State the hypothesis of interest for the first line in the Fixed Effect Tests and your conclusion.

The sex ratio of some insects depends on the temperature at which they are raised.An experiment will be conducted where infested pods from canola plants are placed in a total of 12 cages. A number of parasitoids1are then introduced into each cage. The individual cages are kept at three different temperatures.

The parasitoids lay eggs. These eggs hatch and turn into larvae which eventually turn into adults. The final adults are sexed. We are interested in the effect of the temperature of the cage on the sex ratio of the adult parsitoids. Some output is present at the end of the exam.

1. Draw a picture of the experimental layout and describe the treatment structure, the experimental units, the observational units, and the randomization structures.
2. A student starts with an analysis of data from cages 1–3. What is the null and alternate hypothesis and your conclusion.
3. Draw a suitable graphical display based on the data from cages 1–3. Certain types of displays that start with the letter p will earn you “negative marks”.
4. The student (who has NOT taken Stat403/ 650/ 890 ) submits the results from an analysis of cages 1–3 to the supervisory committee. Unfortunately, the supervisory committee includes a certain faculty member. The response from this faculty member is “Read Hurlbert (1984)”. Explain.
5. The student (who still hasnt taken Stat403/ 650/ 890) then analyzes all of the data from all 12 cages together. The response from the certain faculty member is again “Read Hurlbert (1984)”. Explain.
6. Suggest a way to properly analyze all of the data from this experiment. Be sure to give enough details that this student can run the analysis, i.e. you need to convince a certain faculty member that you know what you are doing!

Part II: Fatty acids in pig fat
Dugan, M.E.R. et al. (2004)2 state:
“Pork has been associated with an unhealthy image due to its fat content and relative proportions of polyunsaturated and saturated fatty acids. Flax seed oil contains approximately 72% polyunsaturates and is the richest oilseed source of linolenic acid (58%). Feeding flax, which contains 40 to 45% oil, to finishing pigs will increase the percentage beneficial omega-3 (n-3) fatty acids in carcass fat and produce pork with value added potential.”
This question is based on an experiment conducted by the Agriculture and Agri-Food Canada experimental station in Alberta. The numbers have been modified to preserve confidentiality.
An experiment was conducted to investigate the impact of different amounts of flax (5%, 10%, and 15%) in the diets of pigs for different amounts of time (4, 8, or 12 weeks) upon the fatty acid composition of backfat. The amount of one of the fatty acids (Fatty Acid 1) was measured in the backfat just after slaughter. Eight pigs were treated with each combination of amount of flax and feeding time. Two pigs of each treatment combination were housed in separate barns (four barns in total), but each pig is in a separate stall within the barn. Some output is available at the end of exam.

1. Draw a picture of the experimental layout (curly tails on the pigs leads to bonus marks) and describe the treatment, experimental unit, and randomization structures.
2. Use the standard “shorthand syntax” and specify the appropriate model, i.e. what is the response variable and what “effect” terms would be used and why.
3. Output is given at the end of the exam and presents some of the statistical tests conducted. State the hypothesis of interest for the last line of the Fixed Effect Tests, and your conclusion.
4. State the hypothesis of interest for the first line in the Fixed Effect Tests and your conclusion.
5. Using the results, construct a “joined lines” diagram (a.k.a. connected letters report) for the (main) effect of Diet showing the results of the Tukey multiple comparison procedure. What do you conclude from this? Explain any “odd” results.
6. Using the results, construct a profile plot. Carefully explain what features of the plot illustrate the main effects of each factor and their interaction.
7. The results for the Time factor were somewhat surprising to the scientists as they had expected to see an effect. Suppose that a difference of 0.2 in the fatty acid response variable leads to differences that need to be detected. Complete the dialogue box for a power analysis as shown in output at the end of the exam with the appropriate values (dont forget to transfer this to your exam book).
8. The results from a sample size determination are shown in the output at the end of the exam. What sample size is needed for a 80% power to detect the important difference above. Express the sample size in terms of the number of animals needed for each COMBINATION of flax and time factor levels. Are you surprised?
9. The experimental design was somewhat constrained because the fatty acid composition could only be measured after slaughtering the animals. But suppose a non-lethal method was available to measure fatty acid composition.
Outline an alternative experimental plan that does not require a separate animal for each combination of flax and time feeding. What are the potential advantages and disadvantages of this design?

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