Applied Statistics and Probability for Engineers 7th Edition

Because the confidence interval contains only negative values, the absorbency of towel 1 is less than that of towel 2. The confidence interval does not contain zero. Therefore, the hypothesis test for the equality of means would reject the null hypothesis (that the means do not differ) at 0.05=.

6) Reject the null hypothesis if 12 0 1 /2, 1, 1 0.975,12,13 0.025,13,12 11 0.308 3.23 nn f f f f = = = = or 120 /2, 1, 1 0.025,12,13 3.15nnf f f = = for 0.05=. 120 /2, 1, 1 0.025,12,13 3.15nnf f f = = for 0.05=. 12 0 /2, 1, 1 0.025,12,13

CHAPTER 10 RESERVE PROBLEMS The following problems have been reserved for your use in assignments and testing and do not appear in student versions of the text. Reserve Problems Chapter 10 Section 1 Problem 1 Consider the hypothesis test 0 1 2 :0H = against 1 1 2 :0H samples below: I

CHAPTER 10 Section 10.1 10.1.1 a) 1) The parameter of interest is the difference in means 1 2. Note that 0 = 0. 2) H0 : 1 2 = 0 or 1 2 3) H1 : 1 2 0 or 1 2 4) The test

(d) 0.1 = , 0.05 = . For a two-sided alternative, the common sample size is 212()npp= ( )( ) ( ) ( )220.85 0.75 0.15 0.25(1.96 1.28 0.85 0.15 0.75 0.25 )2333.8(0.85 0.75)n++++== 334n= 212()npp= ( )( ) ( ) ( )220.85 0.75 0.15 0.25(1.96 1.28 0.85 0.15 0.75 0.25 )2333.8(0.85

b) =0.667d sd = 2.964, n = 12 = 0.05 95% confidence interval: + + /2, 1 /2, 12.964 2.9640.667 2.201 0.667 2.20112 121.216 2.55ddnddndssd t d tnn Because zero is contained within this interval, one cannot conclude that one design language is preferable at a 5% significance

CHAPTER 11 RESERVE PROBLEMS The following problems have been reserved for your use in assignments and testing and do not appear in student versions of the text. Reserve Problems Chapter 11 Section 2 Problem 1 The department of health studied the number of patients who need liver transplantation. The

(c) Delete the two points identified in part (b) from the sample and fit the simple linear regression model to the remaining 18 points. Calculate the value of 2 R for the new model. Is it larger or smaller than the value of 2 R computed in part (a)? Why?

Applied Statistics and Probability for Engineers, 7th edition 2017 11-21 11.7.6 a) R2 = 71.27% b) No major departure from normality assumptions. c) Assumption of constant variance appears reasonable. b) No major departure from normality assumptions. c) Assumption of constant variance appears reasonable. b) No major departure from normality

Applied Statistics and Probability for Engineers, 7th edition 2017 11-32 b) The P-value for the test of the coefficient of load is near zero. Therefore, load has a significant effect on failing performance. b) The P-value for the test of the coefficient of load is near zero.

Applied Statistics and Probability for Engineers, 7th edition 2017 11-1 CHAPTER 11 Section 11-2 11.2.1 a) 01i i i yx = + + 2 6322.28 162674.2 2789.282 250 xx S= = (6322.28)(4757.9)125471.1 5147.996250xyS= = 105147.9961.8462789.28219.032 (1.846)(25.289) 27.643xyxxSS= = == = 27.643 1.846yx= + 1217128.82 1.846(5147.996) 30.7562 2 248T xyEESS SSSMS

5.71 66.5 Assuming that a simple linear regression model is appropriate, fit the regression model relating the rating (y) to the average number of yards gained per pass attempt (x). Find a 95% confidence interval on each of the following: a. Slope b. Intercept c. Mean rating when the average

Applied Statistics and Probability for Engineers, 7th edition 2017 12-1 12-1 12-1 CHAPTER 12 Sections 12.1 12.1.1 Exercise 11.2.1. described a regression model between percent of body fat (%BF) as measured by immersion and BMI from a study on 250 male subjects. The researchers also

