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

In a 2×2 table of 100 observations the chi-squared statistic for independence is calculated as 4.20. At the 5% significance level, which conclusion is correct? (The 5% critical value of chi-squared with 1 degree of freedom is 3.841.)

Reject independence. A 2 by 2 table has one degree of freedom, so the 5% critical value is 3.841, and the statistic of 4.20 exceeds it, giving evidence of association.

  1. AReject independence, since 4.20 exceeds 3.841Correct
  2. BDo not reject independence, since 4.20 is below 5.991
  3. CReject independence, since 4.20 exceeds 5.991
  4. DDo not reject independence, since 4.20 exceeds 3.841
  5. Test is invalid because the sample size is 100

Explanation

A 2×2 table has (2−1)(2−1)=1 degree of freedom, so the critical value is 3.841. Since 4.20 > 3.841 we reject independence. The value 5.991 is for 2 degrees of freedom and so is wrong here.

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