Chapter 15
15.1
:H0
=
1
p
.1,
=
2
p
.2,
=
3
p
.3,
=
4
p
.2,
=
5
p
.2
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 24 300(.1) = 30 -6 1.20
2
2
= 4.54, p-value = .3386. There is not enough evidence to infer that at least one
i
p
is not equal
to its specified value.
15.2
:H0
=
1
p
.1,
=
2
p
.2,
=
3
p
.3,
=
4
p
.2,
=
5
p
.2
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 12 150(.1) = 15 -3 .60
2
2
2
i
p
15.3
:H0
=
1
p
.1,
=
2
p
.2,
=
3
p
.3,
=
4
p
.2,
=
5
p
.2
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 6 75(.1) = 7.5 -1.5 .30
2
2
= 1.14, p-value = .8889. There is not enough evidence to infer that at least one
i
p
is not equal
to its specified value.
15.4 The
2
statistic decreases.
15.5
:H0
=
1
p
.3,
=
2
p
.3,
=
3
p
.2,
=
4
p
.2
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
2
i
p
15.6
:H0
=
1
p
.3,
=
2
p
.3,
=
3
p
.2,
=
4
p
.2
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
i
p
15.7
:H0
=
1
p
.2,
=
2
p
.2,
=
3
p
.2,
=
4
p
.2,
=
5
p
.2
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 28 100(.2) = 20 8 3.20
i
p
15.8
:H0
=
1
p
.15,
=
2
p
.40,
=
3
p
.35,
=
4
p
.10
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 41 233(.15) = 34.95 6.05 1.05
i
p
15.9
:H0
=
1
p
1/6,
=
2
p
1/6,
=
3
p
1/6,
=
4
p
1/6,
=
5
p
1/6,
=
6
p
1/6
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 114 600(1/6) = 100 14 1.96
2
2
15.10
:H0
=
1
p
.05,
=
2
p
.25
=
3
p
.40,
=
4
p
.25
=
5
p
.05
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 11 150(.05) = 7.5 3.5 1.63
2
2
2
= 14.07, p-value = .0071. There is enough evidence to infer that grades are distributed
differently from grades in the past.
15.11
:H0
=
1
p
.2,
=
2
p
.2
=
3
p
.2,
=
4
p
.2
=
5
p
.2
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 8 25(.2) = 5.0 3.0 1.80
15.12
:H0
=
1
p
.72,
=
2
p
.15,
=
3
p
.10,
=
4
p
.03
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 159 250(.72) = 180.0 -21.0 2.45
=33.85, p-value = 0. There is enough evidence to infer that the aging schedule has changed.
15.13
:H0
=
1
p
.15,
=
2
p
.25,
=
3
p
.40,
=
4
p
.20
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 36 250(.15) = 29.55 6.45 1.41
15.14
:H0
=
1
p
.31,
=
2
p
.51,
=
3
p
.18
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 408 1200(.31) = 372 36 3.48
15.15
:H0
=
1
p
.05,
=
2
p
.07,
=
3
p
.04,
=
4
p
.84
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 19 250(.05) = 12.5 6.5 3.38
15.16
:H0
=
1
p
.23,
=
2
p
.40,
=
3
p
.15,
=
4
p
.22
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 63 320(.23) = 73.6 -10.6 1.53
15.17 H0: p1 = .58, p2 = .06, p3 = .11, p4 = .25
H1: At least one pi is not equal to its specified value.
Marital status Observed Expected
Married & separated 794 + 179 = 973 .58(1782) = 1033.6
15.18 H0: p1 = .79, p2 = .13, p3 = .08
H1: At least one pi is not equal to its specified value.
Race Observed Expected
White 1477 .79(1974) = 1559.5
15.19 H0: p1 = .79, p2 = .13, p3 = .08
H1: At least one pi is not equal to its specified value.
Race Observed Expected
White 1550 .79(2044) = 1614.8
15.20 H0: p1 = .566, p2 = .062, p3 = .103, p4 = .269
H1: At least one pi is not equal to its specified value.
