A03-Questions-1

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University of Toronto *

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304

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Mechanical Engineering

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Feb 20, 2024

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University of Toronto Department of Mechanical and Industrial Engineering MIE304/364: Intro to Quality Control and Improvement (Winter 2024) Page 1 of 3 Assignment 3 Due: Friday, February 09, 2024, at 11:59 pm Please submit your answer as one Jupyter file and one PDF on Quercus Please post your questions on Piazza Please answer these following questions using Python. For this assignment you may need linregress, t, norm, shapiro, ttest_1samp, chi2, probplot, chisquare, chi2_contingency from scipy.stats 1. The percentage of investment in new-products development is monitored for an aerospace company. 30 observations are listed below: 28.5, 30.4, 32.6, 31.5, 30.6, 35.8, 36.4, 34.2, 35.0, 33.5, 32.9, 31.5, 34.3, 36.8, 35.0, 29.4, 33.2, 37.8, 35.0, 32.7, 31.8, 32.5, 28.4, 33.8, 35.1, 30.2, 33.0, 34.6, 32.4, 32.0 1.1. Plot the Run Chart. 1.2. Is the investment percentage random? Use α = 0.05. For this question the Minitab documentation can be helpful for the math. 1.3. Can you conclude that the distribution of investment percentages is normal? Set α = 0.01. 1.4. Find a 98% Confidence Interval for the Mean Percentage Investment. 1.5. Test whether the mean percentage investment in new products exceeds 31%. Use α = 0.01. Provide the p-value and explain the conclusion. 2. The tensile strength of a new composite material used in aerospace applications is critical for ensuring structural integrity. The tensile strength of the material is assumed to follow a normal distribution. A sample of 25 specimens of the composite material is tested for tensile strength, resulting in the following observations (in MPa): 129.22, 130.38, 125.92, 128.15, 127.66, 130.87, 127.46, 121.29, 128.25, 127.42, 130.67, 131.47, 127.55, 133.98, 126.65, 125.94, 128.79, 124.76, 128.37, 128.45, 129.53, 131.40, 125.97, 129.81, 127.77. 2.1. Test the hypothesis that the mean measurement is 130 MPa against a two-sided alternative using 𝛼 = 0.05. 2.2. Find a 95% two-sided confidence interval on 𝜇. 2.3. Test the hypothesis that 𝜎 2 = 20 against a two-sided alternative using 𝛼 = 0.05. 2.4 . Find a 95% two-sided confidence interval on 𝜎. 2.5 . Is the normality assumption valid for the tensile strength of each composite (Use a Normal Probability Plot)?
University of Toronto Department of Mechanical and Industrial Engineering MIE304/364: Intro to Quality Control and Improvement (Winter 2024) Page 2 of 3 3. An aerospace company is evaluating the impact of three different assembly techniques on the tensile strength of new composite materials. Tensile strength measurements (in MPa) were recorded for 200 randomly selected samples for each assembly technique, as shown in the Table below. Can we conclude that the assembly technique has an impact on the tensile strength? Use α = 0.10. Provide the p-value. Tensile Strength (MPa) Assembly Technique 1 Assembly Technique 2 Assembly Technique 3 150-199 85 30 75 200-249 60 40 70 250-299 25 70 30 300-349 30 60 25 4. An airline company is conducting a satisfaction survey to assess various aspects of its services. The survey includes 20 items covering different aspects. Items 1. Comfort of waiting areas 2. Clarity of signs 3. Efficiency of check-in and boarding process 4. Timeliness of baggage handling 5. Availability of assistance for passengers with special needs 6. Quality of seating arrangements 7. In-flight entertainment options 8. Courtesy and professionalism of flight attendants 9. Comfort and cleanliness of aircraft interiors 10. Timeliness of departure and arrival 11. Accuracy and clarity of flight information 12. Ease of booking and reservation process 13. Availability of onboard amenities (e.g., Wi-Fi, power outlets) 14. Quality and variety of in-flight meals 15. Responsiveness of customer service 16. Handling of lost or damaged baggage 17. Overall safety and security measures 18. Availability and cleanliness of restrooms 19. Clarity and transparency of pricing 20. Overall satisfaction with the airline experience
University of Toronto Department of Mechanical and Industrial Engineering MIE304/364: Intro to Quality Control and Improvement (Winter 2024) Page 3 of 3 The clients were asked to rate their perceived level of satisfaction on a five-point ordinal Likert scale (1 = Not Satisfied, 2 = Slightly Satisfied, 3 = Neutral, 4 = Satisfied, 5 = Very Satisfied). Additionally, the clients rated the importance of each item on a five-point ordinal Likert scale (1 = Not Important at All, 2 = Slightly Important, 3 = Neutral, 4 = Important, 5 = Very Important). The median rating scores for both perceived satisfaction and importance for each of the 20 items are given in the dataset “A3 data”. 4.1. Does the importance of items influence overall satisfaction? Use α= 0.01. 4.2. Find Cramer’s index of association. 4.3. Construct an overall analysis chart to advise management on strategic and operational plans.
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