IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit
A sample of 200 policyholders from a large portfolio shows 56 who lapsed within a year. Test H0: p = 0.25 against H1: p ≠ 0.25 using the normal approximation. What is the value of the test statistic Z (to 2 decimal places)?
The test statistic is the difference between sample and hypothesised proportions divided by the standard error computed under H0.
- A1.31Correct
- B0.98
- C1.63
- D2.12
- 0.65
Explanation
Sample proportion = 56/200 = 0.28. Standard error under H0 = sqrt(0.25×0.75/200) = sqrt(0.0009375) = 0.030619. Z = (0.28−0.25)/0.030619 = 0.98. Wait: 0.03/0.030619 = 0.98, so the key must be 0.98.
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