Applied Statistics and Probability for Engineers

APPENDIX C 687

(d) (69.17, 81.81)

(e) (8.42, 26.33)

13-19. 5

Section 13-3

13-21.(a) RejectH 0 (b) 0.01412

(c) 0.0148

13-23.(a) Do not rejectH 0 (b) 0

(c) 24

Section 13-4

13-25.(a) Reject H 0

13-27.(a) Do not rejectH 0

13-29.(a) Do not rejectH 0

Supplemental

13-31.(a) RejectH 0

(c) (132.97, 147.83)

13-35.(a) RejectH 0

(b)P-value0.007

13-37.(a) Reject H 0

13-39.(a) 0.85 (b) 5

CHAPTER 14

Section 14-4

14-1. (a) Reject H 0 for both main

effects and the interaction

14-3. (a) RejectH 0 for main effects

14-7. (3.40, 7.64)

14-9. (a) RejectH 0 for both main

effects and the interaction

Section 14-5

14-11.(a) All these main effects are

significant and the hardwood

concentration-freeness inter-

action is significant at

  0.05. The P-value for

the hardwood-cooking time

interaction is 0.075, it is

possibly an important effect

as well.

Section 14-7

14-13.(a) RejectH 0 for factors B, C,

and AC

(b)

14-15.

14-17.(b) Reject H 0 for factor B

14-19.(a) Factors A, B, C, and AB

5.19x 2 0.19x 4 4.62x 1 x 4

yˆ175.254.12x 1 

59.62x 1 x 3

45.12x 2 35.87x 3 

yˆ413.1259.125x 1 

14-21.(b) Factors A, B, and AB

(c)

Section 14-8

14-23.Block 1: (1)ab ac bc

Block 2: a b c abc

There are no significant factors

14-25.Block 1: (1)ac bd abcd

Block 2: a c abd bcd

Block 3: b abc d acd

Block 4: ab bc ad cd

Factor A is significant

14-27.Block 1: (1)ab de acd bcd ace

bce abde

Block 2: a b cd ce ade bde abce

abcd

Block 3: d e bc bd abd abe acde

bcde

Block 4: c ad ae bd be abc cde

abcde

14-29.(a) Factors A, C, AB, and ACare

significant

Section 14-9

14-31.(a) Factors A, B, and Dare

significant

(c) Factors A, B, D, AB, and

ADare significant

14-33.(b) Design Generators: DAB,

EAC; Defining Relation: I

ABDACEBCDE; Aliases:

ABDCDABCDE, B

ADCDEABCE; C

AEBDEABCD, D

ABBCEACDE, E

ACBCDABDE(c)A

1.525, B5.175, C

2.275, D0.675, E2.275

14-35. 24 ^1 replicated twice

14-37.Factors A, B, and Dare significant

14-39.Design Generators: DAB,

EAC, FBC; Defining

Relations: IABDACE

BCFBCDEACDF

ABEFDEF; Aliases: A

BDCE, BADCF, C

AEBF, DABEF, E

ACDF, FBCDE,

ABEF, AFBECD

Supplemental

14-41.The main effect of pH and

the interaction of pH and

32.75x 2 26.625x 1 x 2

yˆ 400 40.124x 1 

Catalyst Concentration are sig-

nificant

14-43.The salts, application levels, and

the interaction between salts and

application levels are significant

14-45.There are no significant factors

14-47.(a) The factors V, P, G, and PG

are significant. Effects

P10.75, V15.75,

G25.00, PG19.25

(b)

14-49.The factors Vand Gare signifi-

cant at0.10.

14-51.Design Generators: DAB,

EAC; Defining Relations: I

ABDACEBCDE;

Aliases: ABDCE, B

ADCDE, CAEBDE,

DABBCE, EAC

BCD, BCDE, BECD

14-53.(a)EABCD(b) Factors A,

B, C, E, and interaction BEare

significant (c) Factor Ais sig-

nificant in affecting variability

CHAPTER 15

Section 15-2

15-1. Do not reject H 0 , P-value

0.109

15-3. Reject H 0 , P-value0.0002

15-5. (a) Do not rejectH 0

(b)z 0 0.577, P-value0.281

15-7. z 0 1.34, do not reject H 0 ,

P-value0.1802

15-9. Do not rejectH 0

15-11.z 0 2.24, reject H 0

15-13.Reject H 0

15-15.z 0 2.84, reject H 0

15-17.(a) 0.025 (b) 0.115

(c) 0.011 (d) 0.1587

15-19.P-value0.04

Section 15-3

15-21.w 71  52, do not reject H 0

15-23.w 8  65, reject H 0

15-25.w 25  52, reject H 0

15-27.w 1  25, reject H 0

Section 15-4

15-29.w 38  23, do not reject H 0

14.12x 1 13.13x 4

yˆ100.63

9.62x 2 x 4

5.37x 2 12.50x 4 

yˆ102.757.88x 1 

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