experimental design

1. The data in the table below show the measurements of hemoglobin (grams per 100 ml) in the blood of brown trout. The trout were placed at random in four dierent troughs (tanks). The sh food added to the troughs contained, respec- tively, 0, 5, 10, and 15 grams of sulfamerasine per 100 lbs. of sh. The measure- ments were made on ten randole selected sh from each trough after 35 days. Sulfamerazine Hemoglobin 0 6.7 7.8 5.5 8.4 7.0 7.8 8.6 7.4 5.8 7.0 5 9.9 8.4 10.4 9.3 10.7 11.9 7.1 6.4 8.6 10.6 10 10.4 8.1 10.6 8.7 10.7 9.1 8.8 8.1 7.8 8.0 15 9.3 9.3 7.2 7.8 9.3 10.2 8.7 8.6 9.3 7.2 Do parts (c)(f) using hand calculations. Use the computer for part (g). (a) Plot the data (hemoglobin versus amount of sulfamerazine) and comment on the results. Does it look like the mean responses differs across the four treat- ment groups? (b) Write down a suitable model for the analysis of these data. Be sure to dene all of the terms in your model and to state the basic assumptions of the model. (c) Estimate the treatment mean associated with 0 grams of sulfamerasine and form a 95% condence interval for this quantity. (d) Conduct the ANOVA table and test the hypothesis of equal means across the four levels of sulfamerazine. Include columns for source of variability, degree of freedom, sums of squares, mean squares, Ftast values, and pvalua; in your ANOVA table. (e) Dene a contrast to compare on sulfamerazine with \"some\" sulfamerazine. Test this hypothesis at level or = .05 and state the conclusion of your test. (f) Test for difference between all pairs of means using both the Bonferronj method and Tukey's HSD method. State your conclusions. (g) Write and run a SAS program to perform [c](f). Conrm your results from the hand calculations. Attach the relevant SAS output and a print out of the program