Questions: Explain the difference between a simple random sample and a systematic sample. (Select all that apply.) In a systematic sample, the only samples possible are those including every kth item from the random starting position. In a simple random sample, every sample of size n has an equal chance of being included.

Explain the difference between a simple random sample and a systematic sample. (Select all that apply.)
In a systematic sample, the only samples possible are those including every kth item from the random starting position.
In a simple random sample, every sample of size n has an equal chance of being included.

Transcript text: Explain the difference between a simple random sample and a systematic sample. (Select all that apply.) In a systematic sample, the only samples possible are those including every kth item from the random starting position. In a simple random sample, every sample of size $n$ has an equal chance of being included.

Solution

Solution Steps

Step 1: Understanding Simple Random Sample

A simple random sample is a sampling method where every possible sample of size $ n $ from the population has an equal probability of being selected. This means that each individual in the population has the same chance of being included in the sample, and the selection of one individual does not influence the selection of another.

Step 2: Understanding Systematic Sample

A systematic sample involves selecting every $ k $-th item from a list after a random starting point. The value of $ k $ is determined by dividing the population size by the desired sample size. This method ensures that the sample is spread evenly across the population, but it does not guarantee that every possible sample of size $ n $ has an equal chance of being selected.

Step 3: Comparing the Two Methods

The key difference between a simple random sample and a systematic sample lies in the selection process. In a simple random sample, every possible combination of $ n $ individuals has an equal chance of being selected. In contrast, a systematic sample only includes samples that consist of every $ k $-th item from a random starting position, which limits the possible samples that can be chosen.

Final Answer

In a systematic sample, the only samples possible are those including every $ k $-th item from the random starting position.
In a simple random sample, every sample of size $ n $ has an equal chance of being included.

\$\boxed{\text{Both statements are correct.}}\$

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

Next >

Thank you for your feedback.

Copied!