practice questions11

Question 1:

When you compare the results of different operatorsusing the same gage taken at different times on the same group of parts , this is referring to _______

Answers:

A. Repeatability

B. Linearity, Bias, and Sensitivity over the sample of parts

C. Reproducibility

remember: Reproducibility = operator

Repeatability = equipment

D. Accuracy

(see BBMJ p82)

Question 2:

Which of the following is not an output of a Measurement

System Analysis?

Answers:

A. Percentage Tolerance

B. Percentage Study Variation

C. Percentage Calibration

D. Percentage Contribution

(see BBMJ p82)

Question 3:

Which of the following is not a component of Measurement

Error?

Answers:

A. Stability/Consistency

B. Calibration

C. Linearity

D. Resolution

(see BBMJ p74)

Question 4:

How many samples should be used for an attribute gage

R&R?

Answers:

A.1-10

B.10-25

C.30-100

D.1-25

(see BBMJ p90)

Question 5:

In a gage R&R, the r chart by operator should be?

Answers:

A. Unstable & out of control

B. Stable & in control

C. Stable with special cause variation

D. Unstable with special cause variation

(see BBMJ pp85-86)

Question 6:

Resolution and discrimination are the terms used to

describe a gages capability to detect the smallest

tolerable changes; therefore in the gage analysis what is

the ideal number of distinct categories?

Answers:

A. 2 to 3

B. 1

C. 5 or more

D. 3 to 4

(see GR&R sheet on PTI 6-Sigma SharePoint site)

Question 7:

Long-term variability is made up of:

I Outliers

II Process drift

III Common cause variation

IV Short-term variability

Answers:

A. I only

B. III only

C. I & III

D. II & IV

Lower spec. Upper spec.

Defects Defects

Short Term Variability.

Drift over time

(see BBMJ p45 or BBTM p204)

Question 8:

Calculate the Z score for a process that has a mean of

40.0, a standard deviation of 10.0 and a point of

interest of 20.

Answers:

A. 2.5

B. 1.5

C. 2.0

z = (X – µµµµ ) /σσσσ

(20- 40 )/10 = -2 Z = 2

D. 1.0

(see BBMJ p41, BBTM p328)

Question 9:

When conducting a capability study, a process was found to have exactly the same values for Cp and Cpk.

Why is this?

Answers:

A. The process is in statistical control

B. The process is operating outside of one of the specification limits

C. The process is operating outside of both specification limits

D. The process is centered exactly on the target value


Question 10: Determine the total area under the curve to the left of the Z point of interest.

Answers:

A.84.13%

B.77.91%

C.90.23%

D.90.32%

BB Memory jogger

Page 250

= 1 – 0.0968 = 0.9032

3210-1-2-3

0.4

0.3

0.2

0.1

0.0

Normal

CD

F

Z=1..30

3210-1-2-3

0.4

0.3

0.2

0.1

0.0

Normal

CD

F

Z=1..30

Question 11:

What is the long-term DPMO of a 3-sigma process (short

term)?

Answers:

A. 500,000

B. 4,661

C. 66,810 (see BBMJ p248)

D. None of the above

Question 12:

Which type of Yield doesn’t take into account hidden

factories?

Answers:

A. Rolled Throughput Yield

B. Final Yield

C. Normalized Yield

D. Throughput Yield.

(see BBTM p74)

Question 13:

An accounting department rejected last month 38 travel expense claims with a total of 45 errors from a total of 560 raised claims. The reasons for rejection were:

– Missing approver’s signature

– Missing receipts

– Incorrect exchange rates

– Expense claims included pay-tv charges

Calculate this process’ DPMO.

Answers:

A. 20,535

B. 20,089

4 ops per unit, 560 x 4 = 2240 total ops

45 defects / 2240 = 0.020089

0.020089 x 1,000,00 = 20,089

C. 80,357

D. 19,643

(see BBTM p87)

Question 14:Please calculate the Rolled Throughput Yield

for the following process.

