Introduction to Confidence Intervals: Videos & Practice Problems

A health researcher collected a random sample of $30$ nightly sleep durations (in hours) from a fitness tracking device. To estimate the population median sleep time, the researcher generated $1000$ bootstrap samples, each of size $30$, by sampling with replacement from the original data. The median sleep time was computed for each bootstrap sample. After sorting the $1000$ bootstrap medians, the researcher found the following percentile values:
${2.5}^{th}$ percentile: $6.25$ hours
${97.5}^{th}$ percentile: $8.15$ hours
The median of all $500$ nightly sleep durations stored in the tracker’s database is known to be $7.1$ hours. How well did the bootstrap method perform in capturing a good estimate of the population median?