19.49
:H0
The two population locations are the same
:H1
The location of population 1 is to the left of the location of population 2
19.50
:H0
The two population locations are the same
:H1
The location of population 1 is to the right of the location of population 2
19.51
:H0
The two population locations are the same
:H1
19.52
:H0
The two population locations are the same
:H1
19.53
:H0
The two population locations are the same
:H1
The location of population 1 is to the right of the location of population 2
19.54
:H0
The two population locations are the same
:H1
The location of population 1 is to the left of the location of population 2
19.55
:H0
The two population locations are the same
:H1
The location of population 1 is different from the location of population 2
19.56
:H0
The two population locations are the same
:H1
The location of population 1 is to the right of the location of population 2
19.57
:H0
The two population locations are the same
:H1
The location of population 1 is to the left of the location of population 2
19.58 H0: The two population locations are the same
H1: The location of population 1 is different from the location of population 2
19.59 H0: The two population locations are the same
H1: The location of population 1 is different from the location of population 2
19.60
0
H
: The locations of all 3 populations are the same.
1
H
: At least two population locations differ.
19.61
:H0
The locations of all 4 populations are the same.
:H1
At least two population locations differ.
19.62
:H0
The locations of all 3 populations are the same.
:H1
At least two population locations differ.
2
2,10.
2
1k,
H= −
19.63
:H0
The locations of all 3 populations are the same.
:H1
At least two population locations differ.
Rejection region:
2
2,05.
2
1k,
H= −
= 5.99
1 Rank 2 Rank 3 Rank
27 8 37 14 19 6
.2195. There is no evidence to conclude that at least two population locations differ.
19.64
:H0
The locations of all 3 populations are the same.
:H1
At least two population locations differ.
Rejection region:
2
2,05.
2
1k,
H= −
= 5.99
1 Rank 2 Rank 3 Rank
25 10.5 19 2 27 12
15 1 21 4 25 10.5
19.65
:H0
The locations of all 4 populations are the same.
:H1
At least two population locations differ.
a H = .899, p-value = .8257. There is not enough evidence to conclude that differences exist
between the ratings of the four printings.
19.66
:H0
The locations of all 4 populations are the same.
:H1
At least two population locations differ.
Rejection region:
2
1k,r
F−
=
2
3,10.
= 6.25
Treatment
Block 1 Rank 2 Rank 3 Rank 4 Rank
1 10 2 12 3 15 4 9 1
1
2
3
4
A B C D
Kruskal-Wallis Test
Group Rank Sum Observations
Printer 1 4889.5 50
19.67
:H0
The locations of all 3 populations are the same.
:H1
At least two population locations differ.
1 7.3 2 6.9 1 8.4 3
3 5.7 1 6.0 2 8.1 3
5 5.9 1 6.1 2 8.0 3
T
1
= 8 T
2
= 8 T
3
= 14
19.68
:H0
The locations of all 4 populations are the same.
:H1
At least two population locations differ.
a
r
F
= 8.00, p-value = .0460. There is enough evidence to infer that differences exist between the
ratings of the four brands of coffee.
1
2
3
4
A B C
Friedman Test
Group Rank Sum
Brand A 65
19.69
:H0
The locations of all 4 populations are the same.
:H1
At least two population locations differ.
a
r
F
= 10.613, p-value = .0140. There is enough evidence to infer that differences exist between the
19.70
:H0
The locations of all 3 populations are the same.
:H1
At least two population locations differ.
2
1k,
H−
2
2,05.
19.71
:H0
The locations of all 4 populations are the same.
:H1
At least two population locations differ.
Rejection region:
2
1k,
H−
=
2
3,05.
= 7.81
1
2
3
4
A B C
Friedman Test
Group Rank Sum
Manager 1 21
19.72
:H0
The locations of all 4 populations are the same.
:H1
At least two population locations differ.
Rejection region:
2
1k,r
F−
=
2
3,05.
= 7.81
Orange Juice Brand
Judge 1 Rank 2 Rank 3 Rank 4 Rank
1 3 1.5 5 4 4 3 3 1.5
2 2 1 3 2 5 4 4 3
19.73a The randomized block experiment of the analysis of variance and the Friedman test should
be considered. The analysis of variance requires the number of pedestrians to be normally
distributed.
b
:H0
The locations of all 3 populations are the same.
:H1
2
1k,r
F−
19.74
:H0
The locations of all 3 populations are the same.
:H1
At least two population locations differ.
Rejection region:
2
1k,r
F−
=
2
2,05.
= 5.99
19.75a The randomized block experimental design of the analysis of variance and the Friedman
test.
b
:H0
The locations of all 3 populations are the same.
:H1
At least two population locations differ.
Rejection region:
2
1k,r
F−
=
2
2,05.
= 5.99
Newspaper
Job Advertised 1 Rank 2 Rank 3 Rank
Receptionist 14 2 17 3 12 1
.0302. There is enough evidence to infer that differences exist between the newspapers.
19.76
:H0
The locations of all 4 populations are the same.
:H1
At least two population locations differ.
2
3,05.
19.77
:H0
The locations of all 4 populations are the same.
:H1
At least two population locations differ.
