If a confidence interval has been correctly constructed, then it should contain the true value of the parameter 95% of the time. In this problem, you will conduct a simulation to study the confidence interval coverage properties of the bootstrap. Note that both the sample mean and sample median are estimators of the population mean for the normal distribution. a. Generate data sets from a normal distribution. Use the boot.ci function to obtain 95% confidence intervals for the population mean, using the sample mean as the estimator. Determine the proportion of 95% bootstrap confidence intervals that contain the true parameter value. Consider Compare to the performance of the confidence interval based on the normal distribution. Determine what happens as you vary sample size and the number of bootstrap replicates. Discuss. b. Repeat a, but instead use the sample median as the estimator for the population mean.