CFA Level I · CFA Level I Exam · Estimation and Hypothesis Testing
An analyst wants to estimate the standard error of the sample median of monthly fund returns, for which no simple closed-form formula is convenient. Which approach is most appropriate?
The bootstrap is most appropriate. It repeatedly draws samples with replacement from the observed data and computes the median for each, and the standard deviation of those medians estimates the standard error. The s divided by root n formula is only valid for the sample mean.
- AUse the sample standard deviation divided by the square root of n
- BApply the central limit theorem to the median directly
- CDraw repeated samples with replacement from the observed data and compute the median of eachCorrect
Explanation
Bootstrap resampling draws many samples with replacement from the observed data and computes the statistic each time, so the spread of the resulting medians estimates the standard error. The formula s/sqrt(n) applies to the sample mean, not the median.
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.
More Estimation and Hypothesis Testing questions
- A researcher tests H0: μ = 0 against Ha: μ ≠ 0 at the 5% significance level and obtains a p-value of 0.03. The researcher's conclusion is mo…
- An analyst bootstraps the mean of a sample of returns using 5 resamples and obtains means of 2.0%, 3.0%, 4.0%, 5.0% and 6.0%. Using these re…
- Which of the following is the most likely advantage of using bootstrap resampling to construct a confidence interval for a statistic?
- Holding the sample and the test statistic constant, a researcher lowers the significance level of a test from 5% to 1%. The change will most…
- A jackknife procedure is applied to a sample of 20 observations to estimate the variability of a statistic. The number of resampled data set…
- An analyst wants to raise the confidence level of an interval for a population mean from 90% to 99% without changing the sample. The interva…