IAI Actuarial Core Principles · Actuarial Statistics · Confidence intervals and prediction intervals
A sample of 9 claim amounts (in thousands of rupees) from a normal distribution has sample mean 50 and sample variance 36 (divisor n-1). Given t(8) at the 97.5% point is 2.306, what is the 95% confidence interval for the mean?
The interval is (45.39, 54.61). The sample standard deviation is 6, the standard error is 6 divided by 3, which is 2, and the t margin is 2.306 times 2, about 4.61, around the mean of 50.
- A(45.39, 54.61)Correct
- B(43.07, 56.93)
- C(46.08, 53.92)
- D(38.46, 61.54)
- (46.13, 53.87)
Explanation
s = 6, standard error = 6/3 = 2. Margin = 2.306 x 2 = 4.612, so the interval is (45.39, 54.61). Option (43.07, 56.93) uses s/sqrt(n) times 2.306 with s=6 not divided by 3 wrongly halved... in fact it uses a standard error of 3 (dividing by sqrt 4). The others use incorrect standard errors.
Did you get it right without looking?
One question tells you little. A timed set on Confidence intervals and prediction intervals shows your real accuracy, how long you take and where you lose marks.
More Confidence intervals and prediction intervals questions
- A random sample of 100 motor claims from a Chennai insurer has sample mean ₹24,000 and sample standard deviation ₹5,000. The claim distribut…
- Two branches of an Indian life insurer sample policy renewals. Branch A: 150 of 200 renewed. Branch B: 120 of 200 renewed. Using the normal …
- A random sample of 25 claim sizes (in Rs thousand) from a normal distribution has sample mean 120 and sample standard deviation 10. Using t(…
- For a sample of n from a normal distribution with unknown mean and variance, which statement about the 95% confidence interval for μ based o…
- A 95% confidence interval for a normal mean with known variance has width 6 using a sample of size 36. Keeping the same confidence level and…
- X1,...,Xn are independent N(mu, sigma^2) with both parameters unknown. Which of the following is a pivotal quantity for mu that can be used …