For each of the following sets of numbers, calculate a \(95 \%\) confidence interval for the mean \((\sigma\) 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. \(9,2,8,16,7,4,12\) (assume \(\sigma=5.00\) )

b. \(1.50, .75,3.22,1.25, .78\) (assume \(\sigma=.30\) )

c. \(116,123,97,108,112,101,119,104\) (assume \(\sigma=15\) )