A.12 Critical Values for the Ryan–Joiner Test of Normality

686



Appendix Tables



P0(Sϩ Ն c1) ϭ P(Sϩ Ն c1 when H0 is true)



Table A.13 Critical Values for the Wilcoxon Signed-Rank Test

n



c1



P0(Sϩ Ն c1)



3

4



6

9

10

13

14

15

17

19

20

21

22

24

26

28

28

30

32

34

35

36

34

37

39

42

44

41

44

47

50

52

48

52

55

59

61

56

60

61

64

68

71

64

65

69

70

74



.125

.125

.062

.094

.062

.031

.109

.047

.031

.016

.109

.055

.023

.008

.098

.055

.027

.012

.008

.004

.102

.049

.027

.010

.004

.097

.053

.024

.010

.005

.103

.051

.027

.009

.005

.102

.055

.046

.026

.010

.005

.108

.095

.055

.047

.024



5



6



7



8



9



10



11



12



13



n



14



15



16



17



18



19



20



c1



P0(Sϩ Ն c1)



78

79

81

73

74

79

84

89

92

83

84

89

90

95

100

101

104

93

94

100

106

112

113

116

104

105

112

118

125

129

116

124

131

138

143

128

136

137

144

152

157

140

150

158

167

172



.011

.009

.005

.108

.097

.052

.025

.010

.005

.104

.094

.053

.047

.024

.011

.009

.005

.106

.096

.052

.025

.011

.009

.005

.103

.095

.049

.025

.010

.005

.098

.049

.024

.010

.005

.098

.052

.048

.025

.010

.005

.101

.049

.024

.010

.005



Appendix Tables



P0(W Ն c) ϭ P(W Ն c when H0 is true)



Table A.14 Critical Values for the Wilcoxon Rank-Sum Test

m



n



c



P0(W Ն c)



3



3

4



15

17

18

20

21

22

23

24

24

26

27

27

28

29

30

24

25

26

27

28

29

30

30

32

33

34

33

35

36

37

36

38

40

41

36

37

39



.05

.057

.029

.036

.018

.048

.024

.012

.058

.017

.008

.042

.024

.012

.006

.057

.029

.014

.056

.032

.016

.008

.057

.019

.010

.005

.055

.021

.012

.006

.055

.024

.008

.004

.048

.028

.008



5

6



7



8



4



4



5



6



7



8



5



5



687



m



n



6



7



8



6



6



7



8



7



7



8



8



8



c



P0(W Ն c)



40

40

41

43

44

43

45

47

48

47

49

51

52

50

52

54

55

54

56

58

60

58

61

63

65

66

68

71

72

71

73

76

78

84

87

90

92



.004

.041

.026

.009

.004

.053

.024

.009

.005

.047

.023

.009

.005

.047

.021

.008

.004

.051

.026

.011

.004

.054

.021

.01

.004

.049

.027

.009

.006

.047

.027

.01

.005

.052

.025

.01

.005



688



Appendix Tables



Table A.15 Critical Values for the Wilcoxon Signed-Rank Interval

n

5

6



7



8



9



10



11



12



Confidence

Level (%)



c



n



93.8

87.5

96.9

93.7

90.6

98.4

95.3

89.1

99.2

94.5

89.1

99.2

94.5

90.2

99.0

95.1

89.5

99.0

94.6

89.8

99.1

94.8

90.8



15

14

21

20

19

28

26

24

36

32

30

44

39

37

52

47

44

61

55

52

71

64

61



13



14



15



16



17



18



19



(xෆ(n(nϩ1)/2Ϫcϩ1), xෆ(c))



Confidence

Level (%)



c



n



99.0

95.2

90.6

99.1

95.1

89.6

99.0

95.2

90.5

99.1

94.9

89.5

99.1

94.9

90.2

99.0

95.2

90.1

99.1

95.1

90.4



81

74

70

93

84

79

104

95

90

117

106

100

130

118

112

143

131

124

158

144

137



20



21



22



23



24



25



Confidence

Level (%)

99.1

95.2

90.3

99.0

95.0

89.7

99.0

95.0

90.2

99.0

95.2

90.2

99.0

95.1

89.9

99.0

95.2

89.9



c

173

158

150

188

172

163

204

187

178

221

203

193

239

219

208

257

236

224



Appendix Tables



Table A.16 Critical Values for the Wilcoxon Rank-Sum Interval



689



(dij(mnϪcϩ1), dij(c))



