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Unformatted text preview: Stat 512 - Assignment 5 Due Monday, April 19 1. From Snedecor and Cochran (1976). A study of of calcium concentration in turnip greens. Four plants were selected, three leaves were taken from each plant, and two 100-mg samples were taken from each leaf. The response is calcium concentration. Data are in the file Turnip.txt : plant leaf sample calcium 1 1 1 3.28 1 1 2 3.09 1 2 1 3.52 1 2 2 3.48 1 3 1 2.88 1 3 2 2.80- lines omitted - 4 3 2 3.31 (a) Fit a nested random-effects model treating plant and leaf as random factors. Report method-of-moments estimates for σ 2 P , σ 2 L and σ 2 , the variance components for plants, leaves, and samples, respectively. Test the null hypotheses H : σ 2 P = 0 and H : σ 2 L = 0. (b) Estimate the correlation between (i) measurements taken from the same leaf, and (ii) measurements taken from the same plant but different leaves. (c) Estimate the population mean μ ··· , and report an exact 95% confidence interval. (Hint: Treat the ¯ Y i ·· ’s, the sample means from the plants, as an independent random sample of size 4 from a normal population with mean μ ··· , and compute a classical one-sample t-interval.) (d) Use lme to compute ML estimates for the variance components. Using the output from...
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- Spring '11
- Statistics, Null hypothesis, Yijk, variance components