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 maritalstatus distribution of 25 to 29yearold U.S. males is the same as that of the
population as a whole.
H
a
: The maritalstatus distribution of 25 to 29yearold 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, nonHispanics received the Ph.D.
degree in 1994.
13.5 Use a
x
2
goodness of fit test. (b) Use a oneproportion
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 agegroup 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
194
13
6851F_ch13_194_209
23/9/02
10:03
Page 194
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195
Note that none of the difference terms is very large. The test statistic is X
2
5
3.76, df
5
3, and the
P
value
5
.2886. There is insufficient evidence to conclude that the distributions are different.
The results of this simulation differ from those in the text; the reason may be due to different
sample sizes or simply chance.
13.7 (a)
H
0
:
p
0
,
p
1
5
p
2
5
. . .
5
p
9
5
0.1 vs.
H
a
: At least one of the
p
’s is not equal to 0.1. (b) Using
randInt (0, 9, 200)
→
L
4
,
we obtained these counts for digits 0 to 9: 19, 17, 23, 22, 19, 20,
25, 12, 27, 16. (e)
X
2
5
8.9, df
5
9,
P
value
5
.447. There is no evidence that the sample data were
generated from a distribution that is different from the uniform distribution.
13.8 Answers will vary. You should be surprised if you get a significant
P
value.
H
0
: The die is fair
(
p
1
5
p
2
5
...
5
p
6
5
1/6).
H
a
: The die is not fair. Use the command
randInt (1, 6, 300)
→
L
1
to simulate rolling a fair die 300 times. In our simulation, we obtained the following frequency
distribution:
Side
1
2
3
4
5
6
Freq.
57
46
55
54
45
43
The expected counts under
H
0
: (300)(1/6)
5
50 for each side. The test statistic is
X
2
5
.98
1
.32
1
.5
1
.32
1
.5
1
.98
5
3.6, and the degrees of freedom are
n
2
1
5
5. The
P
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 Fall '08
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 Statistical hypothesis testing, Minitab output

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