Predictor Coef SE Coef T P Constant 7.6443 0.9530 8.02 0.015 Liquid soap -0.00268 0.05574 -0.05 0.966 Sugar 3.232 3.109 1.04 0.408 Glycerol -0.2643 0.2357 -1.12 0.379 Water -0.2518 0.1520 -1.66 0.239 S = 0.0323160 R-Sq = 71.9% R-Sq(adj) = 15.7% Liquid soap -0.00268 0.05574 -0.05 0.966 Sugar

(b) Calculate a 95% confidence interval on mean stack loss when 180x= , 220x= , and 390x= . (c) Calculate a 95% prediction interval on stack loss for the same values of the regressors used in part (b). (d) Calculate a 95% confidence interval and a 95% prediction interval on

Applied Statistics and Probability for Engineers, 7th edition 2017 12-21 (b) E ==21( ) 1.539jjse c H0: 1 = 0 H1: 1 0 = 0.05 ===101()7.03 4.5681.539tse ==0.025,9 3 0.025,6 2.447tt 0 /2,6| | ,tt Reject H0, 1 is significant in the model at = 0.05. ==22( ) 1.539jjse

CHAPTER 12 RESERVE PROBLEMS The following problems have been reserved for your use in assignments and testing and do not appear in student versions of the text. Reserve Problems Chapter 12 Section 1 Problem 1 During a research, the amount of Internet users was measured. Each time three random

Applied Statistics and Probability for Engineers, 7th edition 2017 Applied Statistics and Probability for Engineers, 7th edition 2017 Applied Statistics and Probability for Engineers, 7th edition 2017 12-41 Applied Statistics and Probability for Engineers, 7th edition 2017 12-42 Sections 12.6 12.6.1 An article entitled A Method

Applied Statistics and Probability for Engineers, 7th edition 2017 12-55 12-55 12-55 (d) Stepwise Regression: W versus GF, GA, ... Backward elimination. Alpha-to-Remove: 0.1 Response is W on 14 predictors, with N = 30 Step 1 2 3 4 5 6 Constant 512.2 513.0

(a) What proportion of total variability is explained by this model? (b) Are there any influential points in these data? SOLUTION The regression equation is Rating Pts 2.99 1.20Pct Comp 4.60Pct TD 3.81Pct Int= + + Predictor Coef Constant 2.986 Pct Comp 1.19857 Pct

Fit a multiple regression model to relate the quarterback rating to the percentage of completions, the percentage of TDs, and the percentage of interceptions. (a) Test for significance of regression using 0.05 = . What is the P-value for this test? (b) Conduct the t-test for each regression coefficient. Use 0.05 = .

0 1 2 3 4: 0;H = = = = 1:0jH at least one 0.05=, ( )44regDF regressors=, ( )16 21 1 4errDF observation estimators= 0.05,4,16 3.01f= 013.45f= 0 0.05,4,16ff, reject 0H at significance level 0.05=. 0 0.01,4,16 4.77ff=, therefore P-value 0.01; 0 0.001,4,16 7.94ff=, therefore P-value 0.001; We

CHAPTER 13 RESERVE PROBLEMS The following problems have been reserved for your use in assignments and testing and do not appear in student versions of the text. Reserve Problems Chapter 13 Section 2 Problem 1 Consider the tensile strength example in the table below. Tensile Strength of Paper (psi)

There is some indication of a greater variability for the FasT method. The normal probability plot looks acceptable. There is some indication of a greater variability for the FasT method. The normal probability plot looks acceptable. There is some indication of a greater variability for the FasT method. The normal

Applied Statistics and Probability for Engineers,7th edition 2017 13-1 CHAPTER 13 Section 13.2 13.2.1 Consider the following computer output. Source DF SS MS F P-value Factor ? 117.4 39.1 ? ? Error 16 396.8 ? Total 19 514.2 (a)

Applied Statistics and Probability for Engineers,7th edition 2017 13-36 13-36 13-36 (c) Analysis of Variance for LEAKAGE VOLTAGE Source DF SS MS F P LENGTH 3 8.1775 2.7258 6.16 0.009 WIDTH 4 6.8380 1.7095 3.86 0.031 Error 12 5.3100 0.4425 Total 19 20.3255 Reject H0. And conclude that

SOLUTION ANOVA output: Source DF SS MS F P Factor 2 0.144 0.072 0.443 0.644 Error 72 11.696 0.1624 Total 74 11.84 Error 72 11.696 0.1624 Total 74 11.84 Error 72 11.696 0.1624 Total 74 11.84 20.1624errorMS== 20.072 0.1624 0.003625treatments errorMS MSn= = =

