Assignments for week 3 (2)

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University Canada West *

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660

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Communications

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May 11, 2024

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Please print the following information: Assignments for week 3 I would like to encourage collaboration on our upcoming assignment, while still requiring each of you to submit individual responses. Here's what I am proposing: ▪ Form small groups (3-4 students) to work together on the assignment. This will allow you to discuss ideas, share perspectives, and support one another in understanding the material. ▪ While working in your groups, please remember that each of you will need to submit your own unique responses to the assignment. Although collaboration is encouraged, copying, or directly reproducing another student's work is not allowed. ▪ As you work together, focus on developing your own critical thinking and problem-solving skills. Use the discussions with your peers to deepen your understanding and to clarify any misconceptions or doubts. ▪ Once you have completed the assignment as a group, take some time to reflect on your own understanding of the material and put together your individual responses. Be sure to express your ideas in your own words and give proper credit to any sources or ideas that came from your group discussions. By working together and submitting individual responses, you will not only develop stronger comprehension of the material, but also improve your communication and teamwork skills. I hope this collaborative approach will enhance your learning experience and lead to a richer understanding of the course content. 1

Questions: 1. Please respond to the weekly forum 3 provided in Week 3. 2. An automatic filling machine is used to fill 2-litres bottles of cola. The machine’s output is known to be approximately Normal with a mean of 2.0 litres and a standard deviation of .018 litres. Output is monitored using means of samples of seven observations. a. Determine the upper and lower control limits that will include roughly 95.44 percent of the sample means. (Round the final answers to 3 decimal places.) b. If the means for 6 samples are 1.990, 1.994, 1.993, 2.008, 2.004, and 1.992, is the process in control? Answer: To determine the control limits for sample means Upper Control Limit (UCL) = Mean + (Z * (Standard Deviation / √n)) Lower Control Limit (LCL) = Mean - (Z * (Standard Deviation / √n)) Given: Mean (μ) = 2.0 litres Standard Deviation (σ) = 0.018 litres Sample Size (n) = 7 Using the formula, we can calculate UCL and LCL UCL = 2.0 + (1.708 * (0.018 / √7)) LCL = 2.0 - (1.708 * (0.018 / √7)) Calculating the values: UCL = 2.007 Litres LCL = 1.993 litres B. Now let's check if the process is in control using the given sample means: The mean of the sample means = 1.990+1.994+1.993+2.008+2.004+1.992= 1.996833 Since the sample means fell within the control limits (UCL and LCL), Therefore, the process is in control. 3. A friend of yours has told you that no matter how much she studies, she does badly in exams. Help her set up a cause-and-effect diagram for her problem. Answer: A cause-and-effect diagram is a crucial instrument for identifying the root causes of a problem and examining the resulting consequences along with possible remedies. In this particular scenario, my acquaintance is experiencing subpar performance in her 2

examinations, regardless of the level of effort she invests. An endeavor is considered futile when its approach does not coincide with the established objective. By utilizing a cause-and-effect diagram, we will endeavor to study the obstacles she has encountered and uncover the underlying factors in order to generate a course of action. When analyzing the problem from a hierarchical perspective, let us focus on identifying the underlying source of the problems experienced by her. Possible root causes of the issue may include: • Inadequate study regimen • Challenges comprehending the curriculum • Insufficient study materials • Limited engagement with the instructor and classmates • Anxiety stemming from past academic performance Outlined above are the various factors that may contribute to the unfavorable outcome attained by my friend. Therefore, it is equally necessary to work on it in order to eliminate the problems. The cause-and-effect diagram examines the problems related to the solution of the daily study routine, including time allocation for comprehension before memorization, conducting further research in the library or online, and receiving regular feedback from the instructor. Regularly engaging in discussions and follow-ups with peers in the same group helps alleviate stress and enhances confidence, leading to improved future outcomes. 4. A quality inspector took five samples, each with four observations, of the length of a part (in centimetres). She computed the mean of each sample (see table below). a. Use the following data to obtain three sigma (i.e., z = 3) control limits for sample mean. Is the process in control? b. If a new sample (sample 6) has values 12.10, 12.19, 12.12, and 12.14, using the sample mean control chart in part a, has the process mean changed (i.e., is there an assignable variation)? It is known from previous experience that the standard deviation of the process is 0.02 cm. Sample Observation 1 1 2 3 4 5 12.11 12.15 12.09 12.12 12.09 2 12.10 12.12 12.09 12.10 12.14 3 12.11 12.10 12.11 12.08 12.13 4 12.08 12.11 12.15 12.10 12.12 ̅ LX 12.10 12.12 12.11 12.10 12.12 3

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