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Q1:Instructions Part A: You will find an excel sheet attached. Ch1 homework data set.xlsx A survey asked three questions to pet owners: 1. How many pets do you own? 2. Do you like cats, dog, or neither cats nor dogs the best? 3. How much time in hours does your pet(s) stay home on average per day? Create an appropriate graph for each question using Minitab. Identify what type of data is obtained from each question (qualitative, quantitative discrete, or quantitative continuous). Use one pie chart, one bar graph and one histogram. Copy the graphs to a word file and indicate which type of data near the graph. You can copy graphs from Minitab and then paste them into a word document and then you will be able to write in the type of data that each is. Note: Histograms are good for continuous data because the bars do not have spaces between them, and continuous data does not have jumps between numbers. Part B:See Answer
Q2:Part B: Visit the Infographics Site for Statistics Canada at https://www150.statcan.gc.ca/n1/pub/11-627-m/index-eng.htm Find a poster (scroll down) that is on a topic that interests you and that contains a pie graph. Be sure you can answer the questions below by looking at your pie graph. 1. Copy the pie graph from the poster and add it to your word document. 2. Pie graphs usually show percentages and should add up to 100%. Does your pie graph add to 100%? If it doesn't, why not? 3. What would have been the question that was asked to gather the data displayed on your pie graph? Remember that the question is usually qualitative. Your written response should be submitted as a pdf file.See Answer
Q3:1. DETAILS DEVORESTAT9 8.3.035.S. MY NOTES The article "Uncertainty Estimation in Railway Track Life-Cycle Cost"+ presented the following data on time to repair (min) a rail break in the high rail on a curved track of a certain railway line. 159 120 480 149 270 547 340 43 228 202 240 218 A normal probability plot of the data shows a reasonably linear pattern, so it is plausible that the population distribution of repair time is at least approximately normal. The sample mean and standard deviation are 249.7 and 145.1, respectively. (a) Is there compelling evidence for concluding that true average repair time exceeds 200 min? Carry out a test of hypotheses using a significance level of 0.05. State the appropriate hypotheses. ⒸM-200 H₁: <200 ⒸM-200 H₂>200 No 200 H₂-200 ⒸM-200 H: 200 ⒸM₂: > 200 MH-200 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) t= P-value= What can you conclude? There is compelling evidence that the true average repair time exceeds 200 min. There is not compelling evidence that the true average repair time exceeds 200 min. (b) Using a 150, what is the type II error probability of the test used in (a) when true average repair time is actually 300 min? That is, what is (300)? (Round your answer to two decimal places. You will need to use the appropriate table in the Appendix of Tables to answer this question.) A(300) - MacBook ProSee Answer
Q4:2. DETAILS DEVORESTAT9 8.4.043.S. A common characterization of obese individuals is that their body mass index is at least 30 (BMI = weight/(height), where height is in meters and weight is in kilograms]. An article reported that in a sample of female workers, 269 had BMIs of less than 25, 158 had BMIs that were at least 25 but less than 30, and 121 had BMIS exceeding 30. Is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese? (a) State the appropriate hypotheses with a significance level of 0.05. ⒸM₂: P = 0.20 HP 0.20 ⒸH₂¹ P >0.20 HP-0.20 H₂ P=0.20 H:p>0.20 ⒸN₂: P-0.20 H₂ p<0.20 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value- What can you conclude? Reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese. Reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese. Do not reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese. Do not reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese. (b) Explain in the context of this scenario what constitutes type 1 error. A type I error would be declaring that 20% or less of the population of female workers is obese, when in fact more than 20% are actually obese. A type I error would be declaring