A History Teacher Believes That Students in an Afternoon Class

Essay

A history teacher believes that students in an afternoon class score higher than the students in a morning class. The results of a special exam are shown below. Can the teacher conclude that the afternoon students have a higher score? Use α=0.01 .
$\begin{array} { l r l } \mathrm { n } _ { 1 } = 36 && \mathrm { n } _ { 2 } = 41 \\\overline { \mathrm { x } } 1 = 78 && \overline { \mathrm { x } } 2 = 81 \\\mathrm {~s} 1 = 5.8 && \mathrm {~s} _ { 2 } = 6.3\end{array}$