In an Effort to Improve Productivity in Its Factory,a Firm

In an effort to improve productivity in its factory,a firm recently instituted a training program for its workers.One of the work crews consisted of 14 workers.Seven workers from this crew were selected at random to attend the training course.All seven workers selected successfully completed the training course.The remaining seven workers served as a control group and did not attend the training course.Three months after the training course,a foreman who did not know which employees attended the training course was asked to rank all 14 employees in terms of their productivity.A rank of 14 indicates the most productive employee in the crew,while a rank of 1 indicates the least productive worker. $$\begin{array} { c c } \text { Trained Ranks } & \text { Untrained Ranks } \\7 & 6 \\12 & 2 \\14 & 9 \\4 & 3 \\8 & 1 \\13 & 5 \\10 & 11\end{array}$$
At ? = .05,can it be concluded that training was beneficial in improving productivity?

A) Reject the null hypothesis;training is beneficial.
B) Do not reject the null hypothesis;we cannot determine if the training makes a difference.
$H _ { 0 } : D _ { \text {Trained } }$ and $D _ { \text {Untrained } }$ are identical probability distributions. or
$H _ { 0 } : \mu _ { D _ { \text {Trained} } } \leq \mu _ { D _ { \text {Untrained } } }$
$H _ { A } : D _ { \text {Trained } }$ is shifted to the right of $D _ { \text {Untrained } }$ or
$H_{A}: \mu_{D_{Trained }}>\mu_{D_{Untrained}}$

$$\begin{array} { l } T _ { \text {Trained } } = 68 \quad T _ { \text {Untrained } } = 37 \\\text { Reject } \mathrm { H } _ { 0 } \text { if } \mathrm { T } \geq \mathrm { T } _ { \mathrm { U } } \\T _ { U } = T _ { .05,7,7 } = 66\end{array}$$