IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit
Two branches of an Indian insurer record claims being rejected: Branch A 30 of 150 claims, Branch B 45 of 150 claims. Test H0: pA = pB against H1: pA ≠ pB using the pooled normal test. What is Z (to 2 decimal places, magnitude)?
Z equals 2.00 using the pooled proportion 0.25.
- A1.97Correct
- B2.45
- C1.73
- D2.00
- 1.50
Explanation
pA=0.2, pB=0.3, pooled p = 75/300 = 0.25. SE = sqrt(0.25×0.75×(2/150)) = sqrt(0.0025)=0.05. Z = 0.10/0.05 = 2.00. So the correct value is 2.00, not 1.97; the unpooled SE sqrt(0.16/150+0.21/150)=0.0497 gives 2.01.
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