| Question Detail:
level of success of publicly traded companies affect the way their board members are paid? Publicly traded companies were divided into four quarters using the rate of return in their stocks to differentiate among the companies. The annual payment (in $1,000s) to their board members was recorded. Can we infer that the amount of payment differs between the four groups of companies?
|
1st quarter
|
2nd quarter
|
3rd quarter
|
4th quarter
|
|
65
|
67
|
81
|
96
|
|
61
|
83
|
89
|
93
|
|
71
|
85
|
82
|
113
|
|
58
|
52
|
70
|
92
|
|
88
|
94
|
68
|
64
|
|
37
|
77
|
72
|
101
|
|
82
|
87
|
93
|
57
|
|
59
|
81
|
98
|
77
|
|
66
|
56
|
87
|
84
|
|
89
|
95
|
75
|
83
|
|
59
|
75
|
40
|
76
|
|
49
|
97
|
73
|
51
|
|
89
|
56
|
105
|
73
|
|
79
|
78
|
88
|
60
|
|
76
|
82
|
70
|
92
|
|
69
|
70
|
67
|
72
|
|
85
|
71
|
64
|
83
|
|
95
|
74
|
89
|
71
|
|
73
|
82
|
53
|
85
|
|
86
|
65
|
73
|
95
|
|
100
|
76
|
94
|
78
|
|
72
|
82
|
89
|
75
|
|
60
|
101
|
82
|
87
|
|
115
|
88
|
69
|
53
|
|
77
|
82
|
116
|
94
|
|
68
|
63
|
63
|
65
|
|
70
|
49
|
71
|
75
|
|
77
|
64
|
78
|
103
|
|
66
|
80
|
84
|
90
|
|
82
|
58
|
72
|
101
|
14.17
In 1994, the chief executive officers of the major tobacco companies testified before a U.S. senate subcommittee. One of the accusations made was that tobacco firms added nicotine to their cigarettes, which made them even more addictive to smokers. Company scientists argued that the amount of nicotine in cigarettes depended completely on the size of the tobacco leaf: During poor growing seasons, the tobacco leaves would be smaller than in normal or good growing seasons. However, because the amount of nicotine in a leaf is a fixed quantity, smaller leaves would result in cigarettes having more nicotine (because a greater fraction of the leaf would be used to make a cigarette). To examinie the issue, a university chemist took random samples of tobacco leaves that were grown in greenhouses where the amount of water was allowed to vary. Three different groups of tobacco leaves were grown. Group 1 leaves were grown with about an average season’s rainfall. Group 2 leaves were given about 67% of groups 1’s water, and group 3 leaves were given 33% of group 1’s water. The size of the leaf (in grams) and the amount of nicotine in each leaf were measured.
- Test to determine whether the leaf sizes differ between the three groups.
- B. Test to determine whether the amounts of nicotine differ in the three groups.
|
Size-Group 1
|
Size-Group 2
|
Size-Group 3
|
Nicotine-Group 1
|
Nicotine-Group 2
|
Nicotine-Group 3
|
|
15.43
|
13.50
|
11.17
|
18.34
|
18.17
|
4.87
|
|
37.34
|
25.73
|
10.90
|
17.26
|
13.10
|
13.64
|
|
25.98
|
22.90
|
21.09
|
11.26
|
15.29
|
12.56
|
|
20.44
|
33.02
|
10.52
|
20.09
|
14.44
|
10.66
|
|
18.76
|
34.46
|
22.65
|
13.71
|
15.35
|
7.72
|
|
28.55
|
23.96
|
16.03
|
16.01
|
11.12
|
5.71
|
|
32.08
|
21.16
|
10.09
|
17.04
|
11.20
|
6.92
|
|
30.88
|
13.76
|
12.75
|
16.43
|
15.06
|
11.22
|
|
19.03
|
26.62
|
25.43
|
12.93
|
13.36
|
11.39
|
|
36.07
|
23.84
|
24.36
|
18.82
|
12.63
|
10.60
|
|
29.77
|
25.19
|
14.73
|
14.59
|
13.84
|
8.58
|
|
26.73
|
4.91
|
17.03
|
14.18
|
14.50
|
10.78
|
|
15.24
|
18.98
|
19.00
|
13.21
|
4.87
|
10.39
|
|
15.97
