FRM Part I · FRM Exam Part I · Hypothesis Testing
A risk manager tests whether the mean daily P&L of a desk differs from zero using 400 observations. The sample mean is 0.08 (in $ thousand) and the known population standard deviation is 0.80 ($ thousand). What is the z statistic, and what is the approximate two-sided p-value conclusion at 5%?
The z statistic is 2.00, because the standard error is 0.80 divided by 20, or 0.04, and 0.08 divided by 0.04 equals 2. This exceeds the 5% two-sided critical value of 1.96, so the null of zero mean P&L is rejected.
- Az = 2.00; reject H0 at 5% (borderline, critical 1.96)Correct
- Bz = 0.10; fail to reject H0
- Cz = 2.00; fail to reject H0 because critical value is 2.58
- Dz = 1.00; fail to reject H0
Explanation
Standard error = 0.80/sqrt(400) = 0.04. z = 0.08/0.04 = 2.00, which exceeds 1.96, so reject at 5%. The 2.58 critical value applies to 1%, not 5%.
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 portfolio's return distribution is unknown, with mean 0 and standard deviation 4%. Using Chebyshev's inequality, what is the minimum proba…
- 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 tests H0: mu = 0 against H1: mu ≠ 0 for the mean daily excess return of a fund and obtains a two-sided p-value of 0.034. Which co…
- 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…
- A regulator applies a one-tailed test to a 99% VaR model, where too many exceptions indicate underestimated risk. Which statement about the …
- A bank backtests a 99% one-day VaR model over 250 trading days and observes 6 exceptions. Assuming exceptions are independent Bernoulli even…