Skip to content

FRM Part I · FRM Exam Part I · Hypothesis Testing

A risk manager tests H0: mu ≤ 2.0 against H1: mu > 2.0 for the mean of a large sample (n = 100) with known population standard deviation 5.0. The sample mean is 3.1. Using a z-test at the 1% level (one-tailed critical z = 2.33), which outcome is correct, and what would happen with a two-tailed test at 1% (critical z = 2.576)?

The standard error is 5.0 divided by 10, or 0.50, so z = (3.1 − 2.0)/0.50 = 2.20. This is below both the one-tailed critical value of 2.33 and the two-tailed value of 2.576, so the null hypothesis is not rejected in either test.

  1. Az = 2.20; fail to reject in the one-tailed test and fail to reject in the two-tailed testCorrect
  2. Bz = 2.20; reject in the one-tailed test but fail to reject in the two-tailed test
  3. Cz = 2.20; reject in both tests
  4. Dz = 22.0; reject in both tests

Explanation

Standard error = 5.0/sqrt(100) = 0.50. z = (3.1 − 2.0)/0.50 = 2.20. This is below 2.33, so the one-tailed test does not reject, and it is below 2.576, so the two-tailed test does not reject either. z = 22.0 comes from forgetting to divide by the square root of n only partly (using 0.05).

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.

Practise Hypothesis TestingFree diagnostic mock

More Hypothesis Testing questions