Question: 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 was 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 givingfish 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.