Answers: A. 80%

B. 83%

C. 65% (See next slide for calculations)D. 61%

Step 1Input 1,000 units

Scrap 20 units

Rework 80 units

Step 2Input 980 unitsScrap 80 units

Rework 100 units

Step 3Input 600 unitsScrap 50 unitsRework 0 units


Rework 10 units


Rework 20 units

(see BBTM p91)

Step 1 Step 2 Step 3a Step 3b Step 4 Final

Units 1000 980 600 300 840 820

Scrap 20 80 50 10 20 180

Rework 80 100 0 10 20 210

TPY .90 .816 .917 .933 .952 N/A

RTY = .90 x .816 x (((6/9) x .917) + ((3/9) x .933)) x .952 = .645 or 65%

Step 1

Input 1,000 units

Scrap 20 units

Rework 80 units


Rework 100 units



Rework 10 units


Rework 20 units

Step 1

Input 1,000 units

Scrap 20 units

Rework 80 units


Rework 100 units



Rework 10 units


Rework 20 units

Question 15:

Tests for normality require how many observations

(minimum)?

Answers:

A. 10

B. 25

C. 50

D. 75

(see BBTM p426)

Question 15:

The minimum recommended number of samples for

constructing a histogram is:

Answers:

A. 50

B. 40

C. 30

D. 20

(see BBTM p426)

Question 16:

What does Final Yield calculate?

Answers:

A. Yield at the end of a process excluding scrap.

B. The yield after the first operation of a process.

C. The expected yield of a process.

D. The average of the last 3 yields of a process.

(see BBTM p76)

Question 17:

What does Rolled Throughput calculate?

Answers:

A. Yield after the second operation of a process.

B. Product of throughput yields across the entire process

C. Final Yield of a process divided by the number of operations in that process.

D. Final input of a particular process.


Question 18:

Why is TPY a more accurate calculation than FY?

Answers:

A. Final Yield does not consider scrap.

B. Throughput Yield includes rework only.

C. Final Yield ignores the hidden factory.

D. Final Yield includes both scrap and rework.


Question 19:

A process with an average cycle time of 25 days with a

standard deviation of 4 days. What are the chances that an

item is not finished within 30 days?

Answers:

A. 12.8 %

B. 26.3 %

C. 10.6 %

Z = (X – µµµµ)/σσσσ = (30-25)/4 = 1.25from pg 250 BB Memory jogger: row Z=1.2, col Z = 0.05

shows the area to the left of X = 0.1056 or 10.6%

D. 11.4 %

Question 20:

Normalized yield (NY) can be defined as:

Answers:

A. The average yield per process step of opportunity

B. The total yield of a projects’ process

C. The probability that all units will pass through the

process without rework

D. The probability that a certain percentage of units will

not pass through the process without rework


Question 21:

A random sample of 10 was taken from a population.

The sample has a variance of zero.

Which of the following statements must be true?

1. The population also has a variance of zero.

2. The sample mean is equal to the sample median.

3. The ten data points in the sample are equal in numerical value.

Answers:

A. 1 only

B. 3 only

C. 1, 2 and 3

D. 2 and 3(see BBMJ p104, BBTM p191)

Question 22:

The normal distribution is a theoretical concept that

Answers:

A. Is completely described by its mean & standard deviation.

B. Represents 99.73 % of the sample data

C. Is Bi-modal



Question 23:P(Z < 0.94) = ?

Answers: A. 0.17361

B. 0.82639P(Z< 0.94) = 1- P(Z =>0.94)

from BB Memory Jogger, page 250find row Z = 0.9 and column Z = 0.04 and find that P(Z=>0.94) = 0.1736, so our answer = 1-0.1736= 0.8263

C. 0.94000

D. 0.0600


Question 24:

Who defines specification limits?

Answers:

A. The process owner

B. The customer

C. The Black Belt

D. The project champion

(BBTM p308)

Question 25:

If Z=.65 at the USL, what is the probability of producing a

defect?

