CFA Quantitative Methods & Statistics 3

Question 1

A sample of 25 observations yields a mean of 8% and a standard deviation of 4%. Assuming normality, the 90% confidence interval for the population mean uses which critical value?

Accepted Answer

t₂₄ = 1.711

Answer

With unknown population variance and n = 25, a t-distribution with 24 degrees of freedom is appropriate; the 90% two-tailed critical value is t₂₄ = 1.711.

Question 2

Which statement about the central limit theorem (CLT) is most accurate?

Accepted Answer

For large n, the sampling distribution of the sample mean is approximately normal regardless of the population distribution

Answer

The CLT states that as sample size increases, the distribution of the sample mean approaches normality regardless of the shape of the underlying population.

Question 3

An investor purchases a bond for $950 and sells it two years later for $1,050, receiving no coupons. The holding period return and annualized HPR are, respectively:

Accepted Answer

10.53% and 5.13%

Answer

HPR = (1050−950)/950 = 10.53%; annualized HPR = (1.1053)^(1/2) − 1 ≈ 5.13%.

Question 4

Which of the following best describes kurtosis in the context of return distributions relevant to risk management?

Accepted Answer

Positive kurtosis (leptokurtic) indicates fatter tails and higher probability of extreme returns than a normal distribution

Answer

Leptokurtic distributions (excess kurtosis > 0) have fatter tails than the normal, meaning extreme outcomes are more probable—a key concern in risk management.

Question 5

A Type II error in hypothesis testing occurs when an analyst:

Accepted Answer

Fails to reject a false null hypothesis

Answer

A Type II error (β) is failing to reject H₀ when H₀ is actually false, which is the missed detection of a real effect.

CFA Practice Test

CFA Practice Test

CFA Quantitative Methods & Statistics 3