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. Next, draw a conclusion about each confidence interval.

a. \(22,29,30,25,21,19,17\)

b. \(10,1,7,4,5,5,6,2\)

c. \(2.25,1.48,3.31,1.90,2.82,3.07,1.98,1.54,2.09,2.56,3.81\)

d. \(15,29,10,14,23,9,19,12,21,34,11,5,17,13,25\)