FRM Part I · FRM Exam Part I · Hypothesis Testing
A researcher runs 20 independent tests of different trading signals, each at the 5% significance level, and all signals truly have no predictive power. What is the approximate probability of at least one false rejection (Type I error)?
About 64.2%. The chance of no false rejection across 20 independent tests is 0.95^20, roughly 35.8%, so the chance of at least one Type I error is about 64.2%. This illustrates multiple-testing risk.
- A5.0%
- B36.0%
- C64.2%Correct
- D95.0%
Explanation
P(no false rejection) = 0.95^20 ≈ 0.3585. So P(at least one) = 1 − 0.3585 ≈ 0.6415, about 64%. The 36% option is the probability of no false rejection, a missed complement.
Did you get it right without looking?
One question tells you little. A timed set on Hypothesis Testing shows your real accuracy, how long you take and where you lose marks.
More Hypothesis Testing questions
- A researcher tests H0: mu = 5 against H1: mu > 5 using a sample of 64 observations with a known population standard deviation of 4. The samp…
- A risk manager backtests a 95% one-day VaR over 500 days and records 35 exceptions. Using the normal approximation to the binomial, with a t…
- A fund manager claims the standard deviation of monthly returns is 4.0%. A sample of 21 monthly returns gives a sample standard deviation of…
- An analyst builds a 95% confidence interval for a mean using a sample of 25 observations from a normally distributed population with unknown…
- Holding the sample size and true parameter value fixed, a researcher lowers the significance level of a two-sided z-test from 5% to 1%. Whic…
- An analyst tests whether the mean daily return of a fund differs from zero. She sets H0: mu = 0 against H1: mu != 0 and chooses a 5% signifi…