CFA Quantitative Methods & Statistics 3 — Questions and Answers
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?
- z = 1.645
- t₂₄ = 1.711 (Correct answer)
- z = 1.960
- t₂₄ = 2.064
Correct answer: t₂₄ = 1.711
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?
- The CLT applies only when the population is normally distributed
- For large n, the sampling distribution of the sample mean is approximately normal regardless of the population distribution (Correct answer)
- The CLT states that population variance equals sample variance for n > 30
- The CLT requires that observations be correlated
Correct answer: For large n, the sampling distribution of the sample mean is approximately normal regardless of the population distribution
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:
- 10.53% and 5.13% (Correct answer)
- 10.53% and 5.26%
- 10.53% and 10.53%
- 5.26% and 2.60%
Correct answer: 10.53% and 5.13%
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?
- Positive kurtosis (leptokurtic) indicates fatter tails and higher probability of extreme returns than a normal distribution (Correct answer)
- Negative kurtosis implies greater peak and thinner tails than a normal distribution
- Kurtosis only measures the degree of skewness in a distribution
- A normal distribution has a kurtosis of zero
Correct answer: Positive kurtosis (leptokurtic) indicates fatter tails and higher probability of extreme returns than a normal distribution
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:
- Rejects a true null hypothesis
- Fails to reject a false null hypothesis (Correct answer)
- Sets the significance level too high
- Uses a one-tailed test instead of a two-tailed test
Correct answer: Fails to reject a false null hypothesis
A Type II error (β) is failing to reject H₀ when H₀ is actually false, which is the missed detection of a real effect.
Question 6: An investment of $1,000 grows to $1,500 after 5 years. The compound annual growth rate (CAGR) is closest to:
- 8.45% (Correct answer)
- 10.00%
- 7.18%
- 9.13%
Correct answer: 8.45%
CAGR = (1500/1000)^(1/5) − 1 = 1.5^0.2 − 1 ≈ 8.45%.
Question 7: Which measure of central tendency is least affected by extreme outliers in a dataset?
- Arithmetic mean
- Weighted mean
- Median (Correct answer)
- Mode
Correct answer: Median
The median is based on rank order and therefore resistant to distortion by extreme values, unlike the arithmetic mean.
CFA Quantitative Methods & Statistics 3
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?