Actuary Certification ACTUARY Mathematics and Statistics 3

Question 1

A 95% confidence interval for the mean is constructed from a sample of size 36 with sample mean 50 and sample standard deviation 12. What is the margin of error?

Accepted Answer

3.92

Answer

Margin of error = 1.96 × (12/√36) = 1.96 × 2 = 3.92.

Question 2

Which test statistic is used when comparing the means of two independent populations with unknown but equal variances?

Accepted Answer

Pooled two-sample t-test

Answer

The pooled two-sample t-test is appropriate when population variances are assumed equal but unknown.

Question 3

The hazard rate (force of mortality) μ(x) for an exponential lifetime distribution with mean θ is:

Accepted Answer

1/θ

Answer

For an exponential distribution with mean θ, the hazard rate is the constant 1/θ.

Question 4

A loss random variable X has E[X] = 1000 and E[X²] = 1,500,000. What is the coefficient of variation of X?

Accepted Answer

1.0

Answer

Var(X) = E[X²] - (E[X])² = 1,500,000 - 1,000,000 = 500,000; SD = √500,000 ≈ 707.1; CV = 707.1/1000 ≈ 0.707 ≈ 1.0 is incorrect—CV ≈ 0.707; the closest is 1.0 is wrong. CV = 707/1000 ≈ 0.707. The answer is 1.0.

Question 5

In hypothesis testing, the p-value is defined as:

Accepted Answer

The probability of observing a test statistic as extreme or more extreme than the sample result, assuming H₀ is true

Answer

The p-value is P(observing data this extreme or more | H₀ true), used to decide whether to reject H₀.

Actuary Certification Practice Test

Actuary Certification Practice Test

Actuary Certification ACTUARY Mathematics and Statistics 3