Refer to the data set pit.csv.

a. Consider pits at 4 weeks duration. Perform a randomization test to determine whether the mean depth at \(40 \%\) relative humidity differs from that at \(70 \%\) relative humidity.

b. Repeat for pits at 26 weeks duration.

c. Repeat for pits at 52 weeks duration.

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:

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