4.(a) (i) no: the sample size
n
(number of flowers in
the plot) is not prespecified.
(ii) yes
(iii) no: flies in the same family are likely to have
the same eye color, so the individuals in the sam
ple are not independent.
It is okay to see this
as a nonconstant probability of having red eyes:
those probabilities are unknown (families are ran
domly sampled) but are probably different across
different families.
(b) (i)
H
0
:
p
=
.
5 vs
H
A
:
p > .
5
(ii) .0985 (iii) mean 49, sd 4.95 (iv)
≈
.
0078
Note: A real experiment done by schoolchildren
reached
n
= 9821 and observed
y
= 6101 ! See
ourworld.compuserve.com/homepages/rajm/
ssrsum.htm
5.(a) mean= 8 (center of symmetry). We know there
is 95% of the area whithin
±
1
.
96
*
sd of the mean,
with 0.025 on each side. This is the area between
≈
7 and 9. Therefore 2 sd
≈
9

8 and sd
≈
0
.
5.
(b) z=0.52 so the value is 0.52 sd above from the
mean: 8mm + 0.52 * 0.5 = 8.26 mm.
(c) (i) for
n
= 1, (ii) for
n
= 8, (iii) for
n
= 2: the
shape looks more like a bell curve when
n
is large.
Also, the variability of the sample mean decreases
as
n
increases (compare the scales).
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 Fall '08
 Staff
 Jack, 8mm, 3.2g, 8.26 mm

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