IAI Actuarial Core Principles · Actuarial Statistics · Random sampling and sampling distributions
A sample of 16 claim amounts from a normal population has mean 50 and sample standard deviation 8 (divisor n-1). What is the t statistic for testing H0: μ = 47?
The t statistic is (50 − 47) divided by 8/√16 = 2, giving 1.5, with 15 degrees of freedom. The standard error uses the square root of the sample size.
- A1.5Correct
- B0.375
- C3.0
- D6.0
- 0.75
Explanation
t = (50-47)/(8/√16) = 3/2 = 1.5, with 15 degrees of freedom. Forgetting to divide by √n gives 0.375; using 8/16 gives 6.0.
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