A pit is considered "deep" if its depth is greater than \(30 \mu \mathrm{m}\). For each of the following durations, find a confidence interval of the specified level for the difference between the proportion of pits that are deep at \(40 \%\) relative humidity and the proportion of pits that are deep at \(75 \%\) relative humidity.

a. Four weeks, \(95 \%\) confidence

b. 26 weeks, \(90 \%\) confidence

c. 52 weeks, \(99 \%\) confidence