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
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