Applied Statistics and Probability for Engineers,7th edition 2017 Applied Statistics and Probability for Engineers,7th edition 2017 Applied Statistics and Probability for Engineers,7th edition 2017 13-21 Applied Statistics and Probability for Engineers,7th edition 2017 13-22 Cross-linker level ---------+---------+---------+---------+ 0.5 (---*---) 1 (---*---) ---------+---------+---------+---------+ -0.50 0.00 0.50 1.00 ---------+---------+---------+---------+

Applied Statistics and Probability for Engineers, 7th edition 2017 Applied Statistics and Probability for Engineers, 7th edition 2017 Applied Statistics and Probability for Engineers, 7th edition 2017 14-21 14.5.5 An article in Journal of Construction Engineering and Management (Analysis of Earth-Moving Systems Using DiscreteEvent Simulation, 1995, Vol. 121(4), pp. 388396)

Applied Statistics and Probability for Engineers, 7th edition 2017 14-80 (c) The normal probability plot does not suggest a departure from normality. The assumption of constant variance may be of concern. It appears that the variability is lower for the high level of the factor A. The

A*B*C*D 1 0.0 0.0 0.03 0.00 0.954 A*B*C*E 1 0.3 0.3 0.28 0.03 0.862 A*B*D*E 1 7.0 7.0 7.03 0.86 0.407 A*C*D*E 1 0.8 0.8 0.78 0.10 0.773 B*C*D*E 1 7.0 7.0 7.03 0.86 0.407 5-Way Interactions 1 0.3 0.3 0.28 0.03 0.862 A*B*C*D*E 1 0.3 0.3 0.28 0.03 0.862

Applied Statistics and Probability for Engineers, 7th edition 2017 14-41 In this model with blocking there are no significant factors. 14.8.5 An article in Quality Engineering [Designed Experiment to Stabilize Blood Glucose Levels (19992000, Vol. 12, pp. 8387)] reported on an experiment to minimize variations

Source DF SeqSS AdjSS AdjMS F P Main Effects 5 0.1944 0.1944 0.0389 3.3 0.051 A 1 0.0946 0.0946 0.0946 8.02 0.018 B 1 0.0298 0.0298 0.0298 2.52 0.143 C 1 0.0176 0.0176 0.0176 1.49 0.250 D 1 0.0410 0.0410 0.0410 3.48 0.092 E 1 0.0116 0.0116 0.0116 0.98 0.345

15 65 0.12 0.75 0 2 0 1.153 16 65 0.5 0.75 0 2 0 6.333 17 65 0.25 0.42 0 0 2 2.533 18 65 0.25 1.33 0 0 2 3.2 19 28 0.25 0.75 2 0 0 3.233 20 150 0.25 0.75 2 0 0 2.967 21 65

CHAPTER 14 RESERVE PROBLEMS Please note that the values in the problem statements for this chapter may not be consistent with the values that appear in your evaluation copy. The following problems have been reserved for your use in assignments and testing and do not appear in student

Applied Statistics and Probability for Engineers, 7th edition 2017 14-1 CHAPTER 14 Section 14.3 14.3.1 An article in Industrial Quality Control (1956, pp. 5 8) describes an experiment to investigate the effect of two factors (glass type and phosphor type) on the brightness of a television tube.

Applied Statistics and Probability for Engineers, 7th edition 2017 Applied Statistics and Probability for Engineers, 7th edition 2017 Applied Statistics and Probability for Engineers, 7th edition 2017 14-61 14.11.5 An article in Tappi (1960, Vol. 43, pp. 3844) describes an experiment that investigated the ash value of paper pulp (a

Reserve Problems Chapter 14 Section 6 Problem 1 An article in the Annals of Nuclear Energy (Statistical Analysis of the Fort Calhoun Reactor Coolant Pump System, Vol. 24(3), 1997) considered the effect of five factors on a recirculating pump motor power input (kW). The factors were

Analysis of Variance for Production (coded units) Source DF Seq SS Adj SS Adj MS F P Blocks 1 10 10 10 0.00 0.947 Main Effects 2 168539 168539 84270 38.32 0.000 NumberTrucks 1 55120 55120 55120 25.07 0.000 Main Effects 2 168539 168539 84270 38.32 0.000 NumberTrucks 1

