For each of the following sets of numbers, calculate a \(95 \%\) confidence interval for the mean ( \(\sigma\) not known); before going through the steps in calculating the confidence interval, the sample mean \(\left(\mathrm{X}^{-}\right)\)and standard deviation \((s)\) must first be calculated.

a. \(12,11,16,9,14,10\)

b. \(3.50,2.25,3.30,4.75,2.60,4.00,3.80\)

c. \(24,31,28,26,19,33,22,17,25\)

d. \(7,4,13,8,6,10,9,5,17,10,7,12\)