Example $8.$ An assembly operation requires approximately a one$-$month training period for a

new employee to reach maximum efficiency. Two groups of nine employees were trained for

a period of three weeks, one group using the new training method, the other group using the

old training method. The length of time required for each employee to assemble the device

was recorded at the end of the three$-$week period. Does the data present significant

evidence to suggest that the mean time to assemble at the end of the week is less for the

new training procedure? Assume equal population variances.