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)The population variances must be approximately equal.
C)Both populations must be approximately normally distributed.
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)The population variances must be approximately equal.
C)Both populations must be approximately normally distributed.
D)The population of paired differences must be approximately normally distributed.

Quizplus · Accepted Answer

The assumption necessary for comparing two paired samples (like comparing outputs from two plans on the same days) is that the population of paired differences must be approximately normally distributed. This ensures that the statistical tests used to compare the means of the two plans are valid.

A Certain Manufacturer Is Interested in Evaluating Two Alternative Manufacturing