Construct the appropriate control chart with 3o limits. Plot the data and determine whether the process is in control.
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- The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file P13_17.xlsx. a. Estimate a simple regression equation involving annual sales (the dependent variable) and the size of the population residing within 10 miles of the restaurant (the explanatory variable). Interpret R-square for this regression. b. Add another explanatory variableannual advertising expendituresto the regression equation in part a. Estimate and interpret this expanded equation. How does the R-square value for this multiple regression equation compare to that of the simple regression equation estimated in part a? Explain any difference between the two R-square values. How can you use the adjusted R-squares for a comparison of the two equations? c. Add one more explanatory variable to the multiple regression equation estimated in part b. In particular, estimate and interpret the coefficients of a multiple regression equation that includes the previous years advertising expenditure. How does the inclusion of this third explanatory variable affect the R-square, compared to the corresponding values for the equation of part b? Explain any changes in this value. What does the adjusted R-square for the new equation tell you?Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem. Sample Size, n Mean Factor, A2 Upper Range, D4 Lower Range, D3 2 1.880 3.268 0 3 1.023 2.574 0 4 0.729 2.282 0 5 0.577 2.115 0 6 0.483 2.004 0 7 0.419 1.924 0.076 8 0.373 1.864 0.136 9 0.337 1.816 0.184 10 0.308 1.777 0.223 12 0.266 1.716 0.284 Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day Mean Bold x overbarx (mm) Range R (mm) 1 154.9154.9 4.04.0 2 151.2151.2 4.44.4 3 153.6153.6 3.93.9 4 155.5155.5 5.05.0 5 158.6158.6 4.3 a) What is the value of x? X = ____ mm b) What is the value of R? R =…Elon Corporation manufactures parts for an aircraft com-pany. It uses a computerized numerical controlled (CNC) machining center to produce a specific part that has adesign (nominal) target of 1.275 inches with tolerancesof 0.024 inch. The CNC process that manufacturesthese parts has a mean of 1.281 inches and a standarddeviation of 0.008 inch. Compute the process capabilityratio and process capability index, and comment onthe overall capability of the process to meet the designspecifications.
- Rajan wanted a radio from Jacky's. It appears that Rajan is particularly interested in purchasing a Radio from the inexpensive retailer's sales manager for consumer electronics. He tells Jacky, the salesperson at the inexpensive store where he thinks he'll get the best deal, that his old radio died and he wants to listen to his favourite tunes. He wants a replacement radio as quickly as possible. In three and a half weeks, Rajan's favourite model will be 10% off.He suspects Rajan won't wait and will find another job. Jacky will earn less on the lowered price. He thinks that telling Rajan of the sale makes little sense.When Jacky tells Rajan that the radio set he wants is no longer available and won't be for another week, Rajan is enraged. Fearing losing the business, Jacky begs his sales manager, Michelle, to speed up delivery. Michelle says it's impossible and suggests Jacky tell Rajan the store can get the set in 24 hours and sell him the demo model. Michelle says the sample is new…3. What is the purpose of the design of experiments? Describe a factorial experiment. Provide some examples of factorial experiments that you might use to solve some types of quality-related problems.In a sausage factory, quality managers are studying the compliance of the sausages with the requirements. Any sausage having pin holes, air pockets, deformation or breakage in its casings is counted as defective and total number of such defective sausages alone is noted in each shift. The following data represents the number of defective sausages in samples of 200 sausages taken from 10 shifts. Sample Defectives Percent Defective 1 40 20% 2 28 14% 3 15 8% 4 23 (a) 5 20 10% 6 21 11% 7 19 10% 8 15 8% 9 16 8% 10 17 9% Calculate the value for (a) in the table above. Calculate p-bar based on the samples above. What is the UCL and LCL for a p chart based on the data provided and a desired control level of 99.74%? Use your control limits from part b along with the data provided to draw a p-chart. Is the process in control? Why or why not? If not in control, suggest some potential reasons.
