MECH5750 DoE Midterm Exam

MECH5750 DoE Midterm Exam

MECH5750 DoE Midterm Exam. Fall 2016, due Midnight Sunday October 16^th. Name _________________

QUIZ C to be answered by student ID last digit 3 or 5. Part II

Please show background Calculations. Think of this problem as a combination of treatments and DoE

1. For the experiment to Minimize the yield of popcorn = # of un-popped Kernels (2 factors and one interaction)

 

Brand              Ratio      Brand*Ratio            Yield (un-popped Kernels)

Test                 Popcorn           of Oil      Interaction    Replication

Number           (1)                    (2)        (12)                  1          2                      SY2     Avg.    Sy       (Sy)2    V

1                      –                       –                ___             6          4                      52        5          10        100      2

2                      +                      –                ___             5          4                      41        4.5       9          81     0.5

3                      –                       +               ___             8                                  64        8          8          64

4                      +                      +               ____           3                                  9          3          3          9

Total    166      5.13     30        254

 

1. Fill in the blanks for the levels of the interaction, and calculate the correction Factor CF = _______

 

2. Complete the anova treatment Table and determine Experiment significance

Please Show Calculations. Use Assignment 3 problem 3.6 as a guide for the ANOVA. Between = Regression and Within = Error

 

Effect	DoF	SS	MS	F ratio	Significant 95%
Between					Yes or No
Within
Total

 

3. Calculate the main effects and their interaction. Make sure to use the average of each experiment line.

Calculate 1 = __________    2 = ________      12 = _______

 

4. Calculate Pooled estimate of Variance _______ using two methods. Indicate methods (they should be equal).

Method 1 _________________ ;    Method 2 __________________ (Hint see assignment 3.4.e solution)

 

 

5. What levels (+ or -) would be best for lowest un-popped kernels (Yield) values? Hint: one answer is intuitive

With Interaction:         Factor 1_____ factor 2 ______           Yield Value______

Without Interaction:    Factor 1_____factor 2 ______           Yield Value______

 

6. Based on CI (factors), which factors are significant: 1_______, 2________12__________

 

7. Calculate the average, standard error (s/√n) and 95% confidence interval for the following:

Hint: several CI (+/-) are the same and one answer is intuitive.

 

5. Total Experiment: Average ___5.13____+/- ________;
6. Treatment 1 (Experiment Line 1) only (6, 4)

Experiment line 1 Average ___5.0____+/ ______ (when considering line 1 only and ignoring experiment)

Experiment line 1 Average ___5.0____+/ ________ (when considering total experiment)

1. Treatment 3 (Experiment Line 3) only (8)

Experiment line 3 Average ___8.0____+/ ________ (when considering line 3 only and ignoring experiment)

Experiment line 3 Average ___8.0____+/ ________ (when considering total experiment