(< 2.18)=( < 2.181717 ) = ( < 3.59)=02.78 18( 2.78) ( ) ( 3.59) 018P U P Z P Z = = = (b) =5 =+3=13+3135=17.84145 3 14 3 19.025Un UCL U n= = + = + = =3=133135= 8.16143 14 3 8.985ULCL U n= = = (>17.84, =

CHAPTER 15 RESERVE PROBLEMS The following problems have been reserved for your use in assignments and testing and do not appear in student versions of the text. Reserve Problems Chapter 15 Section 3 Problem 1 Control charts are to be constructed for samples of size 5n= , and x and

Applied Statistics and Probability for Engineers, 7th edition 2017 15-60 (c) 2 limits + + = + = =( 2 ) ( 2 ) ( 2) ( 2) 2(0.02275) 0.0455P X X P X X P z P z ARL = 1/p = 1/0.0455 = 21.98. This ARL is

Applied Statistics and Probability for Engineers, 7th edition 2017 15-21 15-21 15-21 (b) Consider a hypothesis test on the mean and standard deviation of data before and after the change (with point 20 removed from the before dataset and point 19 removed from after dataset) Hypothesis test on the

Applied Statistics and Probability for Engineers, 7th edition 2017 Applied Statistics and Probability for Engineers, 7th edition 2017 Applied Statistics and Probability for Engineers, 7th edition 2017 15-41 15.8.4 The concentration of a chemical product is measured by taking four samples from each batch of material. The average concentration of

Applied Statistics and Probability for Engineers, 7th edition 2017 15-1 CHAPTER 15 Section 15-3 15.3.1 Control charts are to be constructed for samples of size n = 4, and x and s are computed for each of 20 preliminary samples as follows: = = 20 1 4460 i i x = = 20 1 271.6 i i s (a)

(<|=45)=( << ) XX=(411545<<41+1545)=(4155<<4+155)15 15 15 1540 44 40 44 4 4( ) ( )55n n n nP Z P Zn n n n + += = 4 4 4 4( 3 3) ( 3) ( 3)5 5 5 5n n n nP Z P Z P Z = + = + 4(

Applied Statistics and Probability for Engineers, 7th edition 2017 2-34 (c) If a product does not attain a good review, what is the probability that it will be a highly successful product? Let G denote a product that received a good review. Let H, M, and P denote products

Applied Statistics and Probability for Engineers, 7th edition 2017 2-21 Let A denote the event that the patient was treated with ribavirin plus interferon alfa, and let B denote the event that the response was complete. Determine the following probabilities: (a) P(A B) (b) P(A B) (c) P(A B)

Applied Statistics and Probability for Engineers, 7th edition 2017 2-1 2-1 2-1 CHAPTER 2 Section 2-1 Provide a reasonable description of the sample space for each of the random experiments in Exercises 2.1.1 to 2.1.11. There can be more than one acceptable interpretation of each experiment. Describe any

Applied Statistics and Probability for Engineers, 7th edition 2017 3-1 CHAPTER 3 Section 3-1 3.1.1 The range of X is {0, 1, 2, , 1000}. 3.1.2 The range of X is {0, 1, 2, 3, 4, 5}. 3.1.3 The range of X is {1, 2, ,

Applied Statistics and Probability for Engineers, 7th edition 2017 3-12 c) = = =3[ ] 150.2rEY p c) = = =3[ ] 150.2rEY p c) = = = 3 [ ] 15 0.2 r EY p 3.6.14 Let X denote the number of customers who visit the website to obtain the

Applied Statistics and Probability for Engineers, 7th edition 2017 4.7.14 a) = = =1( ) 4.6EX, then = 0.2174 ==14.6 b) = = =/4.6 10/ 4.6101( 10) 0.11374.6xP X e dx e c) = = =/4.6 /4.61( ) 0.254.6uxxP X x e du e Then, x = 4.6 ln(0.25) =

Applied Statistics and Probability for Engineers, 7th edition 2017 CHAPTER 4 Section 4.1 4.1.1 a) = = = =111(1 ) ( ) 0.3679xxP X e dx e e b) = = = =2.5 2.5 1 2.511(1 2.5) ( ) 0.2858xxP X e dx e e e c)

