IAI Actuarial Core Principles · Actuarial Statistics · Confidence intervals and prediction intervals
A random sample of 16 policy settlement times (in days) from a normal population with known standard deviation 4 days has sample mean 20 days. Using z = 1.96, what is the 95% confidence interval for the population mean?
The interval is (18.04, 21.96). With known sigma of 4 and n of 16, the standard error is 1, and the 95% margin is 1.96 times 1, which is added to and subtracted from the sample mean of 20.
- A(18.04, 21.96)Correct
- B(17.55, 22.45)
- C(19.02, 20.98)
- D(16.08, 23.92)
- (18.37, 21.63)
Explanation
Standard error = 4/sqrt(16) = 1. Margin = 1.96 x 1 = 1.96, giving (18.04, 21.96). Option (19.02, 20.98) uses a margin of 0.98, which comes from dividing by 2 twice. Option (16.08, 23.92) forgets to divide by the square root of n.
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