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. \(N_{1}=6, \bar{X}_{1}=18.50, s_{1}=2.00, N_{2}=6, \bar{X}_{2}=19.00, s_{2}=2.50\)

b. \(\quad N_{1}=13, \bar{X}_{1}=36.23, s_{1}=4.17, N_{2}=13, \bar{X}_{2}=29.59, s_{2}=6.01\)

c. \(N_{1}=29, \bar{X}_{1}=7.80, s_{1}=1.25, N_{2}=29, \bar{X}_{2}=7.17, s_{2}=1.63\)

d. \(N_{1}=38, \bar{X}_{1}=21.14, s_{1}=4.38, N_{2}=38, \bar{X}_{2}=23.29, s_{2}=3.91\)