CFA Level IQuantitative MethodsMedium
A researcher tests the null hypothesis that a fund's mean excess return equals zero, using a 5% significance level. The true mean excess return is actually not zero, but the test statistic fails to reject the null hypothesis. What type of error has occurred?
- ANo error; this is a correct decision
- BSampling error
- CType II error
- DType I error
Show answer & explanationAnswer & explanation
Correct answer: C. Type II error
A Type II error occurs when a false null hypothesis is not rejected. Since the true mean is actually nonzero (H0 is false) but the test failed to reject H0, this is a Type II error.
Why the other options are wrong
- A. An error did occur since the null is false but was not rejected.
- B. Sampling error refers to the difference between a sample statistic and the population parameter, not a hypothesis test outcome.
- D. Type I error is rejecting a true null hypothesis, the opposite situation.
Type II Error
A Type II error occurs when a hypothesis test fails to reject a null hypothesis that is actually false.
- Type I error: rejecting a true null (probability = significance level, alpha)
- Type II error: failing to reject a false null (probability = beta)
- Power of a test = 1 - beta = probability of correctly rejecting a false null
Memory trick: Type I cries wolf; Type II misses the wolf.