John, the owner of Cheng-Kung Company, wants to invest in additional
machinery to meet the new production demands. He discussed with his
purchasing agent the anticipated cost of adding five machines of a type
similar to one they had purchased the year before. These machines were
versatile enough to manufacture a wide variety of parts and components.
The purchasing agent reported to John that they had chosen the old
machine because of its low overall cost of operation. All machines available
then had been evaluated on a number of criteria. Two new companies that
made similar machines claimed their machines were an even better buy.
Both companies agreed to lend John one of their machines for a test of
productive ability. The two machines were randomly assigned jobs of the
same type. The number of parts finished by each machine was recorded at
the end of each day. All partially finished items were included in the count
as work in progress and counted as percent complete. The numbers of
parts completed on each new machine (X and Y ) were recorded. In addition,
the records of the last two weeks provide the production information on the
old machine (Z).
Machine X 18.3 7.5 6.1 7.3 4.5 8.5 5.9 5.1 3.6 11.9 10.5 18.9 11.1 18.6
Machine Y 13.2 10.4 8.1 9.2 10.4 7.8 9.5 7.6 8.3 5.1 13.6 12.7 10.7 13.8
Machine Z 9.5 9.9 7.7 9.8 12.3 14.3 6.7 8.1 11.3 12.5 14.9 13.8 10.4 7.4
(a) Are machine X and Y equal in productive capacity? Explain. (10%)
(b) How does the old machine compare with the better of the new
machines in productive capacity? (10%)
Give three examples to explain why a Possion random variable is usually a
good approximation for the diverse phenomena.
Briefy explain the following terms: (24%)
(1) standard error (5) sampling frame
(2) type II error (6) multicollinearity
(3) Heterogenous subsamples (7) factorial design
(4) residual variance (8) magnitude of effect
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