Applied Statistics and Probability for Engineers

686 APPENDIX C ANSWERS TO SELECTED EXERCISES

(b) (272.44, 308.44)

(c) (257.25, 323.64)

12-31.(a)0.595  2 0.535,

0.229  3 0.812,

0.216  4 0.013,

7.298  5 2.977

(b) (7.982, 10.009)

(c) (6.8481, 11.143)

12-33.(a)0.00003 Temp

0.00012, 0.00203 soaktime

0.00288, 0.02306

soakpct0.05976,

0.00501 DFtime

0.01056, 0.01969 

Diffpct0.01342

(b) (0.0206, 0.0234)

12-35.(a) (0.3882, 0.5998)

(b)y5.767703 

0.496501xPts

(c) (0.4648, 0.5282)

Section 12-5

12-37.(a) 0.82897 (d) No

12-39.(a) 0.985 (b) 0.99

12-41.(b) 0.9937

12-43.(a) 0.9582 (c) 32

12-45.(a) 0.12

(b) 17 and 18

Section 12-6

12-47.(a)

(b)f 0 1858613, reject H 0

(c)t 0 601.64, reject H 0

12-49.(a) 802.943

(b)

12-51.(a)

0.222x 2 0.128x 3 

0.02x 1 x 2 0.009x 1 x 3 

0.003x 2 x 3 0.019x 12 

0.007x 22 0.001x 32

(b)f 0 19.628, reject H 0

(d)f 0 1.612, do not reject H 0

12-55.(a) Min. MSE: x 1 , x 3 , x 4 , x 5 , x 7 ,

x 8 , x 10 , MSE6.58,

Cp5.8, Min. Cp: x 5 , x 8 , x 10 ,

Cp5.02, MSE7.97

(b)

(c) Same as part (b)

(d)

0.246x 8 0.010x 10 ,

MSE7.97, Cp5.02

yˆ0.3412.862x 5 

MSE8.81, Cp5.55

yˆ34.4340.048x 1 ,

yˆ1.7690.421x 1 

0.331x^2

yˆ26204.14189.09x

1.495x^2

yˆ1.6331.232x

12-57.(a)y4.656 0.511x 3 

0.124x 4

(b) Same as part (a)

(c) Same as part (a)

(d) All models are the same

12-59.(a)

(b)

,

12-61.(a) Min. Cp: x 1 , x 9 , Cp1.67

(b) Min. MSE: x 1 , x 7 , x 9 ,

MSE1.67, Cp0.77

(c) Max. adjusted R^2 : x 1 , x 7 , x 9 ,

Adj. R^2 0.98448

Supplemental

12-65.(a)f 0 1323.62, reject H 0

P-value  0.00001

(b) Only regressor x 4 is

significant H 0

12-67.(a) 0.908 5.482x 1 *

1.126x 2 *3.920x 3 * 1.143x 4 *

(b)f 0 109.02, reject H 0 , all

regressors are significant

12-69.(a) 1.0964x 1 

0.1843x 3 3.7456x 4 

0.8343x 5 16.2781x 6 ,

MSE(p) 694.93,Cp5.62

(b) 1.442x 1 

0.209x 3 0.6467x 5 

17.5103x 6 , MSE(p) 

714.20, Cp5.57

(c) Same as model b

12-71.

12-73.(a)f 0 18.28, reject H 0

(b)f 0 2, do not reject H 0

CHAPTER 13

Section 13-2

13-1. (a) RejectH 0

(b) Model is satisfactory

13-3. (a) RejectH 0 (b)P-value  0

13-5. (a) RejectH 0 (c) (140.71,

149.29), (7.36, 24.14)

13-7. (a) Do not rejectH 0

(b)P-value0.214

13-9. (a) RejectH 0

(b)P-value0.002

VIF 1 ˆ 52 28.99

VIF 1 ˆ 42 9.11

VIF 1 ˆ 3 * 2 51.86,

yˆ4280.2

yˆ3982.1

yˆ

Cp4.66, MSE0.004

0.0008x 32

0.022x 2 0.042x 3 

yˆ0.2560.078x 1 

Cp4.04, MSE0.004

0.031x 3 0.004x 22 ,

yˆ0.3040.083x 1 

12-9. (a)

(b) 12 (c)

(d) 91.43

12-11.

Section 12-2

12-13.(a) 260.09, reject H 0

(b) reject H 0 both significant

12-15.(a)f 0 25.7465, reject H 0

P-value 0.000001

(b) Reject H 0 , all coefficients

are significant

12-17.(a)f 0 53.3162, reject H 0

(b) Only  1 is significant

12-19.(a)f 0 10.08, P-value0.005

(b) Only  1 is significant

12-21.(a)f 0 67.92, reject H 0

(b)f 0 1.07, do not reject H 0

(c) 147.0

12-23.(a)f 0 850.55, reject H 0

(b) Regression coefficients for

x 1 and x 3 are significant

12-25.(a)f 0 101.79, reject H 0

(b) Only regression coefficient

for “PTS” is significant

(c)

reject H 0 only regressor

“PTS” is significant

Section 12-3 and Section 12-4

12-27.(a) (0.00657, 0.00122)

(b) 0.497648 (c) (7.16, 9.22)

12-29.(a) 0.0972  1 1.4174,

1.9646  2 17.0026,

1.7953  3 6.7613,

1.7941  4 0.8319

0.004xPPG, f 0 510.12

yˆ5.5310.497xPTS

se 1 ˆ 92 0.1110

se 1 ˆ 82 0.1483,

se 1 ˆ 72 0.038,

se 1 ˆ 62 0.0266,

se 1 ˆ 52 0.2611,

se 1 ˆ 42 0.0515,

se 1 ˆ 32 0.0209,

se 1 ˆ 22 0.0064,

se 1 ˆ 12 0.0481,

ˆ^2 2.32,se 1 ˆ 02 16.18,

0.0407x 8 0.2083x 9

0.0128x 6 0.030x 7

0.0383x 4 0.2068x 5

0.0018x 2 0.0023x 3

yˆ8.01190.494x 1

se 1 ˆ 32 1.312

se 1 ˆ 22 0.2239,

se 1 ˆ 12 3.6916,

se 1 ˆ 02 49.5815,

0.4283x 2 18.2375x 3

yˆ47.1749.7352x 1

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