The 10% condition is used in statistics to determine whether it is appropriate to use probability sampling without replacement. The condition states that the sample size should be no more than 10% of the population size to ensure that the sample does not significantly affect the overall population.
Let's evaluate each scenario:
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A sample of 40 to represent the number of people on a bus: This does not specify the population size of people on the bus, so we cannot determine if the 10% condition applies.
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A population of 1,200 and a sample of 600: The sample size (600) is 50% of the population (1,200), which exceeds the 10% condition. Therefore, the 10% condition does not apply.
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A sample of 10 to represent the number of students in a classroom: Again, this does not specify the population size of students in the classroom, so we cannot determine whether the 10% condition applies.
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A population of 2,000 and a sample of 100: The sample size (100) is 5% of the population (2,000), which is within the 10% limit. Therefore, the 10% condition applies.
In summary, the scenario where the 10% condition applies is:
A population of 2,000 and a sample of 100.