IAI Actuarial Core Principles · Actuarial Statistics · Confidence intervals and prediction intervals
A random sample of n = 25 observations is taken from a normal distribution with unknown mean and known standard deviation 10. The sample mean is 52. What is the 95% confidence interval for the population mean? (Use z = 1.96.)
The interval is (48.08, 55.92). The standard error is 10 divided by 5, which is 2, and the margin of error 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(47.40, 56.60)
- C(50.04, 53.96)
- D(32.40, 71.60)
- (49.55, 54.45)
Explanation
Standard error = 10/sqrt(25) = 2. Margin = 1.96 x 2 = 3.92, so the interval is 52 +/- 3.92 = (48.08, 55.92). Using 10 instead of the standard error gives the very wide interval (32.40, 71.60). Using a margin of 1.96 x 2.5 or similar is wrong.
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