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. \(4,7,3,6,2,5,2,4,3\) (assume \(\sigma=1.50\) )

b. \(43,34,48,31,39,32,45,40,46,37,42\) (assume \(\sigma=6.25\) )

c. \(18, .15, .20, .16, .14, .18, .22, .17, .26, .13, .15, .09, .23, .13\) (assume \(\sigma=.06\) )