4
AssignmentMultiple Choice

Simple Random Sample

Question 4 • VA-Probability and Statistics

A doctor compiles a numbered list of all his 350 patients. He selects every 25th patient to receive a survey after choosing to randomly start with the seventh name on the list. Which statement correctly identifies and justifies whether the scenario represents an SRS?

Answer
A
This represents an SRS because the sample was selected with a chance process.
B
This represents an SRS because there were no restrictions placed on the sample group.
C
This does not represent an SRS because each individual chosen does not have an equally likely chance of being chosen.
D
This does not represent an SRS because each group of patients chosen does not have an equally likely chance of being chosen.

Explanation

A simple random sample (SRS) requires every possible group of 14 patients to have an equally likely chance of being selected. Here, the random start determines a systematic sample: the doctor chooses that starting position and then every 25th name. This allows only a small set of possible groups, so groups of patients are not equally likely to be chosen. The correct statement is that this does not represent an SRS because each group of patients chosen does not have an equally likely chance.

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