This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 100mg 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 randomeffects model treating plant and leaf as random factors. Report methodofmoments 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 onesample tinterval.) (d) Use lme to compute ML estimates for the variance components. Using the output from...
View
Full Document
 Spring '11
 John
 Statistics, Null hypothesis, Yijk, variance components

Click to edit the document details