Smaller Sample Size

5



6



7



8



Larger

Sample Size



Confidence

Level (%)



c



Confidence

Level (%)



c



Confidence

Level (%)



c



Confidence

Level (%)



c



5



99.2

94.4

90.5

99.1

94.8

91.8

99.0

95.2

89.4

98.9

95.5

90.7

98.8

95.8

88.8

99.2

94.5

90.1

99.1

94.8

91.0

99.1

95.2

89.6



25

22

21

29

26

25

33

30

28

37

34

32

41

38

35

46

41

39

50

45

43

54

49

46



99.1

95.9

90.7

99.2

94.9

89.9

99.2

95.7

89.2

99.2

95.0

91.2

98.9

94.4

90.7

99.0

95.2

90.2

99.0

94.7

89.8



34

31

29

39

35

33

44

40

37

49

44

42

53

48

46

58

53

50

63

57

54



98.9

94.7

90.3

99.1

94.6

90.6

99.2

94.5

90.9

99.0

94.5

89.1

98.9

95.6

89.6

99.0

95.5

90.0



44

40

38

50

45

43

56

50

48

61

55

52

66

61

57

72

66

62



99.0

95.0

89.5

98.9

95.4

90.7

99.1

94.5

89.9

99.1

94.9

90.9

99.0

95.3

90.2



56

51

48

62

57

54

69

62

59

75

68

65

81

74

70



6



7



8



9



10



11



12



Smaller Sample Size

9



10



11



12



Larger

Sample Size



Confidence

Level (%)



c



Confidence

Level (%)



c



Confidence

Level (%)



c



Confidence

Level (%)



c



9



98.9

95.0

90.6

99.0

94.7

90.5

99.0

95.4

90.5

99.1

95.1

90.5



69

63

60

76

69

66

83

76

72

90

82

78



99.1

94.8

89.5

99.0

94.9

90.1

99.1

95.0

90.7



84

76

72

91

83

79

99

90

86



98.9

95.3

89.9

99.1

94.9

89.6



99

91

86

108

98

93



99.0

94.8

89.9



116

106

101



10



11



12



690

Appendix Tables



Table A.17 ␤ Curves for t Tests

␤

1.0



␤



␣ ϭ .05, two-tailed



1.0



␣ ϭ .05, one-tailed



df ϭ 1



.8



.8

99

74

49

39

29



.6



.6

29

39

49



.4



.4



.2

19 14 9 6



df ϭ 2



3



4



.2



74

19

99



0



0.4



0.8



1.2



1.6



2.0



2.4



2.8



3.2



d



0



␤



2



0.4



0.8



4

14



9



1.2



3



6



1.6



2.0



2.4



d



2.8



␤



1.0



1.0



␣ ϭ .01, two-tailed



␣ ϭ .01, one-tailed

.8



df ϭ 2



.8

df ϭ 2



.6



.6

3

39



3

49



.4



.2



14

99



0



0.4



9



74



6



1.2



1.6



2.0



2.4



4



.2



4



99



29 19

0.8



39

29

19



.4



74



2.8



3.2



d



0



49

0.4



6

9



14

0.8



1.2



1.6



2.0



2.4



2.8



3.2



d



Answers to Selected

Odd-Numbered Exercises



Chapter 1

1. a. Los Angeles Times, Oberlin Tribune, Gainesville Sun,

Washington Post

b. Duke Energy, Clorox, Seagate, Neiman Marcus

c. Vince Correa, Catherine Miller, Michael Cutler, Ken Lee

d. 2.97, 3.56, 2.20, 2.97

3. a. How likely is it that more than half of the sampled computers will need or have needed warranty service? What is

the expected number among the 100 that need warranty

service? How likely is it that the number needing warranty

service will exceed the expected number by more than 10?

b. Suppose that 15 of the 100 sampled needed warranty

service. How confident can we be that the proportion of all

such computers needing warranty service is between .08

and .22? Does the sample provide compelling evidence for

concluding that more than 10% of all such computers need

warranty service?

5. a. No. All students taking a large statistics course who participate in an SI program of this sort.

b. Randomization protects against various biases and helps

ensure that those in the SI group are as similar as possible to

the students in the control group.

c. There would be no firm basis for assessing the effectiveness of SI (nothing to which the SI scores could reasonably

be compared).

7. One could generate a simple random sample of all singlefamily homes in the city, or a stratified random sample by

taking a simple random sample from each of the 10 district

neighborhoods. From each of the selected homes, values of

all desired variables would be determined. This would be an

enumerative study because there exists a finite, identifiable

population of objects from which to sample.



9. a. Possibly measurement error, recording error, differences

in environmental conditions at the time of measurement, etc.

b. No. There is no sampling frame.



|

|

|

|

|

|

||



11. 6L 430

6H 769689

7L 42014202

7H

8L 011211410342

8H 9595578

9L 30

9H 58

The gap in the data—no scores in the high 70’s.

13. a. 12 2

leaf: ones digit

12 445

12 6667777

12 889999

13 00011111111

13 222222222233333333333333

13 44444444444444444455555555555555555555

13 6666666666667777777777

13 888888888888999999

14 0000001111

14 2333333

14 444

14 77

symmetry

b. Close to bell-shaped, center Ϸ 135, not insignificant dispersion, no gaps or outliers.



691