STAT 350 – Spring 2009 Homework #12 SOLUTION covers through Lecture S 1. An ecologist is studying the trade-offs individuals make between investment in survival and growth and the investment in reproduction. In particular she is studying this relationship in a highly variable species of prairie grasses. She has sampled 25 individual (randomly selected) plants across the range of this species. For each plant, she has measured seed mass and root volume. Let xidenote the root volume (in mL) of the ith plant and yidenote the seed mass (in mg) of the ith plant. She finds 251iix=∑= 926, 251iiy=∑= 1,928, 2521iix=∑= 51,860, 2521iiy=∑= 153,997, and (251iii)x y=∑= 63,677. The root volumes ranged from 8.2 to 102.3 mL and the seed masses ranged from 44.7 to 102.5 mg. Warning: do not round-off too much in intermediate calculations!a. Calculate SSxy. ()()9261928636777,736.1225=−= −b. Calculate SSxx. 29265186017,560.9625−=c. Calculate SSyy. 219281539975309.6425−=d. Calculate the standard deviation of root volume 17560.9627.050771251xxxSSsn===−−e. Calculate the standard deviation of seed mass 5309.6414.873971251yyySSsn===−−f. Give a 95% CI for the true mean seed mass of individuals from this species. N,25 277.1295% CI for :192814.873972.0692525yycrit dfsytnμ=−⎛⎞±⎜⎟⎝⎠⎛⎞±⎜⎟⎝⎠→(70.965, 83.275) Homework #12 – Solution Page 1 of 1
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