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# hw12 - STAT 350 Spring 2009 Homework#12 SOLUTION covers...

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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 x i denote the root volume (in mL) of the i th plant and y i denote the seed mass (in mg) of the i th plant. She finds 25 1 i i x = = 926 , 25 1 i i y = = 1,928 , 25 2 1 i i x = = 51,860 , 25 2 1 i i y = = 153,997 , and ( 25 1 i i i ) 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 SS xy . ( )( ) 926 1928 63677 7,736.12 25 = = − b. Calculate SS xx . 2 926 51860 17,560.96 25 = c. Calculate SS yy . 2 1928 153997 5309.64 25 = d. Calculate the standard deviation of root volume 17560.96 27.05077 1 25 1 xx x SS s n = = = e. Calculate the standard deviation of seed mass 5309.64 14.87397 1 25 1 yy y SS s n = = = f. Give a 95% CI for the true mean seed mass of individuals from this species. N , 25 2 77.12 95% CI for : 1928 14.87397 2.069 25 25 y y crit df s y t n μ = ± ± (70.965, 83.275) Homework #12 – Solution Page 1 of 1

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