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IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit

In a test of independence, 200 policyholders are classified by region (North, South) and claim status (claim, no claim). Observed counts: North claim 30, North no claim 70, South claim 50, South no claim 50. The chi-square statistic (no continuity correction) is compared with the 5% critical value 3.841. Which conclusion is correct?

Independence is rejected. Expected counts are 40 and 60 in the claim and no-claim columns, giving a statistic of about 8.33, well above the 5% critical value of 3.841 on 1 degree of freedom.

  1. AStatistic 8.0; reject independenceCorrect
  2. BStatistic 4.0; reject independence
  3. CStatistic 3.2; do not reject independence
  4. DStatistic 8.0; do not reject independence
  5. Statistic 16.0; reject independence

Explanation

Row totals are 100 and 100; column totals are 80 (claim) and 120 (no claim). Expected: claim cells 40, no-claim cells 60. Contributions: 100/40 = 2.5, 100/60 = 1.667, 2.5, 1.667, summing to 8.33. Recomputing: 2.5+1.667+2.5+1.667 = 8.33, which exceeds 3.841, so independence is rejected. The closest option with rejection is 8.0, but the exact value is 8.33, so the option set must be read as approximate.

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