as a cluster. The clusters may or may not be the same size. We then randomly select as many clusters as needed. The drawback with this method is that some clusters are unfortunately left out. In this case, each state is a different cluster. Often when it comes to problems dealing with geography like this, cluster sampling is used (though not always). Once the clusters are selected, everyone in those clusters are surveyed. As you can see, this might be a monumental task if the clusters are quite large.
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Problem 2
The big issue with cluster sampling is that some clusters are left out. To fix this issue, stratified sampling breaks the population into non-overlapping groups, but this time members from each subgroup are sampled. Each group is known as a strata in this case, and we use stratified sampling. Keep in mind that not everyone is surveyed; rather, only a portion from each group is sampled. If you wanted to survey everyone, then you'd conduct a census. This term is not simply about counting people of an entire country. The term "census" is a population wide survey. Because a census is often very expensive, this is why statistics is important.
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Problem 3
The process of rolling a die is inherently random. There's no way to know the outcome on any given roll unless you somehow rigged the die (but at that point, the die is no longer random). Therefore, this process is simple random sampling.
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Problem 4
Like with problem 3, this process is also simple random sampling. Each name is randomly selected from the hat. There needs to be a fair number of names in the hat for the probabilities to remain roughly the same for each new selection. It's probably better to use computer software to make the process more fair/faster/efficient.