CHAPTER 4 RESERVE PROBLEMS The following problems have been reserved for your use in assignments and testing and do not appear in student versions of the text. Reserve Problems Chapter 4 Section 1 Problem 1 A parabolic satellite dish reflects signals to the dishs focal point. An antenna designer

(d) 117000( ) 0.02.xP X x e = =Therefore, ( ) ( )17000 ln 0.02 66504.39x= = 117000( ) 0.02.xP X x e = =Therefore, ( ) ( )17000 ln 0.02 66504.39x= = 1 17000 ( ) 0.02. x P X x e = = Therefore, ( ) ( ) 17000 ln 0.02 66504.39x= = Reserve

CHAPTER 5 RESERVE PROBLEMS The following problems have been reserved for your use in assignments and testing and do not appear in student versions of the text. Reserve Problems Chapter 5 Section 1 Problem 1 Let the random variable X denote the time until a computer server connects to

From the second equation 20YYYXXXand = = and these can be written as 2XYY Y XXand ==. From the first equation above ( )2222212X=. Because 1x=, the previous equation can be solved for to yield ( )22412= and 0.816=. Then 2222.45 60.816XYYand= = = =. Also, 2.45 0.816 0 01YYXX

Applied Statistics and Probability for Engineers, 7th edition 2017 5-1 CHAPTER 5 Section 5-1 5.1.1 First, f(x,y) 0. Let R denote the range of (X, Y) Then, = + + + + = 1 1 1 1 1 ( , ) 1 4 8 4 2 4 R f x y

Applied Statistics and Probability for Engineers, 7th edition 2017 5-18 Section 5-5 5.5.1 a) percentage of slabs classified as high with probability p1 = 0.05 percentage of slabs classified as medium with probability p2 = 0.85 percentage of slabs classified as low with probability p3 = 0.10

( ) ( ) ( )( 2) 1 0 1 2P Z P Z P Z P Z = = + = + = ( )( ) ( )( )20 1 19 2 18( 2) 1 0.9 20 0.1 0.9 190 0.1 0.9 0.323PZ = + + = (e)

Stem-and-leaf display. Yard: unit = 1.0 1 22 | 6 5 23 | 2334 8 23 | 677 16 24 | 00112444 20 24 | 5578 33 25 | 0111122334444 46 25 | 5555556677899 5 23 | 2334 8 23 | 677 16 24 | 00112444 20

CHAPTER 6 RESERVE PROBLEMS The following problems have been reserved for your use in assignments and testing and do not appear in student versions of the text. Reserve Problems Chapter 6 Section 1 Problem 1 An independent research was made asking 500 people about their bank deposits. Using

C D How does the boxplot compare in interpretive value to the original stem-and-leaf diagram? SOLUTION The boxplot shows the same basic information as the stem-and-leaf plot but in a different format. The boxplot shows the same basic information as the stem-and-leaf plot but in

C D Does it seem reasonable to assume that O-ring joint temperature is normally distributed? SOLUTION Yes, O-ring joint temperature is approximately normally distributed with some departures from the line at the ends of the distribution. Yes, O-ring joint temperature is approximately normally distributed with some

Applied Statistics and Probability for Engineers, 7th edition 6-1 CHAPTER 6 Section 6.1 6.1.1 No, usually not. For example, if the sample is {2, 3} the mean is 2.5 which is not an observation in the sample. 6.1.7 Sample average: == 351.8 43.975 8 x Sample variance: ====8119

Applied Statistics and Probability for Engineers, 7th edition 6-20 a) Median = 67.50, Lower Quartile: Q1=58.50, Upper Quartile: Q3=75.00 b) Data with lowest point removed Variable N Mean Median TrMean StDev SE Mean Temp 35 66.86 68.00 67.35 10.74 1.82 Variable Minimum Maximum Q1 Q3 Temp

15.3 13.1 15.2 15.9 15.1 14.9 13.6 13.7 15.3 15.5 14.5 16.5 13.4 15.2 15.3 13.8 14.3 12.6 15.3 14.8 14.1 14.4 14.3 15.6 14.8 14.6 15.6 15.1 14.8 15.2 15.6 14.5 15.2 14.3 15.8 17.0 14.3 14.6 16.1 12.8 14.5 15.4 13.3 14.9 14.3 16.4 13.9 16.1 14.6 15.2