Answers:

A. 75%

B. 25%

from BB Memory Jogger, page 250

row Z=0.6, column z=0.05,

the are to the right of z=0.65 =0.2578

C. 50%

D. 30%

Question 26:

Why is Measurement System Resolution important?

Answers:

A. Without appropriate resolution the capability to detect the smallest tolerable change is lost

B. It increases the measured –actual process's

performance

C. It is a method to perform random sampling


Question 27:

Calculate DPU given 6 defects and a sample size of 30.

Answers:

A. 6

B 0.20

6/30 = 0.20

C. 1

D. 180


Question 28:

Which of the following does not effect location?

Answers:

A. Precision

B. Linearity

C. Accuracy

D. Stability

(see BBMJ pp74-75, BBTM p223)

Question 29:

Which of the following is not a common source of variation in a measurement system Gage R&R?

Answers:

A. People

B. Machines

C. Timing

D. Environment

(see BBMJ pp81-82, BBTM p240-243)

Question 30:Which statement about the MSA is NOT true?

Answers: A. MSA quantifies a major source of process variation

B. MSA is usually the last step of a 6 Sigma project after an improved solution has been found

C. Measurement System Analysis is often a “project within a project”

D. Each component of measurement error can contribute to variation, causing wrong decisions to be made


Question 31:

Given the R charts from two Gage R&R analyses :

A. (I) indicates a good gage resolution

B. (II) indicates a good gage resolution

C. Both (I) and (II) indicate good gages

D. Both may indicate poor gage resolution

0

0.15

0.10

0.05

0.00

321

R Chart by Operator

Sam

ple

Range

R=0.03833

UCL=0.1252

LCL=0

0

0.005

0.004

0.003

0.002

0.001

0.000

321

R Chart

Sam

ple

Range

R=4.33E-04

UCL=0.001416

LCL=0

(see BBMJ p86, BBTM pp267-268)

Question 32:

Given ten units that have a prescribed length and diameter.

Calculate DPO if 3 units are too long, 2 units have large

diameters, and 3 units are too long and have large

diameters.

Answers:

A. 0.05

B. 0.55

2 ops per unit, 20 total ops

total defects = 3 + 2+ 3 + 3 = 11

11 defects / 20 ops = 0.55

C. 5.5

D. 1.1(see BBMJ p59, BBTM p85)

Question 33:An inspection of 200 units shipped to a supplier revealed a total of 10 defects. Each unit has an opportunity for 10 defects. What is the DPMO?

Answers: A. 50

B. 250,000

C. 25,000

D. 5,000200 units x 10 ops = 2000 opportunities

10 defects total, DPO = 10/2000 = .005

DPMO = DPO x 1,000,000 = 5,000


Question 34:

What can be said about this data?

Answers:

1. The data set is not normally distributed

2. There is an outlier

3. The data is positively skewed

4. 50% of the data points are greater than 1.0005

A. 1

B. 1, 4

C. 2 & 3

D. 2, 3, 4

1.00081.00061.00041.00021.0000

95% Confidence Interval for Mu

1.000451.000401.000351.00030

95% Confidence Interval for Median

Variable: Diameter

1.00030

0.00018

1.00030

Maximum3rd QuartileMedian1st QuartileMinimum

NKurtosisSkewnessVarianceStDevMean

P-Value:A-Squared:

1.00040

0.00030

1.00046

1.000901.000501.000401.000281.00000

30-3.6E-02

0.4583474.86E-080.000221.00038

0.1100.598


95% Confidence Interval for Sigma


Anderson-Darling Normality Test

Descriptive Statistics

Question 35:Twice per shift an operator section cuts a weld to determine weld depth with a micrometer. The data is then recorded in a SPC chart. A black belt wants to validate the measurement system on this process. What should be done?