Marital status Observed Expected
Married & separated 900 + 68 = 968 .566(1974) = 1117.3
15.21 H0: p1 = .566, p2 = .062, p3 = .103, p4 = .269
H1: At least one pi is not equal to its specified value.
Marital status Observed Expected
Married & separated 891+65 = 956 .566(2043) = 1156.3
15.22
:H0
The two variables are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 28 96(84)/188 = 42.89 -14.89 5.17
15.23
:H0
The two variables are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 14 48(42)/188 = 21.45 -7.45 2.59
2
2
2
15.24
:H0
The two variables are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 7 24(21)/188 = 10.72 -3.72 1.29
2
2
2
= 4.77, p-value = .0289. There is enough evidence to infer that the two classifications L and M
are dependent.
15.25 The
2
statistic decreases.
15.26
:H0
The two variables are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
15.27
:H0
The two variables (responses and employee group) are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 67 110(130)/200 = 71.50 -4.50 0.28
15.28
:H0
The two variables (shirt condition and shift) are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 240 570(250)/600 = 237.5 2.5 .03
15.29
:H0
The two variables economic option and political affiliation) are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 101 444(331)/1000 = 146.96 -45.96 14.376
2 282 444(557)/1000 = 233.99 48.01 9.852
3 61 444(142)/1000 = 63.05 -2.05 0.067
4 38 130(331)/1000 = 43.03 –5.03 0.588
5 67 130(557)/1000 = 68.51 -1.51 0.033
15.30
:H0
The two variables (inducement and return) are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 80 300(200)/1000 = 60 20 6.67
2 100 300(300)/1000 = 90 10 1.11
15.31
:H0
The two variables (newspaper and occupation) are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 27 120(89)/ 354=30.2 –3,2 .33
2 18 120(112)/354=38.0 -20.0 10.50
15.32a
:H0
The two variables (predicted change and actual change) are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 65 129(104)/216 = 62.11 2.89 .13
2 39 87(104)/216 = 41.89 -2.89 .20
2
15.33
:H0
The two variables (last purchase and second-last purchase) are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 39 149(153)/559 = 40.78 −1.78 .08
2 36 149(134)/559 = 35.72 .28 0
3 51 149(190)/559 = 50.64 .36 0
Rejection region:
2
>
== −−
2
9,05.
2
1c)(1r(,
16.9
2
= .67, p-value = .9999. There is no evidence of a relationship.
15.34
:H0
The two variables (education and smoker) are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 34 57(460)/1000 = 26.22 7.78 2.31
15.35
:H0
The two variables (education and smoker) are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 60 121(369)/658 =67.9 -7.9 .91
2 23 121(116)/658=21.3 1.7 .13
12 24 132(108)/658=21.7 2.3 .25
13 67 95(369)/658=53.3 13.7 3.54
14 11 95(116)/658=16.7 -5.7 1.97
15 10 95(65)/658=9.4 0.6 .04
16 7 95(108)/658=15.6 -8.6 4.74
24 10 88(108)/658=14.4 -4.4 1.37
Total 658 658
2
= 22.36
2
2
:H0
:H1
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 44 100(167)/400=41.75 2.25 .12
2 11 100(64)/ 400=16.00 -5.00 1.56
3 34 100(121)/ 400=30.25 3.75 .46
4 11 100(48)/ 400=12.00 -1.00 .08
2
Rejection region:
2
>
== −−
2
9,05.
2
1c)(1r(,
16.9
2
15.37
:H0
The two variables (results and financial ties) are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
15.38 H0: The two variables (degree and approach) are independent
H1: The two variables are dependent
Cell i
i
f
i
e
)ef( ii −
i
2
ii e/)ef( −
1 51 75(101)/195 = 38.85 12.15 3.80
2 8 75(31)/195 = 11.92 -3.92 1.29
3 5 75(36)/195 = 13.85 -8.85 5.65
Rejection region:
2
>
==
−−
2
6,05.
2
1c)(1r(,
12.6
2
= 20.89, p-value = .0019. There is sufficient evidence to infer that there are differences in
15.39
:H0
The two variables (year and weapon) are independent
:H1
The two variables are dependent
15.40
15.41
15.42
15.43
15.44
15.45
15.46