The triathlon is a multiple-stage competition involving the completion of three disciplines, in its most popular form, swimming, cycling and running. The following data represents the results of 2017 Hamilton CAMTRI Sprint Triathlon American Cup for men: 00:55:14, 00:55:21, 00:56:00, 00:56:12, 00:56:20, 00:56:23, 00:56:36, 00:56:37, 00:56:50, 00:57:08, 00:58:41, 00:58:44,

13.2 15.1 16.2 11.9 11.7 14.0 15.0 15.1 17.0 16.2 14.2 14.6 14.6 14.8 15.1 15.3 13.6 14.2 16.2 12.2 16.0 12.7 12.9 13.7 16.1 14.4 16.7 12.5 13.4 12.9 Choose the correct histogram for the data. A B C D E SOLUTION Let

7.2.1 The proportion is 10/80 =1/8. 7.2.1 The proportion is 10/80 =1/8. 7.2.1 The proportion is 10/80 =1/8. Applied Statistics and Probability for Engineers, 7th edition 2017 7-1 CHAPTER 7 Section 7.2 7.2.2 n = 6 n = 49 3.5 1.4296Xn= = = 3.5 0.549Xn= =

1 7.35 2 5.14 3 4.74 4 4.65 5 6.18 Here the sample median is computed for each of the bootstrap samples. The standard error is estimated as the standard deviation of these sample medians, and in this case we obtain 1.15. 1 7.35 2 5.14 3 4.74 4 4.65

CHAPTER 7 RESERVE PROBLEMS The following problems have been reserved for your use in assignments and testing and do not appear in student versions of the text. Reserve Problems Chapter 7 Section 1 Problem 1 A random sample of 140 in size is taken from a population with a

CHAPTER 8 RESERVE PROBLEMS The following problems have been reserved for your use in assignments and testing and do not appear in student versions of the text. The following problems have been reserved for your use in assignments and testing and do not appear in student versions of the

A healthcare provider monitors the number of CAT scans performed each month in each of its clinics. The most recent year of data for a particular clinics follows (the reported variable is the number of CAT scans each month expressed as the number of CAT scans per thousand members

Applied Statistics and Probability for Engineers, 7th edition 2017 8-1 CHAPTER 8 Section 8.1 8.1.1 a) The confidence level for 2.14 / 2.14 /x n x n + is determined by the value of z0 which is 2.14. From Table III, (2.14) = P(Z < 2.14)

Applied Statistics and Probability for Engineers, 7th edition 2017 9-1 CHAPTER 9 Section 9.1 9.1.1 a) H0: = 25, H1: 25 Yes, because the hypothesis is stated in terms of the parameter of interest, inequality is in the alternative hypothesis, and the value in the null and

Because 5.166 1.685, we fail to reject the null hypothesis. There is not sufficient evidence to conclude that the true mean coefficient of restitution is greater than 0.635 at 0.05=. Find the P-value. The area to right of -5.166 under the tdistribution is greater than 0.9995 from Table V. Because

(c) ( ) ( )/2 0 0 2011()z p p z p pnpp + = ( ) ( )21.96 0.10 1 0.10 1.28 0.16 1 0.16( ) 3130.16 0.10n = (c) ( ) ( )/2 0 0 2011()z p p z p pnpp + = ( ) ( )21.96

CHAPTER 9 RESERVE PROBLEMS The following problems have been reserved for your use in assignments and testing and do not appear in student versions of the text. Reserve Problems Chapter 9 Section 1 Problem 1 A frequenter of a pub had observed that the new barman poured in average

Applied Statistics and Probability for Engineers, 7th edition 2017 Applied Statistics and Probability for Engineers, 7th edition 2017 Applied Statistics and Probability for Engineers, 7th edition 2017 9-21 9-21 9-21 3) H1: The form of the distribution is not Poisson. 4) The test statistic is ( )==2201.kiiiiOEE 5)

(c) 100:n= ( )2 1001.96 0.4 0.484010= = =. (d) (probability of a type II error) decreases as the sample size increases because the variance of the sample mean decreases. Consequently, the probability of observing a sample mean in the acceptance region centered about the incorrect value of 207ml/h decreases