2. Statistical Methods

Hypothesis Testing — Quiz

Test your understanding of hypothesis testing with 5 practice questions.

Practice Questions

Question 1

In the context of actuarial science, when validating a new mortality model, what is the primary concern regarding Type II errors?

Question 2

Which of the following statements about the relationship between the significance level ($\alpha$) and the power of a test is generally true?

Question 3

An actuary is comparing the average number of claims per year for two different types of insurance policies. The null hypothesis ($H_0$) is that there is no difference in the average number of claims. The alternative hypothesis ($H_1$) is that the average number of claims for Policy A is greater than for Policy B. If the calculated test statistic is $1.95$ and the critical value for a $0.05$ significance level is $1.645$, what is the appropriate conclusion?

Question 4

What is the primary factor that distinguishes a one-tailed test from a two-tailed test in hypothesis testing?

Question 5

An actuary is testing a new investment strategy. The null hypothesis ($H_0$) is that the average annual return is $8\%$ ($\mu = 0.08$). The alternative hypothesis ($H_1$) is that the average annual return is greater than $8\%$ ($\mu > 0.08$). A sample of $50$ annual returns yields a sample mean of $\bar{x} = 0.085$ and a sample standard deviation of $s = 0.02$. Calculate the t-statistic for this hypothesis test.