- 4. Refer to Table S6.1 - Factors for Computing Control Chart Limits (3 sigma) LOADING... for this problem. Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day Mean x (mm) Range R (mm) 1 156.9 4.4 2 155.2 4.4 3 155.6 4.3 4 153.5 4.8 5 156.6 4.7 Part 2 a) What is the value of x? x= _______ mm (round your response to two decimal places). b) What is the value of Upper R overbarR ? Upper R overbarRequals= _______ mm (round your response to two decimal places). c) What are the UCL Subscript x overbarUCLx and LCL Subscript x overbarLCLx using 3-sigma ? Upper Control Limit (UCL Subscript x overbarUCLx ) = _________ mm (round your response to two…A new fly spray is applied to 50 samples each of 5 flies and the number of living fliescounted after an hour. The results were as follows: Number living 0 1 2 3 4 5 frequency 7 20 12 9 1 1 i. Calculate the mean number of living flies per sample and hence an estimate for p, the probability of a fly surviving the sprayii. Using your estimate calculate the expected frequencies (each correct to one decimalplace) corresponding to a binomial distributioniii. Perform a chi – square goodness – of – fit test using a 5% significance level.(c)A production manager at a Contour Manufacturing planthas inspected the number of defective plastic molds in 5 randomsamples of 20 observations each. Following are the number ofdefective molds found in each sample:SampleNumber ofDefectsNumber ofObservationsin Sample11202220322041205020Total 6 100Construct a 3-sigma control chart (z 3) with this information
- Mr. A wants to study the salient factors that may influence the adoption of Social Networking Sites (SNS) for educational purposes. For this, he identifies the variables such as trust (TR), emotional attachment (EA), resource and material sharing (RA), communication (COM), and collaboration (COL) that may affect the adoption of the Social Networking Sites (SNS). Confirmatory Factor Analysis (CFA) was employed to perform reliability and validity checks, and Structural Equation Modelling (SEM) was employed to test the proposed conceptual model. This study could help instructors and managements at higher educational institutions to formulate strategies to encourage the students to use social networking sites for academic purposes. Based on the above information, answer the following questions. Develop the conceptual model of the study. Develop the alternative hypothesis of the study. Develop the research objective of the study. Suggest the target…Jim’s Outfitters, Inc., makes custom fancy shirts for cowboys. The shirts could be flawed in various ways, including flaws in the weave or color of the fabric, loose buttons or decorations, wrong dimensions, and uneven stitches. Jim randomly examined 10 shirts, with the following results:Shirt Defects1 82 03 74 125 56 107 28 49 610 6a. Assuming that 10 observations are adequate for these purposes, determine the three-sigma control limits for defects per shirt.b. Suppose that the next shirt has 13 flaws. What can you say about the process now?The following table contains the measurements of the key length dimension from a fuel injector. These samples of size five were taken at one-hour intervals. Use three-sigma control limits. Use Exhibit 10.13. SAMPLE NUMBER OBSERVATIONS 1 2 3 4 5 1 0.486 0.499 0.493 0.511 0.481 2 0.499 0.506 0.516 0.494 0.529 3 0.496 0.500 0.515 0.488 0.521 4 0.495 0.506 0.483 0.487 0.489 5 0.472 0.502 0.526 0.469 0.481 6 0.473 0.495 0.507 0.493 0.506 7 0.495 0.512 0.490 0.471 0.504 8 0.525 0.501 0.498 0.474 0.485 9 0.497 0.501 0.517 0.506 0.516 10 0.495 0.505 0.516 0.511 0.497 11 0.495 0.482 0.468 0.492 0.492 12 0.483 0.459 0.526 0.506 0.522 13 0.521 0.512 0.493 0.525 0.510 14 0.487 0.521 0.507 0.501 0.500 15 0.493 0.516 0.499 0.511 0.513 16 0.473 0.506 0.479 0.480 0.523 17 0.477 0.485 0.513 0.484 0.496 18 0.515 0.493 0.493 0.485 0.475 19 0.511 0.536 0.486 0.497 0.491 20 0.509 0.490 0.470 0.504 0.512 Calculate the mean and range for the above samples.…