|
26.17
|
12.44
|
14.82
|
12.78
|
9.47
|
|
23.03
|
27.09
|
20.70
|
14.31
|
14.52
|
9.10
|
|
24.86
|
31.27
|
15.78
|
14.51
|
9.84
|
10.55
|
|
19.96
|
29.48
|
14.33
|
17.90
|
12.83
|
12.47
|
|
16.31
|
19.21
|
26.98
|
12.92
|
12.78
|
11.30
|
|
19.45
|
18.43
|
20.92
|
11.30
|
11.91
|
5.73
|
|
33.89
|
25.51
|
16.73
|
13.66
|
13.22
|
11.63
|
|
17.64
|
15.12
|
20.80
|
17.24
|
14.99
|
9.25
|
|
20.03
|
20.25
|
15.54
|
13.58
|
14.23
|
10.17
|
|
35.54
|
25.04
|
21.06
|
15.87
|
11.42
|
10.14
|
|
31.14
|
22.88
|
15.91
|
15.72
|
12.96
|
10.43
|
|
25.78
|
34.16
|
12.69
|
15.28
|
13.35
|
11.75
|
|
18.01
|
20.32
|
22.79
|
16.60
|
13.79
|
11.41
|
|
27.01
|
24.31
|
29.16
|
15.06
|
16.23
|
10.92
|
|
14.24
|
13.21
|
17.27
|
15.69
|
13.07
|
13.26
|
|
23.06
|
13.61
|
14.58
|
14.31
|
13.78
|
11.00
|
|
24.40
|
18.56
|
8.15
|
16.35
|
15.42
|
8.20
|
|
26.64
|
14.71
|
14.17
|
18.12
|
11.76
|
8.55
|
|
18.05
|
12.52
|
10.94
|
16.14
|
14.55
|
8.52
|
|
20.58
|
10.91
|
21.61
|
13.69
|
11.91
|
10.75
|
|
26.51
|
13.07
|
16.56
|
17.12
|
13.60
|
12.55
|
|
33.95
|
22.93
|
14.56
|
15.89
|
12.72
|
6.69
|
|
25.87
|
35.39
|
22.92
|
16.24
|
12.85
|
9.88
|
|
13.49
|
16.04
|
21.57
|
16.17
|
13.45
|
11.04
|
|
27.73
|
32.49
|
10.33
|
13.33
|
12.06
|
10.67
|
|
30.90
|
20.36
|
15.51
|
16.04
|
14.04
|
8.01
|
|
22.36
|
31.56
|
12.91
|
14.18
|
15.12
|
7.44
|
|
24.92
|
7.51
|
2.64
|
14.81
|
13.13
|
10.96
|
|
27.47
|
17.69
|
24.71
|
15.98
|
13.27
|
9.95
|
|
39.81
|
9.97
|
21.20
|
14.68
|
12.76
|
9.29
|
|
14.77
|
26.33
|
24.08
|
15.92
|
14.80
|
11.38
|
|
20.06
|
26.25
|
21.34
|
13.89
|
14.21
|
11.71
|
|
27.96
|
25.60
|
15.21
|
17.83
|
14.46
|
11.37
|
|
21.10
|
12.70
|
27.89
|
19.75
|
14.49
|
9.02
|
|
27.92
|
21.56
|
24.56
|
17.42
|
13.91
|
11.97
|
|
32.14
|
24.61
|
28.16
|
15.04
|
12.07
|
11.05
|
|
39.55
|
27.52
|
19.78
|
14.94
|
14.06
|
11.20
|
14.57
measure the height of the professor, a male student, and a female student. The differences (in centimeters) between the correct dimension and the ones produced by the students are listed here.Can we infer that there are differences in the errors between the subjects being measured? (use a=.05)
Errors in Measuring Heights of
Student Professor Male Student Female Student
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
|
Professor
|
Male student
|
Female student
|
|
Student 1
|
1.4
|
1.5
|
1.3
|
|
Student 2
|
3.1
|
2.6
|
2.4
|
|
Student 3
|
2.8
|
2.1
|
1.5
|
|
Student 4
|
3.4
|
3.6
|
2.9
|
14.71
The data shown here were taken from a 2x3 factorial experiment with four replicas:
|
B1
|
B2
|
|
A1
|
23
|
20
|
|
A1
|
18
|
17
|
|
A1
|
17
|
16
|
|
A1
|
20
|
19
|
|
A2
|
27
|
29
|
|
A2
|
23
|
23
|
|
A2
|
21
|
27
|
|
A2
|
28
|
25
|
|
A3
|
23
|
27
|
|
A3
|
21
|
19
|
|
A3
|
24
|
20
|
|
A3
|
16
|
22
|
- Test at the 5% significance level to determine whether factors A and B interact.
- Test at the 5% significance level to determine whether differences exist between the levels of factor A.
- Test at the 5% significance level to determine whether differences exist between the levels of factor B.
15.8
A multinomial experiment was conducted with k=4. Each outcome is stored as an integer from 1 to 4 and the results of a survey were recorded. Test the following hypotheses.
