HW03 Statistical Techniques in Quality Management

HW03 Statistical Techniques in Quality Management

1. Two Group Mean Comparison

Maggie’s French Fry Study. It is a case from the textbook: page 305. You can find the data at “Data Files for Problems” section of the Blackboard. Please read the case to understand the context of the problem. Then, instead of working on the problems of the book, please conduct following two tests:

1. (10 pts.) Compare the mean of two different locations (1 and 2). Then establish a statistical significance on the mean difference. Please comment on your results.

1. (10 pts.) Compare the non-conforming rate (proportion of nonconforming) between two locations. Then establish a statistical significance on the proportion difference. Please comment on your results. You will need to rely on the third column from the table below.

2. Twoway ANOVA and Interaction

Use ANOVA-Twoway Data, please conduct a Twoway ANOVA analysis and offer some discussion required below. Please ONLY choose GlassType 1 and GlassType 3 and Temp 100 and Temp 150 (2 by 2 design) as the experiment data.

1. Conduct a Twoway ANOVA using Excel and Paste the result in picture in the space below. Please comment on the result. Which one is the sample factor, and which one is the column factor? Please discuss.
2. (10 pts.) What is the amount of total variations that can be explained by these two factors? (Hint: look for the ratio between SSTR/SST)
3. Is there any factor(s) turn out to be not introducing any variations to the responses? (Hint: judging by the p-value associated with the factor?)
4. (10 pts.) Please plot the interaction and paste it here. Do you see interaction effect between two factors? (Hint: Please use attached Interaction Plotting Template)
5. (Optional) Based on the ANOVA result, can you come up with a prediction model of the outcome variable?

3. More on Interaction Effect

This is simple example that is inspired by COVID-19.
Currently, the entire world is struggling to understand why some people experience greater pain and some almost feel nothing when contracted by the COVID-19 virus. The table below shows a fictitious example.  Please answer the following questions.
 

• (2 pts.) Which factor seems to be a “change maker” (a factor that introduces variations between observations)
  1. Gender
  2. Age
  3. Both gender and age
• (2 pts.) Which factor seems to have a greater impact in making differences among people?
  1. Gender
  2. Age
  3. Cannot tell
• (2 pts.) From the experiment design perspective, how many treatment groups are here?
  1. Two
  2. Three
  3. Six
  4. Cannot tell
• (2 pts.) When we talk about the un-explained the variations, in this particular example, which one are we referring to?
  1. Variation among age groups
  2. Variation between gender groups
  3. Variation within each block (e.g., differences among Jane, Eva, and Kamila)
• (2 pts.) Which of the following sentence is describing the interaction effect?
  1. When compared to the younger female group, older male group will experience even greater severity than the older female group.
  2. When compared to the younger female group, older female group will experience greater severity.
  3. When compared to the younger female group, younger male group will experience greater severity.

 
Table: COVID-19 Patient Data – Severity Summary
(Note: The higher the number, the more deadly the symptom is)

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