IAI Actuarial Core Principles · Actuarial Statistics · Confidence intervals and prediction intervals
A random sample of 25 observations from a normal distribution with unknown mean and known standard deviation 10 gives a sample mean of 52. What is the 95% confidence interval for the population mean? (Use z = 1.96.)
The 95% interval is (48.08, 55.92). The standard error is 10 divided by 5, which is 2, and the margin is 1.96 times 2, or 3.92, added to and subtracted from the sample mean of 52.
- A(48.08, 55.92)Correct
- B(42.20, 61.80)
- C(50.04, 53.96)
- D(46.12, 57.88)
- (47.00, 57.00)
Explanation
The standard error is 10/√25 = 2. The margin is 1.96 × 2 = 3.92, so the interval is 52 ± 3.92 = (48.08, 55.92). The interval (42.20, 61.80) uses a standard error of 10, which ignores the division by √n.
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