.... Kindly help. Only begin from 14-6.Thanks!

ment involving a storage battery used in the launching mecha- are as follows: nism of a shoulder-fired ground-to-air missile were presented. (a) Write a model for this experiment. Three material types can be used to make the battery plates. (b) Test the appropriate hypotheses and draw conclusions The objective is to design a battery that is relatively unaffected using the analysis of variance with o = 0.05 by the ambient temperature. The output response from the (c) Graphically analyze the interaction. battery is effective life in hours. Three temperature levels are (d) Analyze the residuals from the experiment. elected, and a factorial experiment with four replicates is run. (e) Use Fisher's LSD method to investigate the differences The data are as follows: between mean effects of insulation type. Use of = 0.05 Temperature ( F) (a) Is there any evidence to support the claim that either poly- silicon doping level or anneal conditions affect base cur- Insulation 1 2 3 rent? Do these variables interact? Use o = 0.05. 6.6 4 4.5 2.2 2.3 0.9 (b) Graphically analyze the interaction. 2.7 6.2 5.5 2.7 5.6 4.9 (c) Analyze the residuals from this experiment. 6 5 4.8 5.8 2.2 3.4 (d) Use Fisher's LSD method to isolate the effects of anneal 3 3.2 3 1.5 1.3 3.3 conditions on base current, with o = 0.05. 2.1 41 2.5 2.6 0.5 1.1 Anneal (temperature/time) 5.9 2.5 0.4 3.5 1.7 900 900 950 1000 5.7 4.4 8.9 7.7 2.6 9.9 60 180 60 15 30 3.2 3.2 7 7.3 11.5 10.5 Polysilicon 1 1020 4.40 8.30 10.15 10.29 11.01 3 5.3 9.7 8 2.2 3.4 6.7 doping 4.60 8.90 10.20 10.30 10.58 7 8.9 12 9.7 8.3 8 2 x 1020 3.20 7.81 9.38 10.19 10.81 7.3 9 8.5 10.8 10.4 9.7 3.50 7.75 10.02 10.10 10.60 8.6 11.3 7.9 10.6 74 14-8. An article in the Journal of Testing and Evaluation 14-6. Johnson and Leone (Statistics and Experimental Design (1988, Vol. 16, pp. 508-515) investigated the effects of cyclic in Engineering and the Physical Sciences, John Wiley, 1977) loading frequency and environment conditions on fatigue crack described an experiment conducted to investigate warping of growth at a constant 22 MPa stress for a particular material. The copper plates. The two factors studied were temperature and data follow. The response variable is fatigue crack growth rate. the copper content of the plates. The response variable is the amount of warping. The data are as follows Environment Air H,O Salt HO Copper Content (% ) Temperature 10 2.29 2.06 1.90 (.C) 40 60 80 100 2.47 2.05 1.93 50 17, 20 16, 21 24, 22 28, 27 2.48 2.23 1.75 2.12 2.03 2.06 75 12.9 18. 13 17, 12 27.31 100 16, 12 18, 21 25, 23 30, 23 2.65 3.20 3.10 Frequency 2.68 3.18 3.24 125 21, 17 23, 21 23, 22 29, 31 2.06 3.96 3.98 2.38 3.64 3.24 (a) Is there any indication that either factor affects the amount of warping? Is there any interaction between the factors? 0.1 2.24 11.00 9.96 Use a = 0.05. 2.71 11.00 10.01 2.81 9.06 9.36 (b) Analyze the residuals from this experiment. 2.08 1 1.30 10.40 (c) Plot the average warping at each level of copper con- tent and compare the levels using Fisher's LSD method. (a) Is there indication that either factor affects crack growth Describe the differences in the effects of the different levels rate? Is there any indication of interaction? Use of = 0.05. of copper content on warping. If low warping is desirable, (b) Analyze the residuals from this experiment. what level of copper content would you specify? (c) Repeat the analysis in part (a) using In(y) as the response. (d) Suppose that temperature cannot be easily controlled in Analyze the residuals from this new response variable and he environment in which the copper plates are to be used. comment on the results. Does this change your answer for part (c)? 14-9. Consider a two-factor factorial experiment. Develop a 14-7. + An article in the IEEE Transactions on Electron formula for finding a 100(1 -0)% confidence interval on the Devices (November 1986, p. 1754) described a study on the difference between any two means for either a row or column effects of two variables-polysilicon doping and anneal condi- factor. Apply this formula to find a 95% CI on the difference tions (time and temperature)-on the base current of a bipolar in mean warping at the levels of copper content 60 and 80% in transistor. The data from this experiment follow. Exercise 14-6. TABLE . E14-1 Data for Antifungal Activities Temperature (C) Carbon(%) 25 30 37 2 25.84 51.86 32.59 51.86 131.33 41.11 41.11 104.11 32.59 5 20.48 25.84 12.87 41.11 104.11 32.59 32.59 82.53 25.84 7.5 20.48 25.84 10.2 65.42 82.53 51.86 51.86 65.42 41.1 1 14-10. An article in Journal of Chemical Technology and extracellular polysaccharides (EPS). It is suspected that Mg+ Biotechnology ["A Study of Antifungal Antibiotic Production and K* (in millimolars) are related to EPS. The data from a full by Thermomonospora sp MTCC 3340 Using Full Factorial factorial design follow. Design" (2003, Vol. 78. pp. 605-610)] considered the effects of several factors on antifungal activities. The antifungal yield (a) State the hypotheses of interest. (b) Test the hypotheses with of = 0.5. was expressed as Nystatin international units per em'. The (c) Analyze the residuals and plot residuals versus the pre- results from carbon source concentration (glucose) and incuba- dicted production. tion temperature factors follow. See Table E14-1. (a) State the hypotheses of interest. (b) Test your hypotheses with o = 0.5. (c) Analyze the residuals and plot the residuals versus the pre- Run Mg * (mM) K* (mM) EPS (g/L) dicted yield. 