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A snowmobile company makes an average of 9 engines/day, with engine average output of 10 horsepower (hp) based on historical record. No other information is available. Please show formulae used in each answer.

1. During the day of Monday, 9 engines were made and tested at with average = 11 hp and sample standard deviation = 5.0. Did the factory experience a problem in materials or methods for the day that was significant?

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Answer significant difference (Monday sample average versus historical record): Yes________, No_________

2. What is the maximum acceptable average engine horsepower that can be produced based on Monday production data (9 engines were made and tested with average = 11 hp and standard deviation = 5.0)?

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Answer maximum acceptable average engine horsepower on Monday______________

3. A check of the company records indicated that over the last week, 30 engines were made, with and average or 10 hp and standard deviation of 3. Given this new information, does the answer in question 1 change?

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Answer significant difference (Monday sample average versus historical record): Yes________, No_________

4. For the situation described in problem 3, (a check of the company records indicated that over the last week, 30 engines were made, with average = 10 and standard deviation of 3). What is the maximum acceptable average engine horsepower that can be produced in this factory for a typical day production of 9 units?

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Max Acceptable average horse power for a typical Day ________

5. Is the variability of the 9 engines made on Monday (with average = 11 hp and standard deviation = 5.0) significantly different from last week’s engine Standard deviation (=3) of 30 engines?

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Answer Significant Variability difference Monday versus last week Yes________, No___________

6. Management decided to check the engines made on Tuesday. Seven (7) engines were made with average = 9 hp and standard deviation = 2.0. Ignoring the historical record and the data from the previous week, is the 7 engines average output = 9 on Tuesday significantly different than the 9 engines on Monday (11 average and sigma = 5.0)? Please extrapolate from the t table for the answer

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Answer Significant Average difference Monday versus Tuesday (w/o historical record) Yes______, No_____

7. Can the management test for the assumption that the engine variances (9 engines on Monday with 11 average and sigma = 5.0 and 7 engines on Tuesday average 9 hp and standard deviation = 2.0 are significant based on the Monday and Tuesday variance outputs?

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Answer Significant Variance difference Monday versus Tuesday Yes________, No___________

8. Historically the engines yields a Mean µ = 10 hp and = 3.0. A new engine is being developed. How many engines are needed to test to insure (95% confidence) that new mean is within .5 hp of the old engine?

Formulas: n =______________; Please show Calculations:

MECH5750 DoE Midterm Exam. Fall 2016, due Midnight Sunday October 16th. 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 Y2 Avg. y (y)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

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.

a. Total Experiment: Average ___5.13____+/- ________;

b. 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)

c. 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