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

question 63

Multiple Choice

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
• \(H_{A}: \mu_{D_{Trained }}>\mu_{D_{Untrained}}\)
• \[\begin{array} { l }
• T _ { \text {Trained } } = 68 \quad T _ { \text {Untrained } } = 37 \\
• \text { Reject } \mathrm { H } _ { 0 } \text { if } \mathrm { T } \geq \mathrm { T } _ { \mathrm { U } } \\
• T _ { U } = T _ { .05,7,7 } = 66
• \end{array}\]

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Definitions:

Predetermined Overhead Rate

A rate used to allocate manufacturing overhead costs to products, calculated before a production period begins.

Direct Labor-Hours

Sum of the working hours spent by workers actively participating in generating products or rendering services.

Machine-Hours

A measure of production time that indicates the total hours machines are operating in the production process.

Machining Department

A specific division within a manufacturing facility where machining processes such as cutting, drilling, or shaping materials are carried out.