Refer to the data set pit.csv. Pits with depths greater than \(30 \mu \mathrm{m}\) are considered "deep." Find a confidence interval of the specified level for the proportion of pits that are deep for each of the following durations and humidity levels.

a. Four weeks at \(40 \%\) relative humidity, \(95 \%\) confidence

b. Four weeks at \(75 \%\) relative humidity, \(95 \%\) confidence

c. Twenty-six weeks at \(40 \%\) relative humidity, \(90 \%\) confidence

d. Twenty-six weeks at \(75 \%\) relative humidity, \(90 \%\) confidence

e. Fifty-two weeks at \(40 \%\) relative humidity, \(99 \%\) confidence

f. Fifty-two weeks at 75\% relative humidity, 99\% confidence

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:

Transcribed Image Text:

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