that 20% or more of the population of female workers is obese, when in fact less than 20% are actually obese. A type 1 error would be declaring that less than 20% of the population of female workers is obese, when in fact 20% or more are actually obese. A type I error would be declaring that more than 20% of the population of female workers is obese, when in fact 20% or less are actually obese. Explain in the context of this scenario what constitutes type 11 error. ( A type II error would be declaring that 20% or less of the population of female workers is obese, when in fact more than 20% are actually obese. A tune II er would be decladog that 300 or more of the population of female workers in ober fact leve than 2016 cu obs MY NOTES MacBook Pro/n3. H₂DU.EU ⒸHOP=0.20 H: P < 0.20 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value= What can you conclude? Reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese. Reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese. Do not reject the null hypothesis. There is sufficient evidence that more than 20% of the population of female workers is obese. Do not reject the null hypothesis. There is not sufficient evidence that more than 20% of the population of female workers is obese. (b) Explain in the context of this scenario what constitutes type 1 error. A type 1 error would be declaring that 20% or less of the population of female workers is obese, when in fact more than 20% are actually obese. A type 1 error would be declaring that 20% or more of the population of female workers is obese, when in fact less than 20% are actually obese A type 1 error would be declaring that less than 20% of the population of female workers is obese, when in fact 20% or more are actually obese. A type 1 error would be declaring that more than 20% of the population of female workers is obese, when in fact 20% or less are actually obese. Explain in the context of this scenario what constitutes type II error. A type II error would be declaring that 20% or less of the population of female workers is obese, when in fact more than 20% are actually obese. A type 11 error would be declaring that 20% or more of the population of female workers is obese, when in fact less than 20% are actually obese. A type II error would be declaring that less than 20% of the population of female workers is obese, when in fact 20% or more are actually obese. A type II error would be declaring that more than 20% of the population of female workers is obese, when in fact 20% or less are actually obese. (c) What is the probability of not concluding that more than 20% of the population is obese when the actual percentage of obese individuals is 27%? (Round your answer to four decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question. Submit Answer DETAILS DEVORESTAT9 9.1.005. MY NOTESSee Answer
Q5:3. Submit Answer DEVORESTAT9 9.1.005. DETAILS Persons having Raynaud's syndrome are apt to suffer a sudden impairment of blood qrculation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm2/min) was measured. For m = 8 subjects with the syndrome, the average heat output was - 0.65, and for n=8 nonsufferers, the average output was 2.01. Let #, and , denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal with o,-0.1 and %₂=0.3. (a) Consider testing H₁ H₁-H₂=-1.0 versus H: ₂-₂-1.0 at level 0.01. Describe in words what H, says, and then carry out the test. OH, says that the average heat output for sufferers is the same as that of non-sufferers. ⒸH, says that the average heat output for sufferers is less than 1 cal/cm³/min below that of non-sufferers. CH, says that the average heat output for sufferers is more than 1 cal/cm²/min below that of non-sufferers. Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) 2= P-value- State the conclusion in the problem context. Fail to reject H₂. The data suggests that the average heat output for sufferers is the same as that of non-sufferers. Reject Ho. The data suggests that the average heat output for sufferers is more than 1 cal/cm/min below that of non-sufferers. Fail to reject H. The data suggests that the average heat output for sufferers is less than 1 cal/cm2/min below that of non-sufferers. Reject Ho. The data suggests that the average heat output for sufferers is the same as that of non-sufferers. (b) What is the probability of a type II error when the actual difference between ₁ and ₂ is ₁-₂ -1.5? (Round your answer to four decimal places.) (c) Assuming that m-n, what sample sizes are required to ensure that = 0.1 when H₁-H₂=-1.5? (Round your answer up to the nearest whole number.) subjects You may need to use the appropriate table in the Appendix of Tables to answer this question. MY NOTES MacBook ProSee Answer