H0: p1=.15 p2=.40 p3=.35 p4=.10
H! At least one pi is not equal to its specified value
|
Outcomes
|
|
2
|
|
2
|
|
2
|
|
3
|
|
2
|
|
2
|
|
2
|
|
1
|
|
2
|
|
2
|
|
2
|
|
1
|
|
1
|
|
3
|
|
1
|
|
2
|
|
1
|
|
2
|
|
2
|
|
2
|
|
3
|
|
2
|
|
1
|
|
2
|
|
2
|
|
4
|
|
2
|
|
2
|
|
2
|
|
3
|
|
2
|
|
3
|
|
2
|
|
1
|
|
2
|
|
2
|
|
4
|
|
3
|
|
1
|
|
3
|
|
3
|
|
3
|
|
3
|
|
2
|
|
2
|
|
2
|
|
3
|
|
2
|
|
1
|
|
1
|
|
1
|
|
2
|
|
2
|
|
2
|
|
3
|
|
1
|
|
2
|
|
3
|
|
2
|
|
3
|
|
4
|
|
2
|
|
3
|
|
2
|
|
4
|
|
3
|
|
1
|
|
3
|
|
3
|
|
3
|
|
1
|
|
2
|
|
1
|
|
3
|
|
2
|
|
2
|
|
2
|
|
1
|
|
4
|
|
2
|
|
4
|
|
1
|
|
2
|
|
1
|
|
2
|
|
2
|
|
2
|
|
1
|
|
2
|
|
2
|
|
3
|
|
2
|
|
3
|
|
1
|
|
4
|
|
2
|
|
2
|
|
1
|
|
4
|
|
2
|
|
4
|
|
2
|
|
2
|
|
3
|
|
3
|
|
2
|
|
3
|
|
4
|
|
1
|
|
3
|
|
2
|
|
2
|
|
3
|
|
3
|
|
2
|
|
2
|
|
2
|
|
3
|
|
2
|
|
3
|
|
2
|
|
2
|
|
2
|
|
1
|
|
3
|
|
2
|
|
3
|
|
2
|
|
2
|
|
2
|
|
2
|
|
2
|
|
2
|
|
3
|
|
1
|
|
4
|
|
2
|
|
1
|
|
3
|
|
2
|
|
3
|
|
3
|
|
2
|
|
3
|
|
2
|
|
3
|
|
2
|
|
2
|
|
2
|
|
3
|
|
3
|
|
3
|
|
3
|
|
2
|
|
3
|
|
2
|
|
3
|
|
4
|
|
1
|
|
2
|
|
4
|
|
2
|
|
2
|
|
2
|
|
3
|
|
3
|
|
1
|
|
1
|
|
2
|
|
2
|
|
2
|
|
2
|
|
3
|
|
3
|
|
2
|
|
4
|
|
2
|
|
2
|
|
2
|
|
1
|
|
2
|
|
3
|
|
3
|
|
1
|
|
3
|
|
1
|
|
1
|
|
2
|
|
3
|
|
2
|
|
2
|
|
2
|
|
2
|
|
2
|
|
3
|
|
2
|
|
3
|
|
3
|
|
2
|
|
2
|
|
3
|
|
1
|
|
4
|
|
3
|
|
2
|
|
2
|
|
2
|
|
3
|
|
3
|
|
3
|
|
1
|
|
2
|
|
4
|
|
4
|
|
2
|
|
3
|
|
1
|
|
3
|
|
3
|
|
1
|
|
3
|
|
1
|
|
3
|
|
1
|
|
2
|
|
3
|
|
4
|
|
2
|
|
1
|
|
4
|
|
1
|
|
2
|
|
1
|
15.11
Pat Statdud is about to write a multiple choice exam but as usual knows absolutely nothing. Pat plans to guess one of the five choices. Pat has been given one of the professor’s previous exams with the correct answers marked. The correct choices were recorded where 1=(a), 2=(b), 3=(c), 4=(d), and 5=(e). Help Pat determine whether this professor does not randomly distribute the correct answer over the five choices? If this is true, how does it affect Pat’s strategy?
|
Correct choice
|
|
3
|
|
2
|
|
3
|
|
1
|
|
5
|
|
1
|
|
4
|
|
1
|
|
1
|
|
1
|
|
4
|
|
1
|
|
4
|
|
1
|
|
4
|
|
3
|
|
4
|
|
4
|
|
2
|
|
2
|
|
5
|
|
1
|
|
4
|
|
4
|
|
2
|
15.28
The operations manager of a company that manufactures shirts wants to determine whether there are differences in the quality of workmanship among the three daily shifts. She randomly selects 600 recently made shirts and carefully inspects them. Each shirt is classified as either perfect or flawed, and the shift that produced it is also recorded. The accompanying table summarizes the number of shirts that fell into each cell. Do these data provide sufficient evidence to infer that there are differences in quality between the three shifts?
Shift
SHIRT CONDITION 1 2 3
Perfect XXXXXXXXXX
Flawed XXXXXXXXXX
|