A company is interested in surveying their employees. There are 600 employees, and they list them out alphabetically. They would like to have exactly 30 participants in their survey. If they invoke systematic sampling, what is the probability of selecting a particular sample?

Question

BlackTom AI · Accepted Answer

We start by identifying the key parameters of systematic sampling in this scenario. The population size N is 600, and the sample size n is 30. The sampling interval k is N/n = 600/30 = 20, meaning we will select every 20th person after choosing a random starting position between 1 and 20.

Option 1: 0.002. This would correspond to a probability of 0.2%, which is far smaller than the probability of choosing any specific sample under systematic sampling with a fixed interval of 20. Since there are only 20 possible samples (one for each possible starting point from 1 to 20), the chance of landing on a particular one is not this tiny value.

Option 2: 0.050. This is 5% and aligns with the reasoning that there are 20 equally likely samples, each with probability 1/20 = 0.05. A single specific sample under this procedure would therefore have probability 0.05.

Option 3: <0.001. This would imply a probability less than 0.1%, which contradicts the fact that there are only 20 possible samples in this systematic design. The chance of selecting any one of those samples cannot be so small.

Option 4: 0.033. This equals 3.3%, which would be the probability if there were roughly 30 possible samples (1/30 ≈ 0.033). However, in systematic sampling with N = 600 and n = 30, the number of possible samples is 20, not 30, so this value is not correct.

In summary, systematic sampling with a fixed interval of 20 yields 20 equally likely samples, giving a probability of 1/20 = 0.05 for a particular sample. The option that matches this value is 0.050.

A company is interested in surveying their employees. There are 600 employees, and they list them out alphabetically. They would like to have exactly 30 participants in their survey. If they invoke systematic sampling, what is the probability of selecting a particular sample? 单项选择题

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