13.1 (a) (i) 0.20
,
P
,
0.25. (ii)
P
5
0.235. (b) (i) 0.02
,
P
,
0.025. (ii)
P
5
0.0204. (c) (i)
P
.
0.25.
(ii)
P
5
0.3172.
13.2
H
0
: The marital-status distribution of 25- to 29-year-old U.S. males is the same as that of the
population as a whole.
H
a
: The marital-status distribution of 25- to 29-year-old U.S. males is dif-
ferent from that of the population as a whole. Expected counts: 140.5, 281.5, 32, 46.
X
2
5
161.77,
df
5
3.
P
-value
5
7.6
3
10
2
35
<
0.0000. Reject
H
0
. The two distributions are different.
13.3
H
0
: The genetic model is valid (the different colors occur in the stated ratio of 1:2:1).
H
a
:
The genetic model is not valid. Expected counts: 21 GG, 42 Gg, 21 gg.
X
2
5
5.43, df
5
2.
P
-value
5
P
(
X
2
2
.
5.43)
5
0.0662. There is no compelling reason to reject
H
0
(though the
P
-value
is
a
little on the low side).
13.4
H
0
: The ethnicity distribution of the Ph.D. degree in 1994 is the same as it was in 1981.
H
a
:
The ethnicity distribution of the Ph.D. degree in 1994 is different from the distribution in 1981.
Expected counts
5
300
3
(1981 percents)
5
237, 12, 4, 8, 1, 38.
X
2
5
61.98, df
5
5.
P
-value
5
P
(
X
5
2
.
61.98)
5
4.734
3
10
2
12
<
0.0000. We reject
H
0
and conclude that the ethnicity distri-
bution of the Ph.D. degree has changed from 1981 to 1994. (b) The greatest change is that
many more nonresident aliens than expected received the Ph.D. degree in 1994 over the 1981
figures. To a lesser extent, a smaller proportion of white, non-Hispanics received the Ph.D.
degree in 1994.
13.5 Use a
x
2
goodness of fit test. (b) Use a one-proportion
z
test. (c) You can construct the inter-
val; however, your ability to generalize may be limited by the fact that your sample of bags is not
an SRS. M&M’s may be packaged by weight rather than count.
13.6
H
0
: The age-group distribution in 1996 is the same as the 1980 distribution.
H
a
: The age-
group distribution in 1996 is different from the 1980 distribution. One simulation produced
observed counts: 37, 35, 15, 13. The expected counts: 41.39, 27.68, 19.64, and 11.28 are stored in
list L
4
, and the difference terms
are assigned to L
5
.
1
O
2
E
2
2
/
E
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