Certain statistics are difficult to bootstrap. One such statistic is the median. Consider the following to see why.

(a) Simulate obtaining a random sample of 12 IQ scores. Recall IQ scores are approximately normally distributed with mean 100 and standard deviation 15 .

(b) Given that IQ scores are normally distributed, what is the median IQ score?

(c) Obtain 1000 bootstrap samples from the data in part (a). Find the median of each bootstrap sample.

(d) Draw a histogram of the bootstrap medians from part (c). What do you notice about the distribution? Find the \(95 \%\) confidence interval based on the 1000 bootstrap medians using the percentile method.

(e) Repeat parts (a) through (d) using a random sample of 13 IQ scores.

(f) Conclude that finding confidence intervals for medians is best if done where the sample size is even.