Case 12.2 McLaughlin Salmon Works John McLaughlin’s father correctly predicted that a combination

Case 12.2
McLaughlin Salmon Works
John McLaughlin’s father correctly predicted that a combination
of declining wild populations of salmon and an increase in demand
for fish in general would create a growing market for salmon
grown in “fish farms.” Over recent years, an increasing percentage
of salmon, trout, and catfish, for example, come from commercial
operations. At first, operating a fish farm consisted of finding an
appropriate location, installing the pens, putting in smelt, and feeding
the fish until they grew to the appropriate size. However, as the
number of competitors increased, successful operation required
taking a more scientific approach to raising fish.
Over the past year, John has been looking at the relationship
between food intake and weight gain. Since food is a major cost of
the operation, the higher the weight gain for a given amount of
food, the more cost-effective the food. John’s most recent effort
involved trying to determine the relationship between four component
mixes and three size progressions for the food pellets. Since
smaller fish require smaller food pellets but larger pellets contain
more food, one question John was addressing is at what rate to
move from smaller to larger pellets. Also, since fish are harder to
individually identify than livestock, the study involved constructing
small individual pens and giving fish in each pen a different
combination of pellet mix and size progression. This involved a
reasonable cost but a major commitment of time, and John’s father
wasn’t sure the cost and time were justified. John had just gathered
his first set of data and has started to analyze it. The data are shown
in the file called McLaughlin Salmon Works. John is not only
interested in whether one component mix, or one pellet size progression,
seemed to lead to maximum weight gain but would really
like to find one combination of mix and size progression that
proved to be superior.
Required Tasks:
1. Identify the major issues in the case.
2. Identify an appropriate statistical analysis to perform.
3. Explain why you selected the test you choose in (2)
4. State the appropriate null and alternative hypotheses for the
statistical test you identified.
5. Perform the statistical test(s). Be sure to state your
conclusion(s).
6. Is there one combination of mix and size progression that is
superior to the others?
7. Summarize your analysis and findings in a short report.