Data set: ChiSq
a. Take a simple random sample of size n = 40 from the ChiSq data. Create a bootstrap distribution of the median by taking 1000 resamples (with replacement). Describe the shape of the boot-strap distribution and explain why bootstrap confidence intervals are unlikely to be reliable.
b. Take a second simple random sample of size n = 40 from the ChiSq data. Create a second boot-strap distribution of the median by taking 1000 resamples (with replacement). Describe the shape of the second bootstrap distribution. With a sample size of 40, why are bootstrap distributions of medians unlikely to be normal?
c. Bootstrap distributions for medians are unlikely to be normally distributed, and means tend to be influenced by outliers. The trimmed mean is a common measure of center that tends to better represent the average value with bootstrap methods. Trimmed means are calculated by first trimming the upper and lower values of the sample. For example, the 25% trimmed mean is the mean of the middle 50% of the sample data.
Take a simple random sample of size n = 40 from the ChiSq data. Create a bootstrap distribution of the 25% trimmed mean by taking 1000 resamples (with replacement). In other words, for each resample calculate the mean of the middle 20 observations (remove the smallest 10 and largest 10 values in each resample). Create a histogram of the 1000 trimmed means and describe the shape of this bootstrap distribution. Create a bootstrap t confidence interval and a bootstrap percentile confidence interval to estimate the 25% trimmed mean.