Question

what is the difference between a random sample and a simple random sample?

choose the correct answer below.

a. with a random sample, each individual has the same chance of being selected. with a simple random sample, all samples of the same size have the same chance of being selected.
b. with a random sample, all samples of the same size have the same chance of being selected. with a simple random sample, each individual has the same chance of being selected.

Explanation:

⚡ Using what you learned: Sampling Methods

Step 1: Define a Random Sample

A random sample is a sampling method where every individual member of the population has an equal (or known) chance of being selected. This focuses on the probability of selecting individual members.

Step 2: Define a Simple Random Sample (SRS)

A simple random sample of size \( n \) is a more restrictive type of sample. It requires not only that every individual has the same chance of being chosen, but also that every possible group/sample of size \( n \) has the exact same chance of being selected.

For example, if you select a sample by choosing entire pre-determined clusters (like classrooms), every individual student might have an equal chance of being selected, but certain combinations of students (samples) are impossible to form. In a simple random sample, every possible combination must be equally likely.

Step 3: Compare the Options

• Option A states: "With a random sample, each individual has the same chance of being selected. With a simple random sample, all samples of the same size have the same chance of being selected." This matches our definitions.
• Option B reverses these definitions incorrectly.

Answer:

A. With a random sample, each individual has the same chance of being selected. With a simple random sample, all samples of the same size have the same chance of being selected.