A Statistics Teacher Believes That Students in an Evening Statistics $\alpha = 0.01$

Essay

A statistics teacher believes that students in an evening statistics class score higher than the students in a day
class. The results of a special exam are shown below. Assume the two samples are random and independent.
Can the teacher conclude that the evening students have a higher score? Use $\alpha = 0.01$ $$\begin{array} { l l } \text {Day Students}&\text {Evening Students}\\\mathrm { n } _ { 1 } = 36 & \mathrm { n } _ { 2 } = 41 \\\overline { \mathrm { x } } 1 = 75 & \overline { \mathrm { x } } 2 = 78 \\\mathrm {~s} _ { 1 } = 5.8 & \mathrm {~s} _ { 2 } = 6.3\end{array}$$