STAT 350 – Lab #10
For her senior thesis, an undergraduate in biology wanted to study the effect of crowding (population
density) on fecundity (egg production) using
Tribolium
(flour) beetles.
She had 100 jars of flour.
She
controlled the density (number of beetles per jar) in her experiment and then would measure the number
of eggs produced.
Dividing the number of eggs by the number of adults would give a measure of the
fecundity of the population (she decided it would be impossible to sex all the beetles which is why she is
not measuring fecundity as #eggs per female).
She used density levels ranging from 100 to 2500 beetles
per jar and replicated each density level 4 times. The results of her experiment are given in the
accompanying Excel file.
All plots and analyses for this lab should be done in SAS.
Do not worry about making the plots look
"nice".
1.
This part you may do in Excel:
Get some summary information on the independent (
x
) variable.
Find
the average density, the variance and standard deviation of the density, and
S
xx
(note – you can get
S
xx
easily from the variance of
x
).
Average density:
d
= 1300
Variance of density:
s
d
2
= 525252.5
Standard deviation of density:
s
d
= 724.7431
S
xx
(here
S
dd
):
=
S
dd
= (
n
-1)
s
d
2
= 52,000,000
2.
One thing that she is interested in is estimating the fecundity when the population density is 1000.
Using the 4 observations for fecundity when density was 1000, give a point estimate for the predicted
# eggs/female and give a 95% prediction interval (
consider this early review – this has nothing to do
with regression
).
There were
n
=4 jars with densities of 1000 beetles.
For these 4 jars, the average fecundity was 3.01 with a standard deviation of 1.305322
The point estimate is 3.01 eggs/adult.
The resulting prediction interval is then:
(
)
1
3.01
3.182 1.305322
1
4
±
+
⇒
(-1.6338, 7.6538)
Clearly it is not possible to have negative eggs, so the interval can be adjusted to (0, 7.6538)
1

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