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question 15,16,17

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Table 3.13 Data for the Trout Experiment Code Hemoglobin (grams per 100I ml]I 1 6.? 7.8 5.5 8.4 ?.0' ?.8 8.6 ?.4 5.8 7.0 2 9.9 8.4 10.4 9.3 10.? 11.9 ?.1 6.4 8.6 10.6
3 10.4 8.1 10.6 8.? 10.? 9.1 8.8 8.1 228 8.0
4 9.3 9.3 7.2 ?.8 9310.2 8.? 8.6 9.3 7.2 Source: GutsellJ. 5. {1951). Copyright ® 1951 International Biometric
Society. Reprinted with permission. The fish food added to the troughs contained, respectively, 0, 5, 10, and 15 grams of
sulfamerazine per 100 pounds of fish (coded l, 2, 3, 4). The measurements were made
on ten randomly selected fish from each trough after 35 days. (a) Plot the data and comment on the results. (b) Write down a suitable model for this experiment. (c) Calculate the least squares estimate of the mean response for each treatment. Show
these estimates on the plot obtained in (a). Can you draw any conclusions from
these estimates? (d) Test the hypothesis that sulfameraziue has no eflect on the hemoglobin content of
trout blood. (e) Calculate a 95% upper confidence limit for 0'2. 16. "It-out experiment, continued
Suppose the trout experiment of Exercise 15 is to be repeated with the same I: = 4
treatments , and suppose that the same hypothesis, that the treatments have no effect on hemoglobin content. is to be tested. (a) For calculating the number of observations needed on each treatment, what would
you use as a guess for 0'2? (b) Calculate the sample sizes needed for an analysis of variance test with or = 0.05 nnJ— .nlu .. J— ”n

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(b) Calculate the sample sizes needed for an analysis of variance test with a = 0.05
to have power 0.95 if (i) A = 1.5. (ii) A = 1.0. (iii) A = 2.0.
17. Soap experiment, continued
In Example 3.6.2, page 53, a sample size calculation was made for the number of
observations needed to detect, with probability (0.25) = 0.90, a difference in weight
loss of at least A = 0.25 grams in v = 3 difference types of soap, using an analysis
of variance with a probability of a = 0.05 of a Type I error. The calculation used an
estimate of 0.007 grams for o and showed that r = 4 observations were needed on
each type of soap. The experiment was run with r = 4, and the least squares estimate
for o was 0.0772. If the true value for o was, in fact, 0.08, what power did the test
actually have for detecting a difference of A = 0.25 grams in the weight loss of the
three soaps?

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