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

A 2×3 contingency table has row totals 60 and 40, column totals 30, 50 and 20, and a grand total of 100. Under the null hypothesis of independence, what is the expected frequency in the cell for the first row and second column?

The expected count is 30. Under independence, the expected frequency in a cell equals the row total times the column total divided by the grand total, so 60 times 50 divided by 100 gives 30.

  1. A20
  2. B25
  3. C30Correct
  4. D33
  5. 15

Explanation

Expected frequency = row total × column total / grand total = 60 × 50 / 100 = 30. The value 20 comes from using the third column total (60×20/100 = 12) or other mix-ups; 25 uses 50% of the grand total of 50 for columns without the row proportion. 15 is 30×0.5 and has no basis.

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