# Question: A random sample tends not to be an exact replica

A random sample tends not to be an exact replica of its parent population. This fact has a number of implications. Indicate which are true and which are false.

(a) All possible random samples can include a few samples that are exact replicas of the population, but most samples aren’t exact replicas.

(b) A more representative sample can be obtained by handpicking (rather than randomly selecting) observations.

(c) Insofar as it misrepresents the parent population, a random sample can cause an erroneous generalization.

(d) In practice, the mean of a single random sample is evaluated relative to the variability of means for all possible random samples.

(a) All possible random samples can include a few samples that are exact replicas of the population, but most samples aren’t exact replicas.

(b) A more representative sample can be obtained by handpicking (rather than randomly selecting) observations.

(c) Insofar as it misrepresents the parent population, a random sample can cause an erroneous generalization.

(d) In practice, the mean of a single random sample is evaluated relative to the variability of means for all possible random samples.

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