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Practice Problems for 8.1
1.
Crosses of mice will produce either black, brown, or albino offspring.
Mendel’s
model predicts that the probability of a black offspring is
9
/
16
;
the probability
of a brown offspring is
3
/
16
;
and the probability of an albino offspring is
4
/
16
.
An experiment to assess the validity of Mendel’s theory produces the following
data:
35 black offspring;
20 brown offspring;
and 25 albino offspring.
Perform
a goodness of fit test in this setting.
a)
State
H
0
and
H
1
.
b)
Find the expected frequencies under
H
0
.
c)
Calculate the values of the
Q
test statistic.
d)
Find the critical value
2
α
χ
at
α
= 0.05.
e)
State your decision
( Accept
H
0
or
Reject
H
0
)
at
α
= 0.05.
f)
Find the critical value
2
α
χ
at
α
= 0.10.
g)
State your decision
( Accept
H
0
or
Reject
H
0
)
at
α
= 0.10.
2.
Suppose the experiment in Problem #1 is repeated, but with twice as many
observations.
Suppose also that we happened to get the same proportions,
namely,
70 black offspring;
40 brown offspring; and 50 albino offspring.
Repeat Problem #1 in this case, using
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 Fall '11
 STEPHANOV
 Probability

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