A certain manufacturer is interested in evaluating two alternative manufacturing plans consisting of different machine layouts. Because of union rules, hours of operation vary greatly for this particular manufacturer from one day to the next. Twenty-eight random working days were selected and each plan was monitored and the number of items produced each day was recorded.
Some of the collected data is shown below: $$\begin{array} { c | c | c }
\text { DAY } & \text { PLAN 1 OUTPUT } & \text { PLAN 2 OUTPUT } \
\hline 1 & 1234 \text { units } & 1311 \text { units } \
2 & 1355 \text { units } & 1366 \text { units } \
3 & 1300 \text { units } & 1289 \text { units }
\end{array}$$ What assumptions are necessary for the above test to be valid?
A) None of these listed, since the Central Limit Theorem can be applied.
B) Both populations must be approximately normally distributed.
C) The population variances must be approximately equal.
D) The population of paired differences must be approximately normally distributed.

Question

A certain manufacturer is interested in evaluating two alternative manufacturing plans consisting of different machine layouts. Because of union rules, hours of operation vary greatly for this particular manufacturer from one day to the next. Twenty-eight random working days were selected and each plan was monitored and the number of items produced each day was recorded.
Some of the collected data is shown below: $$\begin{array} { c | c | c } 
\text { DAY } & \text { PLAN 1 OUTPUT } & \text { PLAN 2 OUTPUT } \
\hline 1 & 1234 \text { units } & 1311 \text { units } \
2 & 1355 \text { units } & 1366 \text { units } \
3 & 1300 \text { units } & 1289 \text { units }
\end{array}$$ What assumptions are necessary for the above test to be valid?
A) None of these listed, since the Central Limit Theorem can be applied.
B) Both populations must be approximately normally distributed.
C) The population variances must be approximately equal.
D) The population of paired differences must be approximately normally distributed.

Quizplus · Accepted Answer

The test involves paired differences, so the population of paired differences must be approximately normally distributed for the test to be valid.

A Certain Manufacturer Is Interested in Evaluating Two Alternative Manufacturing