Rejection region:
2
1k,r
F−
=
2
3,05.
= 7.81
19.78
:H0
The locations of all 3 populations are the same.
:H1
At least two population locations differ.
2
2,05.
19.79
:H0
The locations of all 3 populations are the same.
:H1
At least two population locations differ.
Rejection region:
2
1k,
H−
=
2
2,05.
= 5.99
19.80a The one-way analysis of variance and the Kruskal-Wallis test should be considered.
b
:H0
The locations of all 4 populations are the same.
:H1
At least two population locations differ.
2
1k,
H−
2
3,05.
19.81
:H0
The locations of all 3 populations are the same.
:H1
At least two population locations differ.
2
2,05.
19.82
:H0
The locations of all 4 populations are the same.
:H1
At least two population locations differ.
Rejection region:
2
1k,
H−
=
2
3,05.
= 7.81
19.83
:H0
The locations of all 4 populations are the same.
:H1
At least two population locations differ.
Rejection region:
2
1k,
H−
=
2
3,05.
= 7.81
19.84 H0: The locations of all 5 populations are the same.
H1: At least two population locations differ.
2
1k,
H−
2
4,05.
19.85 H0: The locations of all 5 populations are the same.
H1: At least two population locations differ.
19.86 H0: The locations of all 3 populations are the same.
H1: At least two population locations differ.
19.87 H0: The locations of all 5 populations are the same.
H1: At least two population locations differ.
19.88 H0: The locations of all 5 populations are the same.
H1: At least two population locations differ.
19.89 H0: The locations of all 3 populations are the same.
H1: At least two population locations differ.
19.90 H0: The locations of all 3 populations are the same.
H1: At least two population locations differ.
19.91 H0: The locations of all 3 populations are the same.
H1: At least two population locations differ.
19.92 H0: The locations of all 5 populations are the same.
H1: At least two population locations differ.
H = 33.69, p-value = 0. There is enough evidence to infer that Democrats, Independents, and
Conservatives differ in their perception about whether the economy has gotten better or worse in
the previous year.
19.94 Rejection region:
96.1zzz 025.2/ −=−=−
or
96.1zzz 025.2/ ==
,61.1150)23(.1nrz S=−=−=
p-value = 2P(Z > 1.61) = 2(1 – .9463) = .1074 There is not
enough evidence to reject the null hypothesis.
0:H S0 =
19.96
0:H S0 =
0:H S1
Mathematics a Economics b a2 b2 ab
4 5.5 5 6.5 30.25 42.25 35.75
−
−
=
=
=n
a
a
1n
1
s
2
n
1i
i
n
1i
2
i
2
a
=
,250.4
7
)28(
5.137
17
12
=
−
−
062.2250.4ss 2
aa ===
6931.
)041.2)(062.2(
917.2
ss
s
r
bb
ab
S===
19.97
0:H S0 =
0:H S1
Number a Rating b a2 b2 ab
1 1 4 7 1 49 7
2 2 5 8 4 64 16
−
−
=
==
=n
ba
ba
1n
1
s
n
1i
i
n
1i
i
n
1i
iiab
=
786.4
8
36)(36(
5.128
18
1−=
−
−
8497.
)299.2)(450.2(
786.4
ss
s
r
bb
ab
S−=
−
==
0:H S0 =
0:H S1
Rejection region:
643.rS
or
643.rS−
There is enough evidence to infer a relationship between the number of commercials and the
rating.
19.98
0:H S0 =
0:H S1
Stock 1 a Stock 2 b a2 b2 ab
–7 4.5 6 8.5 20.25 72.25 38.25
–4 6.5 6 8.5 42.25 72.25 55.25
=
n
1i
i
a
= 91
=
n
1i
i
b
= 91
=
n
1i
2
i
a
= 817
=
n
1i
2
i
b
= 817
=
n
1i
ii ba
= 677.5
,00.15
13
)91(
817
113
12
=
−
−
873.300.15ss 2
−
−
=
=
=n
a
a
1n
1
s
2
n
1i
i
n
1i
2
i
2
a
=
,00.15
13
)91(
817
113
12
=
−
−
873.300.15ss 2
aa ===
2250.
)873.3)(873.3(
375.3
ss
s
r
bb
ab
S===
0:H S0 =
0:H S1
Experience a Rating b a2 b2 ab
1 1.5 1 2 2.25 4 3
17 13 4 16 169 256 208
20 17 4 16 289 256 272
20 17 5 21.5 289 462.25 365.5
21 20 3 11 400 121 220
19 15 2 6 225 36 90
1 1.5 1 2 2.25 4 3
=
n
1i
i
a
= 300
=
n
1i
i
b
= 300
=
n
1i
2
i
a
= 4,895
=
n
1i
2
i
b
= 4,850.5
=
n
1i
ii ba
= 4,012.25
−
−
=
==
=n
ba
ba
1n
1
s
n
1i
i
n
1i
i
n
1i
iiab
=
40.11
24
)300)(300(
25.012,4
124
1=
−
−
2336.
)917.6)(056.7(
40.11
ss
s
r
bb
ab
S===
Rejection region:
S
r
.409 or
S
r
−.409
There is not enough evidence to infer a relationship between experience and quality.