(Solution) - A researcher wants to select 1 of the 10 000 subjects -(2025 Original AI-Free Solution)

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A researcher wants to select 1% of the 10,000 subjects from the sampling frame. She selects subjects by picking one of the first 100 on the list at random, and then skipping 100 names to get the next subject, skipping another 100 names to get the next subject, and so on. This is called a systematic random sample.
a. With simple random sampling, (i) every subject is equally likely to be chosen, and (ii) every possible sample of size n is equally likely. Indicate which, if any, of (i) and (ii) are true for systematic random samples. Explain.
b. An assembly-line process in a manufacturing company is checked by using systematic random sampling to inspect 2% of the items. Explain how this sampling process would be implemented.