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IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions

A statistician wants to estimate the mean monthly premium paid by all motor policyholders of an Indian insurer. She lists all 50,000 policyholders, numbers them, and uses a random number generator to select 400 policy numbers so that every possible set of 400 policies is equally likely. This sampling scheme is best described as:

This is simple random sampling without replacement, because every possible set of 400 policies from the numbered list of 50,000 is equally likely to be chosen. No strata, clusters, fixed intervals or quotas are used in the selection.

  1. ASimple random sampling without replacementCorrect
  2. BStratified sampling with proportional allocation
  3. CSystematic sampling with a random start
  4. DCluster sampling
  5. Quota sampling

Explanation

Every possible subset of 400 policies has the same chance of selection, which is the definition of simple random sampling without replacement. There are no strata, clusters or fixed intervals, and quota sampling is non-random.

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