Q6:DETAILS DEVORESTAT9 9.2.028.5. As the population ages, there is increasing concern about accident-related injuries to the elderly. An article reported on an experiment in which the maximum lean angle-the farthest a subject is able to lean and still recover in one step-was determined for both a sample of younger females (21-29 years) and a sample of older females (67-81 years). The following observations are consistent with summary data given in the article: YF: 29, 35, 31, 27, 28, 32, 31, 34, 32, 29 OF: 19, 15, 21, 13, 12 Does the data suggest that true average maximum lean angle for older females (OF) is more than 10 degrees smaller than it is for younger females (YF)? State and test the relevant hypotheses at significance level 0.10. (Use , for younger females and #₂ for older females.) Hoi H₁ H₂O Mo 1-₂-10 H₂H₁-H₂> 10 ⒸH²H₁-H₂10 H₂H₁₂ <10 ⒸHM₁₂0 H₂H₂-H₂>0 P-value- Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.) tm MY NOTES State the conclusion in the problem context. Fall to reject M. The data suggests that true average lean angle for older females is more than 10 degrees smaller than that of younger females. Fail to reject Ho. The data suggests that true average lean angle for older females is not more than 10 degrees smaller than that of younger females. Reject Ho. The data suggests that true average lean angle for older females is not more than 10 degrees smaller than that of younger females. Reject Ho. The data suggests that true average lean angle for older females is more than 10 degrees smaller than that of younger females.See Answer
Q7:5. DETAILS DEVORESTAT9 9.3.040. Lactation promotes a temporary loss of bone mass to provide adequate amounts of calcium for milk production. A paper gave the following data on total body bone mineral content (TBBMC) (g) for a sample both during lactation (L) and in the postweaning period (P). Subject 2 3 5 6 7 L 1929 2546 2825 1923 1628 2175 2112 2621 1843 2542 1 4 8 9 10 P 2127 2885 2895 1943 1750 2183 2164 2626 2006 2626 (a) Does the data suggest that true average total body bone mineral content during postweaning exceeds that during lactation by more than 25 g? State and test the appropriate hypotheses using a significance level of 0.05. [Note: The appropriate normal probability plot shows some curvature but not enough to cast substantial doubt on a normality assumption.] (Use H₂Hp - H₂.) ⒸH₂= 25 H₂H ≤ 25 Hoo-25 H₂H25 ⒸH₂=25 H₂H > 25 H₂H25 H₂H <25 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t= MY NOTES P-value- State the conclusion in the problem context. Fall to reject Ho. The data suggests that the true average total body bone mineral content during postweaning exceeds that during lactation by more than 25 g. Reject Ho. The data suggests that the true average total body bone mineral content during postweaning does not exceed that during lactation by more than 25 g. Reject Ho. The data suggests that the true average total body bone mineral content during postweaning exceeds that during lactation by more than 25 g. Fall to reject Ho. The data suggests that the true average total body bone mineral content during postweaning does not exceed that during lactation by more than 25 g./n6. HoHo 25 H₂HD > 25 ⒸHo Ho - 25 H:H₂ < 25 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) to P-value= State the conclusion in the problem context. ⒸFall to reject H₂. The data suggests that the true average total body bone mineral content during postweaning exceeds that during lactation by more than 25 g. Reject Ho. The data suggests that the true average total body bone mineral content during postweaning does not exceed that during lactation by more than 25 g. Reject Ho. The data suggests that the true average total body bone mineral content during postweaning exceeds that during lactation by more than 25 g. Fall to reject Ho. The data suggests that the true average total body bone mineral content during postweaning does not exceed that during lactation by more than 25 g. (b) Calculate an upper confidence bound using a 95% confidence level for the true average difference between TBBMC during postweaning and during lactation. (Round your answer to two decimal places.) 9 (c) Does the (incorrect) use of the two-sample t test to test the hypotheses suggested in (a) lead to the same conclusion that you obtained there? Explain. Yes, if the two samples were independent, the result would be the same. No, if the two samples were independent, the result would not be the same. You may need to use the appropriate table in the Appendix of Tables to answer this question. DETAILS Submit Answer DEVORESTAT9 9.5.064. The following observations are on time (h) for an AA 1.5-volt alkaline battery to reach a 0.8 voltage. Brand A: 8.65 R.84 R.91 8.82 875 8 52 872 878 876 MY NOTESSee Answer
Q8:6. DETAILS DEVORESTAT9 9.5.064. The following observations are on time (h) for an AA 1.5-volt alkaline battery to reach a 0.8 voltage. Brand A: 8.65 8.84 8.91 8.82 8.75 8.52 8.72 8.78 8.76 Brand B: 8.86 8.71 8.71 8.8 8.73 8.76 8.78 8.74 8.79 Normal probability plots support the assumption that the population distributions are normal. Does the data suggest that the variance of the Brand A population distribution differs from that of the Brand B population distribution? Test the relevant hypotheses using a significance level of 0.05. [Note: The two-sample t test for equality of population means gives a P-value of 0.733.] The Brand A batteries are much more expensive than the Brand B batteries. State the relevant hypotheses. (Use a, for Brand A batteries and a₂ for Brand B batteries.) ⒸH₂0₁ ¹0₂² ⒸH: 0²-0₂² M₂: 0,² > 0₂² H₁: 0 ₁ ² = 0₂² M₂:0₂ ² = 0₂² Calculate the test statistic. (Round your answer to two decimal places.) fm What can be said about the P-value for the test? ⒸP-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 OP-value < 0.001 MY NOTES State the conclusion in the problem context. Reject H. The data suggests that there is difference in the population variances of the two battery brands./nⒸH₂:0₁ ²0₂ ² H₂: 0₂² 20₂² ⒸH₂:0₁²-0₂² Calculate the test statistic. (Round your answer to two decimal places.) f= What can be said about the P-value for the test? OP-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 OP-value < 0.001 State the conclusion in the problem context. Reject Ho. The data suggests that there is difference in the population variances of the two battery brands. Fail to reject Ho. The data does not suggest that there is difference in the population variances of the two battery brands. Fail to reject Ho. The data suggests that there is difference in the population variances of the two battery brands. Reject Ho. The data does not suggest that there is difference in the population variances of the two battery brands. You may need to use the appropriate table in the Appendix of Tables to answer this question. Submit Answer Home My Assignments Request ExtensionSee Answer
Q9: Background PROCESS OPTIMISATION AND CONTROL Air Enhanced Process Understanding Data Analysis and Principal Component Analysis The focus of the two assignments for this module is based on data collected from the fluidised bed reactor 'A' at BASF, Seal Sands, Teesside. The ultimate objective of the analysis was to attain reliable on-line predictions of 7 quality variables, in particular AN (Acrylonitrile) yield, to be able to provide an estimate of AN Yield to the process operators at the same frequency as the process variable measurements. Yield information is normally provided by the on-line Gas Chromatograph with a 40 minute cycle time. The reactor is cooled by a number of internal cooling coils in the bed of the reactor. The coil coolant flow rates are fixed. As the coils foul, their thermal efficiency is reduced and the flow of raw materials into the reactor change through the action of the multi-loop controllers. During reactor operation, the cooling coils are switched in and out as part of a de-fouling recycling procedure to maintain optimum bed cooling and good production. The operational staff select the required cooling coil patterns based upon experience, observation of changing operating conditions and increases in the bed temperatures as the cooling coils become fouled. The cooling coils are periodically taken off-line to allow fouling deposits to be removed by the high temperatures in the reactor bed. A schematic of the process is provided below. COOLER REACTOR CAPE3321 To boiler Catalyst in/out Gas chromatograph QUENCH Propylene Ammonia To atmosphere Oxygen meter Refrigerated de-mineralised water ABSORBER Product rich water Data Information The process data was five minute averaged data. The initial data set comprised a total of forty-eight variables and 14344 samples. A sub-set of the data will be used for the assignment (391 samples and 25 process and calculated variables). Not all bed temperatures are provided in this data set as detailed in the overview. Please note the focus is on the reactor and not the other elements of the process. The variable names are provided below. The process data is available in Minerva in CAPE3321 Assessment and Feedback - CAPE3321 - Data Analysis and PCA Data Set 2024 Assignment.xlsx Assignment Task Explore the data using appropriate pre-screening techniques and then develop a Principal Component Analysis (PCA) representation. The objective of the analysis is to obtain an understanding of the underlying behaviour of the process from the analysis of the data. The outputs from the graphical representations and the principal component analysis and any other information/representations must be interpreted in the context of the industrial application. Provide a Report and ensure you follow the directions below in terms of the structure. Submission - Maximum 6 pages - does not include Title Page but includes references. 1 page - Executive Summary (definition provided below) 5 pages analysis including interpretation of results based on appropriate figures and tables Font Calibri 11pt, Single Line Spacing, Page Margins (2cm top, bottom, LHS and RHS) An Executive Summary summarises a longer report in such a way that the reader can rapidly become acquainted with a large body of material without having to read it all. The overview is a brief introduction / summary - a paragraph. Marks Breakdown Executive Summary: 20% Overview: 10% Analysis: 30% Interpretation of Results: 30% Conclusions: 10% Summary of Variables 1 2 3 4 5 6 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Propylene flow rate Ammonia flow rate Air flow rate T.M.F. (total mass flow) rate Catalyst inventory Pressure Propylene partial pressure Ammonia partial pressure Oxygen partial pressure Nitrogen partial pressure Ammonia/Propylene ratio Air/Propylene ratio Velocity W.W.H. (Weight of propylene feed/ Weight of catalyst/hr) Contact time Bed Temperature 1 Bed Temperature 2 Bed Temperature 3 Bed Temperature 4 Bed Temperature 5 Bed Temperature 7 Bed Temperature 8 Bed Temperature 11 Bed Temperature 16 Bed Temperature 21 Process Process Process Calculated Process Process Calculated Calculated Calculated Calculated Calculated Calculated Calculated Calculated Calculated Process Process Process Process Process Process Process Process Process ProcessSee Answer
Q10:6.1 question 1. An experiment was performed to study the effects of humidity and temperature at time of manufacture on the degradation of a chemical product. The experiment used three levels of humidity and four levels of temperature in a full factorial design. The experiment de- sign was replicated three times and blocked on replicates. The orders of the humidity and temperature levels were randomized within blocks. (a) Complete the calculations of the ANOVA table shown below including the summary statistics (standard error, R-squared, and R-squared-adjusted) and interpret the re- sults. (b) Refine the model using Occam's Razor, recalculate the summary statistics, and inter- pret the results. Source Block df SS MS F P 20 Humidity 122 Temperature 450 Interaction 33 Error Total 240See Answer
Q11:6.4 4. A sailboat manufacturer wishes to identify a single epoxy that has high strength at all temperatures. He designs a factorial experiment to evaluate the strength of epoxies from three different manufacturers at low, intermediate, and high temperatures. He performs the experiment in a completely randomized manner by randomly selecting an epoxy and temperature for each run until all experimental runs are completed. The strength data are shown below. Analyze the data by two-way ANOVA and construct an interaction plot. Which manufacturer should he use and what considerations should be made? 20 A 216, 239, 234 Temperature 25 30 344, 335, 348 372, 366, 385 Manufacturer B 278, 299, 271 311, 319, 327 360, 366, 361 с 309, 295, 315 321, 312, 325 371, 361, 349See Answer
Q12:6.8 8. An experiment was performed to compare the lumen measurements obtained by four pho- tometry labs. A collection of six lamps was prepared and circulated to each of the labs. Each lab measured each lamp twice and measurements were made in completely random order. Analyze the data and interpret the results. Construct an appropriate error statement. for this data set. A #71522 2409, 2494 #71533 4477, 4182 Lamp #71534 8861, 8739 #71535 10213, 10281 #71536 20601, 22996 #71537 35985, 40224 Lab B 2465, 2693 4485, 4283 9638, 9084 11138, 11560 23797, 23625 42457, 41064 C 2499, 2365 4131, 4076 9272, 8904 10479, 10468 22106, 20773 39140, 37987 D 2556, 2498 4297, 4481 9579, 8479 11151, 11015 20884, 22430 39049, 37204See Answer
Q13:3.11 11. An experiment was performed to determine if a new technician was proficient in performing a critical test used to evaluate the effectiveness of vacuum cleaners. The test procedure is to uniformly distribute 100g of dirt consisting of fine stones, sand, and talc over two square yards of test carpet. The dirt is then rolled into the carpet with a 25 pound roller for three minutes. Finally, the carpet is vacuumed for three minutes using a prescribed motion and rate. The recovered dirt in grams is determined from the weight change of the filter bag before and after the vacuuming step. Test carpets are vacuumed aggressively and weighed between trials to guarantee that they are clean before the dirt is applied. To demonstrate the new (2) technician's proficiency his recovery was compared to that of an experienced (1) technician for eight different carpet samples. For the new technician to be considered proficient, the mean recovery difference between the technicians must be less than 4g with 90% confidence. The recovery data were: Plush Multi-level Shag Level-loop 1 2 Technician 1 2 1 2 1 2 12 55.3 54.4 58.2 65.0 23.5 25.7 56.1 55.6 61.2 63.3 23.6 27.7 76.3 70.5 74.9 | 69.6See Answer
Q14: Design of Experiment: Six Sigma Spring 2024 Homework 4 (please submit your homework to the Assignment Submission Folder "Homework 4" in our course website on BrightSpace) A sales organization wishes to improve its revenue. To do so they are considering the impact of four factors; different sales people, sales person incentives, regional differences and advertising / marketing effectiveness. Their plan is to run a full factorial experiment and vary factors to determine their impact on monthly sales revenue. They will run a total of 16 runs twice (32 months). Total revenue is then analyzed to determine the potential impact the changes have on revenue. The experimental design layout is as follows: Factor Low Level (-1) High Level (+1) Level Description Sales Person Percentile Sales Person B Incentive Plan Traditional Enhanced Sales Person A Region North South Person A comes from a group that is in the top 10 percentile of the historically performing sales people - Sales Person B comes from the bottom 10 percentile The traditional incentive plan is the historical plan deployed. The enhanced plan is a sliding scale aimed at providing more incentive for high performers The region is the geographical distinction in where the sales occur Advertising 5% 10% The advertising represents the percent of revenue spent on advertising + C1 StdOrder RunOrder PtType C2 C3 C4 Blocks The uncoded and coded experiment designs are shown below: C5-T C6-T C7-T C8 Sales Person Incentive Plan Region Advertising Percent 67 34567890 1234567890123456 1 1 1 1B Standard North 5 2 2 1 1B Standard North 10 3 1 1B Standard South 5 4 1 1B Standard South 10 5 1 1B Enhanced North 5 1 1B Enhanced North 10 7 1 1 B Enhanced South 5 8 1 1 B Enhanced South 10 9 1 1 A Standard North 5 10 11 11 12 13 14 15 15 16 0123456 1 1A Standard North 10 1 1 A Standard South 5 1 1 A Standard South 10 1 1 A Enhanced North 5 1 1 A Enhanced North 10 1 1A Enhanced South 5 16 1 1A Enhanced South 10 C1 C2 C3 C4 C5-T C6-T C7-T C8 StdOrder | RunOrder PtType Blocks Sales Person Incentive Plan Region Advertising Percent 12 1 1 1 1-1 -1 -1 -1 2 2 2 1 1-1 -1 -1 1 3 3 3 1 1-1 -1 1 -1 4 4 4 1 1-1 -1 1 1 5 5 6 7 8 9 0123456 11 11 5678 678901 1 1-1 1 -1 -1 1 1-1 1 -1 1 1 1-1 1 1 -1 1 1-1 1 1 1 9 1 11 -1 -1 -1 10 11 11 1 11 -1 -1 1 1 11 -1 1 -1 12 12 1 11 -1 1 1 14 15 16 3456 13 1 11 1 -1 -1 14 1 11 1 -1 1 15 1 11 1 1 -1 16 1 11 1 1 1 The results of revenues are shown below: StdOrder RunOrder CenterPt Blocks Sales Pers Incentive Region Advertisin Results 1 1 1 1A Standard North 5 $86,117.00 2 2 1 1B Standard North 5 $65,109.00 3 3 1 1A Enchanced North 5 $97,120.00 4 4 1 1B Enchanced North 5 $68,930.00 5 5 1 1A Standard South 5 $89,121.00 6 6 1 1B Standard South 5 $83,460.00 7 7 1 1A Enchanced South 5 $131,670.00| 8 8 1 1B Enchance South 5 $119,001.00 9 9 1 1 A Standard North 10 $121,091.00 10 10 1 1B Standard North 10 $99,407.00 11 11 1 1A Enchanced North 12 12 1 1B Enchanced North 10 $123,378.00| 10 $119,872.00 13 13 1 1A Standard South 10 $89,584.00| 14 14 1 1B Standard South 10 $69,018.00 15 15 1 1A Enchance South 10 $98,710.00 16 16 1 1B Enchance South 10 $75,822.00 17 17 1 1 A Standard North 5 $73,002.00 18 18 1 1B Standard North 5 $62,010.00 19 19 1 1A Enchanced North 5 $68,201.00| 20 20 1 1B Enchanced North 5 $52,967.00 21 21 1 1A Standard South 5 $100,921.00 22 22 1 1B Standard South 5 $90,019.00 23 23 1 1A Enchance South 5 $135,978.00 24 24 1 1B Enchance South 5 $128,000.00| 25 25 1 1A Standard North 10 $117,000.00 26 26 1 1B Standard North 10 $109,213.00 27 27 1 1A Enchance North 10 $149,021.00 28 28 1 1B Enchance North 10 $138,650.00| 29 29 1 1A Standard South 10 $78,904.00| 30 30 1 1B Standard South 10 $69,690.00 31 31 1 1A Enchance South 10 $86,540.00 32 32 1 1B Enchance South 10 $79,059.00 (1) Use Minitab to generate the full factorial design of experiment (2) Run analysis to identify the significant factors (3) Create main effect and two way interaction plotsSee Answer
Q15:2. A 23 experiment with two replicates in blocks was performed to study the flight time of paper helicopters. The design variables and their levels are shown in the following table. The width and length variables refer to the blade geometry and the folds variable indicates the number of one inch folds in the helicopter's bottom leg. The run order was randomized within each block. Variable -1 +1 Units A: Width 1.25 2 inch B: Length 2 C: Folds 4 inch 1 2 NA The experimental flight times were measured in seconds and are reported below. Analyze the data and include a term for blocks in the model. What helicopter geometry is predicted to give maximum flight time? Extrapolate your model to recommend another helicopter geometry that would give even longer flight time. What are the risks associated with this recommendation? B|C - + + Block 1 2 2.99 2.90 2.99 2.99 - 5.13 5.58 + + 5.21 5.41 + 2.82 2.93 + + 2.95 2.62 + + - 4.41 4.62 + + + 4.39 4.97 5-See Answer
Q16:15. One cause of lumen degradation of metal halide are lamps is contamination inside of the are chamber and lamp jacket. A brainstorming session to address excessive lumen degradation identified four variables that might affect contamination. To test for variable effects a 2* full factorial experiment design with two replicates in blocks was built using the following variables matrix: Variable A: HF seld wash B1: Cadmium concentration || C: Vacuum exhaust time. D: Jacket getter + No Yes 24 Units NA % 30 60 seconds. 16 mm The experimental run matrix is shown below. The lumen maintenance response, LM, is the ratio of 1000 hour lumens to 100 hour lumens. (a) Analyse the data and refine the model. (b) Us the model to make a recommendation to improve lumen maintenance. Std Run Block | A BCD LM Std Run Block A BCD LM 10 1 0.948 27 17 2 -1 1 16 2 1 1 0.065 26 18 2 -1 1 1 0.935 1.008 3 T DIDIDI|-1 | 0.839 31 19 2 -I 13 4 1 -1 -1 1 0.855 29 20 2 1 1 П 1 -1 -1 1-10.855 21 21 2 -1 -1 1 -10,8 6 -1 -1 T | 0.901 22 22 2 -L 10.906 0.565 0.940 7 7 1 -1 1 -1 0.885 17 23 2 -1 -1 -1 -1 0.885 12 8 1 1 1 1 1 0.973 20 24 2 1 1 -1 -10.982|| 14 9 1 -1 1 0.941 19 25 2 -1 1 -1 -1 0.893 8 10 1 1 1 1 -1 0.950 28 26 2 1 1 -1 1 0.970 2 11 1 1 -1 -1 -1 0.928 2:3 27 2 -1 1 1 10,890 4 12 1 -1 -1 0.973 30 28 2 1 -1 1 0.949 15 13 -1 1 1 0.905 24 29 2 1 1 1 -1 0.967 3 14 1 1 1 -1 1 0.5537 18 30 2 1 -1 -1 -1 0.957 6 15 1 1 -1 1 -1 0.965 32 31 2 1 I 1 0.944 9 16 1 -1 -1 -1 1 0.833 25 32 2 -1 -1 -1 1 0.865See Answer
Q17:factors:). Use the Designs submenu to specify a full factorial design with two repli- cates, blocked on replicates. Use the Factors submenu to specify the variable names (Length, Width, and Clip exactly) and their low and high physical levels. (b) Use Stat> DOE> Display Design> Coded units to display the experiment design in coded units. Then use the correlate.mac macro (type %correlate c5-c7 at the command line) to create the correlation matrix. Inspect the matrix for correlations between terms in the model. Return the data display back to uncoded/physical units. (c) Make sure that your run matrix is displayed in uncoded/physical units. Copy the Paper Helicopter Simulation.mtb macro file to your MINITAB Macros Macros Vrx\ folder and use Tools> Run an Exec (V18) or File> Run an Exec (V19) to run the macro. The macro should create simulated flight time data in the c8 (Time) column. (d) Use Stat> DOE> Factorial> Analyze Factorial Design to analyze the Time response. Use the Terms submenu to specify terms up through order 3 and include a term for blocks in the model. Use the Graphs submenu to enable the residuals four- in-one plot and one or more of the effect plots, e.g. Pareto. Check the model residuals to make sure that they meet the requirements of the analysis method. (e) Use Stat> DOE> Factorial> Factorial Plots to create main effect and interaction plots. Interpret the plots. (f) Use Occam's razor to refine the model from the Terms submenu. (g) Use Stat> DOE> Factorial> Response Optimizer to determine the geometry of the paper helicopter that will have maximum flight time.See Answer
Q18:the paper helicopter that will have maximum flight time. Q-10.3 3. The model for a full factorial 24 experiment is: y = 54-13x1 +14x2 + 52x319x4 + 2x12 - 6x13+5x14 - 1x23+5x24 - 8x34 where the coefficients shown are the parameters. If a 2+ experiment was built with gener- ator 4=123, then what terms could be modeled and what would the coefficients become?See Answer
Q19:Question 1 The editor of a UK college magazine is checking the latest edition of the magazine before it goes to print, but they have found some problems. (a) Three stories each have a piece of data missing. The topics of the three stories are: Story 1: A science project to find the fastest reaction time when mixing certain chemicals. Story 2: An interview with the winner of the inter-collegiate 1500 metre race. Story 3: The results of a survey to find the average time it took students to travel from their home to the entrance of the college campus. The three pieces of data are: A: 5 minutes 33 seconds B: 42 minutes C: 31.4567 seconds Match each story with the most appropriate piece of data, justifying your answer. (b) A story about the campus shop says that students spend on average £4.5682351 per visit. The editor rightfully thinks that this level of accuracy is unjustified. Round £4.5682351 to an appropriate level of accuracy, justifying your answer. (c) The word counts for the main articles in the latest magazine edition are: 220, 470, 1300, 250, 1100, 540, 380, 670. (i) Calculate by hand the median word count. Show your working. (ii) Calculate by hand the range of word counts. Show your working. See Answer
Q20:Question 2 A biologist is studying the development of a small population of rabbits. The length of each rabbit is recorded at the age of 3 weeks old and again at the age of 6 weeks old. The Minitab worksheet rabbits.mwx contains two columns. The column 3 weeks gives the length of each rabbit in millimetres at 3 weeks old and the column 6 weeks gives the corresponding length of the same rabbit in millimetres at 6 weeks old. Run Minitab and open this worksheet.See Answer

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