FRM Part I · FRM Exam Part I · Common Univariate Random Variables
A risk analyst has a sample of 16 independent daily returns assumed to be normally distributed. She builds a t-statistic for the sample mean using the sample standard deviation. How many degrees of freedom does the resulting Student's t distribution have?
The t-statistic has 15 degrees of freedom. With a sample of 16 observations, one degree of freedom is lost because the sample mean is estimated from the data when computing the sample standard deviation, giving n - 1 = 15.
- A14
- B15Correct
- C16
- D17
Explanation
The t-statistic for a mean uses the sample standard deviation, which costs one degree of freedom, so df = n - 1 = 16 - 1 = 15. Choosing 16 ignores the estimation of the mean; 14 subtracts twice.
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