Skip to content

CFA Level I · CFA Level I Exam · Estimation and Hypothesis Testing

A portfolio manager claims the standard deviation of a fund's annual returns is 10%. A sample of 25 annual returns, drawn from a normal population, has a sample standard deviation of 13%. The chi-square test statistic for testing the null hypothesis that the population variance equals 0.01 is closest to:

The statistic is about 40.6. It equals (n minus 1) times the sample variance divided by the hypothesized variance: 24 times 0.0169 divided by 0.01 equals 40.56, with 24 degrees of freedom.

  1. A30.5
  2. B40.6Correct
  3. C42.3

Explanation

Chi-square = (n-1)s²/σ0² = 24 × 0.0169 / 0.01 = 40.56, about 40.6. Using standard deviations without squaring (24×13/10 = 31.2) gives a wrong value, and using n instead of n-1 gives 42.25.

Did you get it right without looking?

One question tells you little. A timed set on Estimation and Hypothesis Testing shows your real accuracy, how long you take and where you lose marks.

Practise Estimation and Hypothesis TestingFree diagnostic mock

More Estimation and Hypothesis Testing questions