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IAI Actuarial Core Principles · Actuarial Statistics · Purpose and function of data analysis

A pension fund wants to estimate average retirement age among its 50,000 members. It lists members by employer: 40,000 work for large firms and 10,000 for small firms. It plans to sample 500 members, with 400 drawn at random from large-firm members and 100 at random from small-firm members. Which statement is correct?

It is proportionate stratified sampling. The population is split into large-firm and small-firm strata and random samples are drawn from each at the same 1% fraction (400 of 40,000 and 100 of 10,000), unlike cluster sampling, which selects entire groups.

  1. AIt is simple random sampling, since selection within each group is random
  2. BIt is proportionate stratified sampling, with a sampling fraction of 1% in each stratumCorrect
  3. CIt is cluster sampling, since members are grouped by employer
  4. DIt is quota sampling, since numbers are fixed in advance
  5. It is systematic sampling with interval 100

Explanation

Members are divided into two strata and sampled randomly within each. Sampling fractions are 400/40,000 = 1% and 100/10,000 = 1%, so allocation is proportionate. Cluster sampling would select whole groups, and quota sampling would not use random selection within groups.

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