Problem 1- Suppose that the National Transportation Safety Board (NTSB) wants to examine the safety of compact cars, mid-size cars, and full-size cars. It collects a sample of three for each of the treatments (car types). Using the hypothetical data below, test at 5% level of significance, whether the mean pressure (lower the better) applied to the driver's head during a crash test is the same for all the three types.
|
Compact Cars
|
Mid-size Cars
|
Full-size Cars
|
|
643
|
469
|
484
|
|
655
|
427
|
456
|
|
702
|
525
|
402
|
If the means are not all equal, perform LSD test for pair-wise comparisons, and identify all observations that are significant. Use a 5% level of significance.
Problem 2- A research study was conducted to examine the clinical efficacy of a new antidepressant. Depressed patients were randomly assigned to one of three groups: a placebo group, a group that received a low dose of the drug, and a group that received a moderate dose of the drug. After four weeks of treatment, the patients completed the Beck Depression Inventory test and received the following scores. The lower the score, the better it is.
|
Placebo
|
Low Dose
|
Moderate Dose
|
|
38
|
22
|
14
|
|
47
|
19
|
26
|
|
39
|
8
|
11
|
|
25
|
23
|
18
|
|
42
|
31
|
5
|
At 5% level of significance, test whether the mean scores are equal for all of the above 3 treatments. If the means are not all equal, perform LSD test for pair-wise comparisons, and identify all observations that are significant (Use a 5% level of significance).
Problem 3-
Bearings, Inc. manufactures stainless steel ball bearings 22 mm in diameter (the target value). A tolerance of 7 mm above the target and 4 mm below the target is acceptable to purchasers. The mean and standard deviation of the manufacturing process (assuming normal distribution) are calculated to be 25 mm and 2 mm respectively. Assume that the data is stable. Assume also that the process is considered capable only if each of the 3 process capability ratios (Cp, Cpk, and Cpm) is at least 1.5. Is the process capable?
Problem 4- Bearings, Inc. manufactures stainless steel ball bearings 22 mm in diameter (the target value). A tolerance of 4 mm above the target and 7 mm below the target is acceptable to purchasers. The mean and standard deviation of the manufacturing process (assuming normal distribution) are calculated to be 25 mm and 1 mm respectively. Assume that the data is stable. Assume also that the process is considered capable only if Cp is at least 1.5, andCpk is at least 0.3, and Cpm is at least 0.5. Is the process capable?
Problem 5-
|
Product Defective?
|
Julian - Morning
|
Julian - Afternoon
|
|
1
|
Yes
|
Yes
|
|
2
|
No
|
No
|
|
3
|
Yes
|
No
|
|
4
|
No
|
Yes
|
|
5
|
Yes
|
No
|
|
6
|
Yes
|
Yes
|
|
7
|
No
|
No
|
|
8
|
Yes
|
Yes
|
|
9
|
Yes
|
Yes
|
|
10
|
Yes
|
Yes
|
An appraiser is considered well-consistent with himself/herself if his/her Cohen's Kappa is at least 0.7. Is Julian well-consistent with himself?
Problem 6-
|
Product Defective?
|
Amy - Morning
|
Amy - Afternoon
|
|
1
|
Yes
|
Yes
|
|
2
|
No
|
No
|
|
3
|
Yes
|
Yes
|
|
4
|
No
|
Yes
|
|
5
|
Yes
|
Yes
|
|
6
|
Yes
|
Yes
|
|
7
|
No
|
No
|
|
8
|
Yes
|
Yes
|
|
9
|
Yes
|
Yes
|
|
10
|
Yes
|
Yes
|
An appraiser is considered well-consistent with himself/herself if his/her Cohen's Kappa is at least 0.7. Is Amy well-consistent with herself?
I will have an online quiz about 6 sigma, ANOVA and Minitab. I'm attaching more sample questions and solutions. The quiz will cover only these sample files. In this exam, I have to submit excels and minitabs for solutions.
Attachment:- Assignment.rar