Questions: Determine whether the statement is true or false. If it is false, rewrite it as a true statement. Using a systematic sample guarantees that members of each group within a population will be sampled. Choose the correct answer below. A. False. Using a cluster sample guarantees that members of each group within a population will be sampled. B. False. Using a stratified sample guarantees that members of each group within a population will be sampled. C. True.

Solution Steps

• The statement claims that using a systematic sample ensures that members of each group within a population will be sampled.

• Systematic sampling involves selecting every \( k \)-th member from a list of the population after a random start. It does not inherently ensure that each group within a population is represented.

• Stratified sampling is the method that guarantees members of each group within a population will be sampled. In stratified sampling, the population is divided into strata (groups), and random samples are taken from each stratum.

• Option A: False. Cluster sampling involves dividing the population into clusters and randomly selecting entire clusters, which does not guarantee representation of each group.
• Option B: False. Stratified sampling is the correct method that ensures representation of each group.
• Option C: True. This option incorrectly states that systematic sampling guarantees representation of each group.

• The statement is false. The correct answer is Option B: Using a stratified sample guarantees that members of each group within a population will be sampled.

Final Answer