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hw6 - STAT424 Spring 2010 Homework#6 Homework 6 Due Tuesday...

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STAT424 Spring 2010 Homework #6 Apr 27, 2010 Homework 6 Due: Tuesday, May 4, 2010 1) Although tea is the world’s most widely consumed beverage after water, little is known about its nutritional value. Folacin is the only B vitamin present in any significant amount in tea, and recent advances in assay methods have made accurate determination of folacin content feasible. Consider the accompanying data on folacin content for randomly selected four brands of green tea. Brand Observations 1 7.9 6.2 6.6 8.6 8.9 2 5.7 7.5 9.8 6.1 8.4 3 6.8 7.5 5.0 7.4 5.3 4 6.4 7.1 7.9 4.5 5.0 (a) Consider a one-way random effects model y ij = μ + α i + e ij for this data. Construct a 95% CI for μ . (b) Does this data suggest that there are differences between the brands. State your H 0 and H a and use α = 0 . 05. (c) Based on the result in (b), will you change your answer to (a)? (d) What are the ML estimates for σ 2 A and σ 2 ? (e) What are the REML estimates for σ 2 A and σ 2 ? 2) Suppose an experimenter sets out to estimate σ 2 A and σ 2 from a balanced one-way random effects model where N
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