15.66
:H0
=
1
p
1/3,
=
2
p
1/3,
=
3
p
1/3
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
i
2
ii e/)ef( −
15.67
: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.
1
2
3
4
5
6
7
8
9
A B C D
Chi-Squared Test of Normality
Difference
Mean 19.75
Standard deviation 30.63
Observations 40
Intervals Probability Expected Observed
(z <= -1) 0.1587 6.35 6
Cell i
i
f
i
e
i
2
ii e/)ef( −
1 87 362(.2) = 72.4 14.6 2.94
2
2
2
= 4.77, p-value = .3119. There is not enough evidence to infer that absenteeism is higher on
some days of the week.
15.68
:H0
The two variables (shift and day) are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
i
2
ii e/)ef( −
1 52 181(87)/362 = 43.50 8.50 1.66
2 28 181(62)/362 = 31.00 -3.00 0.29
2
Rejection region:
2
>
==−−
2
4,10.
2
1c)(1r(,
7.78
2
15.69
:H0
The two variables (satisfaction and relationship) are independent
:H1
The two variables are dependent
Cell i
i
f
i
e
i
2
ii e/)ef( −
1 21 171(91)/447 = 34.81 -13.81 5.48
2 25 171(122)/447 = 46.67 -21.67 10.06
3 54 171(114)/447 = 43.61 10.39 2.48
Rejection region:
2
>
==−−
2
6,05.
2
1c)(1r(,
12.6
2
= 74.47, p-value = 0. There is sufficient evidence to infer that the level of job satisfaction
depends on boss/employee gender relationship.
15.70
:H0
The two variables (Country and stress) are independent
:H1
The two variables are dependent
2
1
2
3
4
5
6
A B C D E
Contingency Table
Stress
Country 1 2 TOTAL
1266 315 581
2347 276 623
15.71
:H0
The two variables (method and quit) are independent
:H1
The two variables are dependent
15.72
:H0
The two variables (education and section) are independent
:H1
The two variables are dependent
15.73a The expected frequency is 1/49.
:H0
1
2
3
4
5
6
A B C D E F G
Contingency Table
Quit
Method 1 2 3 4 TOTAL
1104 125 32 49 310
214 17 5 9 45
1
2
3
4
5
6
A B C D E F G
Contingency Table
Section
Education 1 2 3 4 TOTAL
1 4 21 31 14 70
227 32 18 279
Number i
i
f
i
e
i
2
ii e/)ef( −
1 5 312(1/49) = 6.37 -1.38 0.29
2 6 312(1/49) = 6.37 -0.38 0.02
2
15.74 Binomial probabilities with n = 5 and p = .5: P(X = 0) = .0313, P(X = 1) = .1563, P(X = 2) =
.3125, P(X = 3) = .3125, P(X = 4) = .1563, P(X = 5) = .0313
:H0
=
0
p
.0313,
=
1
p
.1563,
=
2
p
.3125,
=
3
p
.3125,
=
4
p
.1563,
=
5
p
.0313
:H1
At least one
i
p
is not equal to its specified value.
Cell i
i
f
i
e
i
2
ii e/)ef( −
0 8 200(.0313) = 6.26 1.74 0.48
2
2
= 4.13, p-value = .5310. There is not enough evidence to infer that at the number of boys in
families with 5 children is not a binomial random variable with p =.5.
15.75
:H0
The two variables (cold and group) are independent
:H1
The two variables are dependent
15.76
:H0
The two variables (faculty and retire) are independent
:H1
The two variables are dependent
15.77
:H0
The two variables (tree choice and age category) are independent
:H1
The two variables are dependent
1
2
3
4
5
6
A B C D E
Contingency Table
Group
Cold 1 2 TOTAL
117 11 28
212 13 25
1
2
3
4
5
A B C D E F G H
Contingency Table
Retire
Faculty 1 2 3 4 5 TOTAL
1174 51 113 42 86 466
15.78
:H0
The two variables (network and ask) are independent
:H1
The two variables are dependent
15.79 a
:H0
The two variables (education and group) are independent
:H1
The two variables are dependent
1
2
3
4
5
A B C D E F
Contingency Table
Tree choice
Age category 1 2 3 TOTAL
1136 309 158 603
1
2
3
4
5
A B C D E F
Contingency Table
Ask
Network 1 2 3 TOTAL
119 30 43 92
b
:H0
The two variables (education and buy Special X) are independent
:H1
The two variables are dependent
5
15.80 a
:H0
The two variables (gender and vote) are independent
:H1
The two variables are dependent
1
2
3
4
5
A B C D E F G
Contingency Table
Group
Education 1 2 3 4 TOTAL
1 5 113 73 40 231
1
2
3
4
A B C D E F G
Contingency Table
Buy Sp X
Education 1 2 3 4 TOTAL
b
:H0
The two variables (education and vote) are independent
:H1
The two variables are dependent
are related.
c
:H0
The two variables (income category and vote) are independent
:H1
The two variables are dependent
1
2
3
4
5
A B C D E
Contingency Table
Votes
Gender 1 2 TOTAL
1189 169 358
1
2
3
4
A B C D E F G
Contingency Table
Votes
Educ 1 2 3 4 TOTAL
15.81
:H0
The two variables are (type of work and segment) independent
:H1
The two variables are dependent
15.82
:H0
The two variables (value and segment) are independent
:H1
The two variables are dependent
1
2
3
4
5
A B C D E F G
Contingency Table
Votes
Income 1 2 3 4 TOTAL
138 186 105 29 358
1
2
3
4
5
A B C D E F
Contingency Table
Segment
Work 1 2 3 TOTAL
1157 44 217 418
15.83
:H0
The two variables (breakfast and group) are independent
:H1
The two variables are dependent
1
2
3
4
5
6
A B C D E F
Contingency Table
Segment
Value 1 2 3 TOTAL
1147 135 136 418
2221 155 160 536
1
2
3
4
5
A B C D E F G
Contingency Table
Group
Breakfast 1 2 3 4 TOTAL
1 3 15 29 222 269