For each of the following, calculate the standard error of the difference (left(s_{bar{X}_{1}-bar{X}_{2}} ight)) and the (t)-test

For each of the following, calculate the standard error of the difference \(\left(s_{\bar{X}_{1}-\bar{X}_{2}}\right)\) and the \(t\)-test for independent means.

a. \(\quad N_{1}=11, \bar{X}_{1}=12.00, s_{1}=2.00, N_{2}=11, \bar{X}_{2}=10.00, s_{2}=3.00\)

b. \(N_{1}=21, \bar{X}_{1}=39.85, s_{1}=5.23, N_{2}=21, \bar{X}_{2}=44.16, s_{2}=4.60\)

c. \(N_{1}=33, \bar{X}_{1}=4.37, s_{1}=1.07, N_{2}=33, \bar{X}_{2}=4.92, s_{2}=.94\)

d. \(N_{1}=57, \bar{X}_{1}=53.98, s_{1}=6.96, N_{2}=57, \bar{X}_{2}=50.74, s_{2}=6.03\)