Refer to the data set pit.csv.

a. Generate 1000 bootstrap samples from the pit depths at four weeks and 75\% humidity. Find the 2.5 and 97.5 percentiles.

b. Compute a \(95 \%\) bootstrap confidence interval for the mean, using method 1 as described on page 395 .

c. Compute a \(95 \%\) bootstrap confidence interval for the mean, using method 2 as described on page 395 .

Pit Data Set:

In an experiment to measure corrosion in stainless steel, several pieces of stainless steel were exposed to salt particles for various lengths of time, at relative humidities of \(40 \%\) and \(75 \%\). The exposure caused pits to form. After exposure, the depths of the pits were measured, and those greater than \(10 \mu \mathrm{m}\) were reported.
Each row of the data set represents one pit. Variables are the depth of the pit, the duration of exposure, and the relative humidity. Following is a list of the variables in this data set:

Duration Duration of exposure (in weeks) Humidity (in %) Humidity Depth Depth of pit (in m)