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IAI Actuarial Core Principles · Actuarial Statistics · Confidence intervals and prediction intervals

Two large independent samples of policies give claim proportions: 120 claims out of 400 for scheme A and 90 out of 450 for scheme B. Using z = 1.96 and unpooled standard error, what is the 95% confidence interval for pA - pB?

The difference in proportions is 0.30 - 0.20 = 0.10. The unpooled standard error is sqrt(0.000525 + 0.000356) = 0.0297, giving a margin of 0.058. The interval is about (0.042, 0.158), closest to (0.040, 0.160).

  1. A(0.040, 0.160)
  2. B(0.030, 0.170)
  3. C(0.044, 0.156)Correct
  4. D(0.020, 0.180)
  5. (0.058, 0.142)

Explanation

pA = 0.30, pB = 0.20, difference 0.10. Var = 0.3x0.7/400 + 0.2x0.8/450 = 0.000525 + 0.000356 = 0.000881. SE = 0.02968. Margin = 1.96 x 0.02968 = 0.0582. Interval = (0.0418, 0.1582), closest to (0.044, 0.156) but option A (0.040, 0.160) is nearer; the correct computed limits are 0.042 and 0.158, so A matches best.

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