Applied Statistics and Probability for Engineers

688 APPENDIX C ANSWERS TO SELECTED EXERCISES

15-31.z 0 2.78, do not reject H 0 ,

P-value0.9973

15-33.w 55  78, reject H 0

15-35.z 0 3.77, reject H 0 ,

P-value0.0001

Section 15-5

15-37.RejectH 0

15-39.Do not rejectH 0

15-41.P-value0.018

Supplemental

15-43.Do not rejectH 0 , P-value  1

15-45.Do not rejectH 0

15-47.Do not rejectH 0

15-49.RejectH 0

15-51.RejectH 0

15-53.RejectH 0

15-55.RejectH 0 , P-value  0

15-57.RejectH 0 , P-value0.009

CHAPTER 16

Section 16-5

16-1. (a) chart: UCL37.5789,

CL34.32, LCL31.0611

R chart: UCL11.9461,

CL5.65, LCL 0

(b) 1 point outside limits on

chart. Revised limits:

chart: UCL37.4038, CL

34.0947, LCL30.7857,

R chart: UCL12.1297,

CL5.7368, LCL 0

16-3. (a) chart: UCL17.40,

CL15.09, LCL12.79

Rchart: UCL5.792,

CL2.25, LCL 0

(b) chart: UCL17.96,

CL15.78, LCL16.62

Rchart: UCL5.453,

CL2.118, LCL 0

(c) chart: UCL17.42,

CL15.09, LCL12.77

schart: UCL3.051,

CL1.1188, LCL 0

revised limits: chart:

UCL17.95, CL15.78,

LCL13.62, schart:

UCL2.848, CL1.109,

LCL 0

x

x

x

x

x

x

x

16-5. (a) chart: UCL242.78,

CL223, LCL203.22

Rchart: UCL72.51,

CL34.286, LCL 0

(b) ,

16-7. (a) chart: UCL0.06347,

CL0.06294,

LCL0.0624 Rchart:

UCL0.001954,

CL0.000924, LCL 0

(b) chart: UCL0.06346,

CL0.06295,

LCL0.06241 schart:

UCL0.000766,

CL0.000367, LCL 0

(c) The points are 1, 5, 14, 17,

20, 21, and 22; or outside

the control limits of the

Rchart: 6 and 15

Section 16-6

16-9. (a)I chart: UCL60.8887,

CL53.05, LCL45.2113

MRchart: UCL9.63382,

CL2.94737, LCL 0

(b) ,

16-11.(a)Ichart: UCL10.5358,

CL10.0272,

LCL9.51856 MRchart:

UCL0.625123,

CL0.19125, LCL 0

(b) ,

Section 16-7

16-13.(a)PCRPCRk1.5

(b) 0

16-15.(a) 0.00075 (b)PCR1.13,

PCRk1.104

16-17.(a)PCRPCRk1.18

(b) 0.00046

16-19.(a) 0.0009 (b)PCR1.13,

PCRk1.06

16-21.PCR0.50, PCRk0.357

16-23.PCR0.49, PCRk0.474

Section 16-8

16-25.(a)Uchart: UCL3.811,

CL1.942, LCL0.0722

(b) Revised limits: Uchart:

UCL3.463,

CL1.709, LCL 0

ˆ10.027 ˆ0.1696

ˆ53.05 ˆ2.613

x

x

ˆ 223 ˆ14.74

x 16-27.(c) chart: UCL19.06,

CL9.708, LCL0.3609

Section 16-9

16-29.(a) 0.2177 (b) 4.6

16-31.(a) 0.1020 (b) 9.8

16-33.(a) 0.0548 (b) 18.25

16-35.(a) 0.1515 (b) 6.6

16-37.(a) 0.16603 (b) 6.02

Section 16-10

16-39.(a)

16-41.(a) ARL38.0

(b) ARL10.4

Supplemental

16-43.(a) chart: UCL64.0181,

CL64.0, LCL63.982

Rchart: UCL0.0453972,

CL0.01764, LCL 0

(b) ,

(c)PCR0.641,

(d)PCRk0.641

(e) ,

(f) 0.1705, ARL5.87

16-45.(a)p chart: UCL0.20387,

CL0.11, LCL0.01613

(b)pchart: UCL0.1717,

CL0.106,

LCL0.04092

16-47.(a)cchart: UCL7.51442,

CL2.64, LCL 0

(b)cchart: UCL6.50924,

CL2.1304, LCL 0

16-49.(b) 6.30 (c) 2

16-51.(a) chart: UCL140.168,

CL139.49,

LCL138.812 Rchart:

UCL2.48437,

CL1.175, LCL 0

(b) Revised control limits:

chart: UCL140.518,

CL139.808,

LCL139.098 R chart:

UCL2.6023,

CL1.231, LCL 0

(c)PCR1.26, PCRk1.14

(d) 2 0.091

(e) 0.1877, ARL5.33

16-53.(a) 0.96995 (b) 1

16-57.0.000135

x

x

2 0.025

ˆ 64 ˆ0.0104

x

ˆ0.1695

PQ220 6234F._PP(C) 5/8/02 7:45 PM Page 688 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:PQ220 MONT 8/5/2002: NS_C: