.6.13 Use Pareto analysis to investigate the following data collected on a printed-circuit-board assembly line: DEFECT NUMBER OF DEFECT OCCURRENCES Components not adhering 143 Excess adhesive Misplaced transistors Defective board dimension 71 601 146 Mounting holes improperly positioned 12 Circuitry problems on final test 90 Wrong component 212 a. Prepare a graph of the data. b. What conclusions do you reach?
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- A company was experiencing a chronic weld-defect problem with a water-outlet-tube assembly. Each assembly manufactured is leak tested in a water tank. Data were collected on a gap between the flange and the pipe for 6 bad assemblies that leaked and 6 good assemblies that passed the leak test. Leaked 0.290 0.104 0.207 0.145 0.104 0.124 Did not Leak 0.207 0.124 0.062 0.301 0.186 0.124 Calculate the sample mean for both the assemblies that leaked and those that did not. Calculate the sample standard deviation for both the assemblies that leaked and those that did not. Does there appear to be a major difference in gap between assemblies that leaked and those that did not?22. Recall the study, reported in Exercise 7.8.1, in which Dora et al. (A-37), investigated spinal canal dimensions in 30 subjects symptomatic with disc herniation selected for a discectomy and 45 asymptomatic individuals (control group). One of the areas of interest was determining if there is a difference between the two groups in the spinal canal cross-sectional area (cm) between vertebrae L5/S1. The data in the following table are simulated to be consistent with the results reported in the paper. Do these simulated data provide evidence for us to conclude that a difference in the spinal canal cross-sectional area exists between a population of subjects with disc herniations and a population of those who do not have disc herniations? Let a = .05. Herniated Disc Group Control Group 2.62 2.57 1.98 3.21 3.59 3.72 4.30 2.87 3.87 2.73 5.28 3.67 3.32 1.60 1.80 3.91 2.56 1.53 1.33 2.36 1.64 3.54 3.63 2.39 2.67 3.53 2.26 2.82 4.26 3.08 4.00 2.76 3.58 2.05 1.19 3.01 2.39 3.61 3.11 3.94 4.39…4. If the normality or equal variance assumptions are violated, what can be done? Select all that apply a. Apply a transformation to the data, say, using square-roots, logs, or Box-Cox b. Use a non-parametric alternative to ANOVA, like Kruskal-Wallis c. Ask for help from a statistician or scour the web for an answer d.Give up.
- 3. Two companies compete in the production of laser printers. The impact strength of a printer measured in foot-pounds is an important characteristic. A random sample of n = 10 gears from company 1 results in T = 290 and s1 = 12, and another random sample of n2 = 16 gears from the second company results in F2 = 321 and s2 = 22. (a) Is there evidence to support the claim that company 2 provides gears with higher mean impact strength? Use a = 0.05, and assume that both populations are normally distributed with potentially unequal variance. Report the p-value for the test you have performed. (b) Do the data support the claim that the mean impact strength of gears from company 2 is at least 25 foot-pounds higher than that of supplier 1?1.8 EZ-Windows, Inc. manufacturers replacement windows for the home remodeling business. In January, the company produces 15,000 windows and ended the month with 9,000 windows in inventory. EZ-Windows’ management team would like to de- velop a production schedule for the next three moths. A smooth production schedule is obviously desirable because it maintains the current workforce and provides a sim- ilar month-to-month operation. However, given the sales forecasts, the production capacities, and the storage capabilities as shown in Table 2, the management team does not think a smooth production schedule with the same production quantity each month possible. The company’s cost accounting department estimates that increasing production by one window from one month to the next will increase total costs by $1.00 for each unit increase in the production level. In addition, decreasing production by one unit from one month to the next will increase total costs by $0.65 for each unit…7.6 A leading researcher in the study of interstate highway accidents proposes that a major cause of many collisions on the interstates is not the speed of the vehicles but rather the difference in speeds of the vehicles. When some vehicles are traveling slowly while other vehicles are traveling at speeds greatly in excess of the speed limit, the faster-moving vehicles may have to change lanes quickly, which can increase the chance of an accident. Thus, when there is a large variation in the speeds of the vehicles in a given location on the interstate, there may be a larger number of accidents than when the traffic is moving at a more uniform speed. The researcher believes that when the standard deviation in speed of vehicles exceeds 10 mph, the rate of accidents is greatly increased. During a 1-hour period of time, a random sample of 50 vehicles is selected from a section of an interstate known to have a high rate of accidents, and their speeds are recorded using a radar gun. The data…
- b. A best-fit line has been included on the calibration curve via a least squares analysis. By simple visual inspection of the figure to the right (do not re-create it), explicitly write out the equation/model for this calibration curve including units. c. Using your model (i.e. not just visual) from part-b of this question, what would be the analyte concentration when the detector response is 250 mV (show your work)?d. Using your model from part-b and extrapolating, what would be measured detector response when the concentration is 73.7 uM? (show your work)?6.6 The Department of Natural Resources (DNR) received a complaint from recreational fish- ermen that a community was releasing sewage into the river where they fished. These types of releases lower the level of dissolved oxygen in the river and hence cause damage to the fish resid- ing in the river. An inspector from the DNR designs a study to investigate the fishermen’s claim. Fifteen water samples are selected at locations on the river upstream from the community and fifteen samples are selected downstream from the community. The dissolved oxygen readings in parts per million (ppm) are given in the following table. Upstream 5.2 4.8 5.1 5.0 4.9 4.8 5.0 4.7 4.7 5.0 4.6 5.2 5.0 4.9 4.7 Downstream 3.2 3.4 3.7 3.9 3.6 3.8 3.9 3.6 4.1 3.3 4.5 3.7 3.9 3.8 3.7 a. In order for the discharge to have an impact on fish health, there needs to be at least an .5 ppm reduction in the dissolved oxygen. Do the data provide sufficient evidence that there is a large enough reduction in the mean…1. A textile company is interested in knowing if there is a difference in the breaking strength offour different kinds of thread. A test was conducted where five measurements (in ounces) weretaken for each kind of thread. Dummy variables were created named threada, threadb, andthreadc, which indicated if a strength reading was obtained on thread a, b, or c, respectively. Aregression analysis was performed with breaking strength as the dependent variable and threada,threadb, and threadc as independent variables, the results are attached at the end of the sheet. a) Write the linear model for the regression analysis, give the F statistic and P valuefor the test of equality of breaking strength means for the four threads, and state your conclusionfor the test using alpha = .05. b) Use the printout from the regression analysis to give estimates of the mean breakingstrength for each of the four thread groups. c) On the regression analysis printout on the row with information about threadb…
- 3.6 The article "The Need to Be Plugged In" (Associated Press, December 22, 2005) described the results of a sur- vey of 1006 adults who were asked about various tech- nologies, including personal computers, cell phones, and DVD players. The accompanying table summarizes the re sponses to questions about how essential these technolo- gies were. Relative Frequency Personal Cell DVD Response Computer Phone Playe Cannot imagine living without .46 41 .19 Would miss but could do without .28 .25 .35 Could definitely live without .26 .34 .46 Construct a comparative bar chart that shows the distribu- tion of responses for the three different technologies.2. Two suppliers manufacture a plastic gear used in a laser printer. The impact of these gears measured in foot-pounds is an important characteristic. Assume the impact strength from both suppliers are independent of each other and normally distributed. A random sample of 10 gears from supplier 1 results in T1 = 289.3 and s = (35.5)². Another sample of 16 gears from supplier 2 results in 2 321.5 and s = (21.1)². Supplier 2 claims to provide gears with higher mean impact strength than supplier 1. (a) from two suppliers have the same impact strength variance. Use a F test with a = 0.1 to determine whether the plastic gears (b) Determine whether the claim of supplier 2 is correct. Use a = 0.05.5.6.5 WP An article in Knee Surgery Sports Traumatology, Arthroscopy ["Effect of Provider Volume on Resource Utilization for Surgical Procedures" (2005, Vol. 13, pp. 273–279)] showed a mean time of 129 minutes and a standard deviation of 14 min- utes for ACL reconstruction surgery for high-volume hospitals (with more than 300 such surgeries per year). If a high-volume hospital needs to schedule 10 surgeries, what are the mean and variance of the total time to complete these surgeries? Assume that the times of the surgeries are independent and normally distributed.