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- A pharmaceutical company fills a drug which is in a powder form into a bottle. It has an automatedprocess consisting of a filling machine and a sealing unit. After filling the bottle, it is automaticallysealed with a metallic cap. To monitor the quality of the process, samples of size 5 are drawnperiodically from the process and the quantity filled is measured. The table below has data on 12such observations.Sample 1 2 3 4 51 9.21 8.87 8.71 9.08 9.342 9.06 8.97 9.13 8.46 8.853 9.35 8.95 9.20 9.03 8.444 9.21 8.71 9.05 9.35 8.875 9.01 9.17 9.21 9.05 9.536 8.74 8.35 8.50 9.06 8.897 9.21 9.05 9.00 8.78 9.238 9.15 9.20 9.23 9.15 9.069 8.98 8.81 8.90 9.13 9.0510 9.03 9.10 9.26 9.44 8.4811 9.49 9.05 9.12 8.88 8.9312 8.95 9.10 9.02 9.04 8.96(a) Establish the upper and lower control limits for the X bar chart and the R Chart(b) Construct a control chart and investigate if the process is in controlValues for setting the control charts are A2 = 0.577, D3 = 0, D4 = 2.114Chest Deceleration Measurements (g) from a Standard Crash Test Small 44 39 37 54 39 44 42 Midsize 36 53 43 42 52 49 41 Large 32 45 41 38 37 38 33 SPSS Results Sum of Squares df Mean Square F Sig. Between Groups 200.857 2 100.429 3.288 0.061 Within Groups 549.714 18 30.540 Total 750.571 20Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottleneck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (inch) from the last six samples are: BOTTLE Sample 1 2 3 4 1 0.694 0.622 0.698 0.69 2 0.687 0.611 0.697 0.613 3 0.671 0.680 0.695 0.602 4 0.610 0.615 0.685 0.678 5 0.680 0.624 0.618 0.614 6 0.685 0.693 0.607 0.669 What would be the upper control limit of a 3-sigma R chart? Answer:
- Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottleneck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (inch) from the last six samples are: BOTTLE Sample 1 2 3 4 1 0.694 0.622 0.698 0.69 2 0.687 0.611 0.697 0.613 3 0.671 0.680 0.695 0.602 4 0.610 0.615 0.685 0.678 5 0.680 0.624 0.618 0.614 6 0.685 0.693 0.607 0.669 What would be the lower control limits of a 3-sigma ?¯x¯ chart? Answer:Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottleneck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (inch) from the last six samples are: BOTTLE Sample 1 2 3 4 1 0.694 0.622 0.698 0.69 2 0.687 0.611 0.697 0.613 3 0.671 0.680 0.695 0.602 4 0.610 0.615 0.685 0.678 5 0.680 0.624 0.618 0.614 6 0.685 0.693 0.607 0.669 What would be the lower control limits of a 3-sigma ?¯x¯ chart? ( x bar chart )Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottleneck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (inch) from the last six samples are: BOTTLE Sample 1 2 3 4 1 0.694 0.622 0.698 0.69 2 0.687 0.611 0.697 0.613 3 0.671 0.680 0.695 0.602 4 0.610 0.615 0.685 0.678 5 0.680 0.624 0.618 0.614 6 0.685 0.693 0.607 0.669 What would be the center line of a 3-sigma ?¯x¯ chart?
- An agronomist undertook an experiment to investigate the factors that potato harvest. In his research, agronomist decided to divide the farm into 30 half hectare plots and apply varies level of fertilizer. Potato was then planted and the harvest at the end of the season was recorded. Fertilizer(Kg) Harvest (tons) 210 43.5 220 40.0 230 48.0 240 65.0 250 80.0 260 85.0 270 95.0 280 80.0 290 97.3 Note: No excel ANOVA output allowed. Students need to show all the steps in calculations. You are required to; Find the simple regression line and interpret the coefficients. Find the coefficient of determination and interpret its value. Does the model appear to be a useful tool in predicting the potato harvest? If so, predict the harvest when 250KG of fertilizer is applied. If not explain why not.GreenLawns provides a lawn fertilizing and weed control service. The company is adding a special aeration treatment as a low-cost extra service option, which it hopes will help attract new customers. Management is planning to promote this new service in two media: radio and direct-mail advertising. A media budget of $4,000 is available for this promotional campaign. Based on past experience in promoting its other services, GreenLawns has obtained the following estimate of the relationship between sales and the amount spent on promotion in these two media: S = -2R2 − 12M2 − 9RM + 20R + 39M, Where S = total sales in thousands of dollars R = thousands of dollars spent on radio advertising M = thousands of dollars spent on direct-mail advertising GreenLawns would like to develop a promotional strategy that will lead to maximum sales subject to the restriction provided by the media budget. (a) What is the value of sales if $3,000 is spent on radio advertising and $1,000 is…Lyme disease is an inflammatory disease that results in a skin rash and flulike symptoms. It is transmitted through the bite of an infected deer tick. The following data represent the number of reported cases of Lyme disease and the number of drowning deaths for a rural county. Cases_of_Lyme_Disease Drowning_Deaths Month3 0 J2 1 F2 2 M4 1 A5 3 M15 9 J22 17 J13 5 A6 3…
- An engineer wants to know if producing metal bars using a new experimental treatment rather than the conventional treatment makes a difference in the tensile strength of the bars (the ability to resist tearing when pulled lengthwise). At α=0.10, answer parts (a) through (e). Assume the population variances are equal and the samples are random. If convenient, use technology to solve the problem. Treatment Tensile strengths (newtons per square millimeter) Experimental 449 354 450 360 433 388 400 Conventional 370 376 374 424 378 450 438 404 352 376 (a) Identify the claim and state H0 and Ha. The claim is "The new treatment ▼ makes a difference does not make a difference in the tensile strength of the bars." What are H0 and Ha? The null hypothesis, H0, is ▼ mu 1 equals mu 2μ1=μ2 mu 1 less than or equals mu 2μ1≤μ2 mu 1 greater than or equals mu 2μ1≥μ2 . The alternative hypothesis, Ha,…An engineer wants to know if producing metal bars using a new experimental treatment rather than the conventional treatment makes a difference in the tensile strength of the bars (the ability to resist tearing when pulled lengthwise). At α=0.02, answer parts (a) through (e). Assume the population variances are equal and the samples are random. If convenient, use technology to solve the problem. Treatment Tensile strengths (newtons per square millimeter) Experimental 400 413 434 409 420 377 392 Conventional 381 446 436 350 404 354 375 361 355 386 (a) Identify the claim and state H0 and Ha. The claim is "The new treatment ▼ makes a difference does not make a difference in the tensile strength of the bars." What are H0 and Ha? The null hypothesis, H0, is ▼ mu 1 equals mu 2μ1=μ2 mu 1 less than or equals mu 2μ1≤μ2 mu 1 greater than or equals mu 2μ1≥μ2 . The alternative…Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (in.) from the last six samples are Bottle Sample 1 2 3 4 1 0.592 0.612 0.598 0.623 2 0.584 0.572 0.584 0.573 3 0.596 0.622 0.618 0.586 4 0.606 0.614 0.585 0.598 5 0.582 0.586 0.608 0.611 6 0.583 0.571 0.605 0.625 LOADING... Click the icon to view the table of factors for calculating three-sigma limits for the x-chart and R-chart. Part 2 Suppose that the specification for the bottle neck diameter is 0.600±0.050 in. and the population standard deviation is 0.013 in. a. What is the process capability index? The Cpk is enter your response here. (Enter your response rounded to two…