40 5 3.88 (d) Using Fisher's LSD method, compare the means of antifun- 50 4.23 gal activity for the different carbon source concentrations. 40 10 4.67 14-11. An article in Bioresource Technology ["Quantita- 30 5.86 tive Response of Cell Growth and Tuber Polysaccharides 50 4.50 Biosynthesis by Medicinal Mushroom Chinese Truffle Tuber 50 3.62 Sinense to Metal Ion in Culture Medium" (2008, Vol. 99(16). 30 3.84 pp. 7606-7615)] described an experiment to investigate 40 3.25 the effect of metal ion concentration to the production of 30 4.1814-14. + An engineer is interested in the effect of cutting Replicate speed (A). metal hardness (#). and cutting angle (C) on the life Treatment of a cutting tool. Two levels of each factor are chosen, and two Combination replicates of a 2' factorial design are run. The tool life data (in (1) 163 hours) are shown in the following table. 168 175 Treatment Replicate 158 163 Combination I II 166 168 175 178 221 311 325 435 ac 179 183 354 348 be 173 168 552 472 abe 179 182 440 453 164 159 406 377 187 189 60S 500 163 159 410 185 191 (a) Analyze the data from this experiment. 168 174 (b) Find an appropriate regression model that explains tool life aced 197 199 in terms of the variables used in the experiment. 170 174 (C Analyze the residuals from this experiment. abed 194 198 14-15. Four factors are thought to influence the taste of a soft-drink beverage: type of sweetener (), ratio of syrup to 14-16. The following data represent a single replicate of a 25 water (8). carbonation level (C), and temperature () Each design that is used in an experiment to study the compressive factor can be run at two levels. producing a 2' design. At each strength of concrete. The factors are mix (A), time (By, labora- fun in the design, samples of the beverage are given to a test tory [Q. temperature (D), and drying time (E). panel consisting of 20 people. Each tester assigns the beverage = 700 = 800 a point score from I to 10. Total score is the response variable. = 1201 and the objective is to find a formulation that maximizes total = 3400 = 3500 score. Two replicates of this design are run, and the results are ab arbe shown in the table. Analyze the data and draw conclusions. Use = DOD = 600 a = 01.05 in the statistical tests. are = 3010 hre = 3006 (a) What is an appropriate statistical model for this experiment? = 5300 abce = 5500 (bj Analyze the data and draw conclusions. dde = 1901 c) Analyze the residuals from this experiment. Are there any = 1100 ade = 1500 bde = 4000 problems with model adequacy? = 6100 abde = 6500 14-19. + An experiment was run in a semiconductor fab- cade = 1500 rication plant in an effort to increase yield. Five factors, each acde = 2000 at two levels, were studied. The factors (and levels) were A = = 3300 bede = 3400 aperture setting (small, large), 8 = exposure time (20% below abode = 6800 nominal. 20% above nominal). C = development time (30 and (a) Estimate the factor effects. 45 seconds). D = mask dimension (small. large). and E = etch (b) Which effects appear important? Use a normal probabil- time (14.3 and 15.5 minutes). The following unreplicated 23 ity plot. design was run: (c) If it is desirable to maximize the strength. in which direc- tion would you adjust the process variables? = 12 (d) Analyze the residuals from this experiment. = 35 = 55 14-17. + An article in IEEE Transactions on Sendcondar. = 52 C = 16 = 15 for Manufacturing (1992, Vol. 5, pp. 214-222) described an = 20 (Ne = 22 experiment to investigate the surface charge on a silicon wafer. = 40 ixe = 45 The factors thought to influence induced surface charge are abc = 60 INNe = 65 cleaning method (spin rinse dry or SRD and spin dry or SD) 8 = 6 and the position on the wafer where the charge was measured. = 10 = 10 The surface charge (x 10" q/em ) response data follow: bade = 30 and = 50 = 53 Test Position = 18 = 15 ced = 21 actde = 20) 1.66 1.84 aed = 44 bede = 41 abcde = 63 SD 1.90 1.84 abcd = 61 Cleaning 1.92 1.62 (a) Construct a normal probability plot of the effect estimates. Method Which effects appear to be large? 4.21 -7.58 (h) Conduct an analysis of variance to confirm your findings SRD -1.35 -2.20 for part (a). -5.36 ") Construct a normal probability plot of the residuals. Is the [a) Estimate the factor effects. plot satisfactory? (b) Which factors appear important? Use o = 0.05. (d) Plot the residuals versus the predicted yields and versus (c) Analyze the residuals from this experiment. each of the five factors. Comment on the plots. 14-18. + An article in Oikos: A Journal of Ecology ["Regu- (c) Interpret any significant interactions. lation of Root Vole Population Dynamics by Food Supply and If) What are your recommendations regarding process operat- Predation: A Two-Factor Experiment" (2005, Vol. 109. pp. ing conditions? 387-395)1 investigated how food supply interacts with preda- (2) Project the 2" design in this problem into a 2' for r