Answers: A. Conduct a nested Gage R&RB. Review the SPC chart and look for out of control

conditions

C. Conduct a crossed Gage R&R

D. Black belt should conduct several weld depth readings on a randomized number of parts and compare against readings taken by the operator

(see BBTM p417)

Question 36:

Which chart is negatively skewed?

#1 #2

A. #1

B. #2

C. Neither

D. both

1.00121.00101.00081.00061.00041.00021.0000


1.00051.00041.0003


Variable: Diameter

1.00030

0.00025

1.00035



P-Value:A-Squared:

1.00050

0.00039

1.00055

1.001301.000601.000401.000201.00000

380.9809981.05984

9.17E-080.000301.00045

0.0110.995






1.00161.00121.00081.00041.0000


1.001341.001241.001141.001041.000941.00084


Variable: Diameter_1

1.00090

0.00036

1.00087



P-Value:A-Squared:

1.00130

0.00057

1.00116

1.001801.001301.001151.000701.00000

38-1.0E-01-6.9E-011.95E-070.000441.00102

0.0290.829






(see BBMJ p103)

Question 37:

A Black belt has collected this data to conduct a MSA on a measurement system. What should his next step be?

Answer:

A. Normality is established and proceed with Gage R&R

B. Define a data collection plan for the Gage R&R

C. Collect additional samples and rerun Normality test

D. Establish SOP for the Gage R&R

121086420


65432


Variable: length

2.0000

2.1577

2.7679



P-Value:A-Squared:

6.0000

4.6480

6.0321

12.0000 6.0000 4.0000 2.0000 0.0000

152.103131.149818.685712.947154.40000

0.0770.639






(BBTM p425)

Question 38:

A Black belt has collected this data to conduct a MSA on a measurement system. What should his next step be?

Answer:

A. Normality is established and proceed with Gage R&R

B. Define a data collection plan for the Gage R&R

C. Establish SOP for the Gage R&R

D. Investigate data collection process and rerun Normality test

8078767472


777675


Variable: Sodium

75.0411

1.8741

75.3383



P-Value:A-Squared:

77.0178

2.9376

76.8017

81.000077.625075.350074.225072.1000

40-6.1E-01

0.4017305.23395 2.2878

76.0700

0.3280.410






(BBTM p340)

Question 40:

The throughput yields of 5 sub-processes in series to

execute in order are: 90%, 92%, 91%, 91.3%, and 89%,

respectively. What is the probability that the order executed

through this 5 sub-processes in series is defect free?

A. 0.89

B. not enough information

C. 0.61

.90 x 0.92 x 0.91 x .913 x .89 = 0.61

D. 0.70

(BBTM p77)

Question 41:

Dangers of a histogram being used to understand the process distribution shape are:

Answers

A. It will be misleading if process is not stable, AND a histogram does not take into account the sequence of points, and hence trends can not be detected.

B. It will be misleading if process is not stable.

C. A histogram does not take into account the sequence of points, and hence trends can not be detected.

D. None of the other answers are correct. A histogram can be used for any process to understand the shape of the process.

(BBTM p339)

Question 41:

What does the acronym SIPOC stand for?

Answers:

A. Solution Input People Output Characterisitics

B. Supplier Input Process Output Customer

C. Solve Input Process Owner Customer

D. Supplier Internal Process Owner Customer

E. Supplier Interview Process Output Customer


Question 42:

For a skewed distribution, which of the following is a better indicator of the central tendency?

Answers:

A. Standard deviation

B. Variance

C. Median

D. Mean


Question 43:Identify a tool that is typically used in the measure phase of Six Sigma DMAIC, and is useful in developing high level process maps.

Answers:

A. Cause and effect diagram

B. Hypothesis test

C. SIPOC

D. FMEA


Question 44:A Project Champion can best be described by:

Answers:

A. They are always the process owner

B. They are responsible for removing roadblocks and providing linkage of your project to the business

C. They are the provider of all 6-Sigma Expertise

D. They are a required team member to all project meetings


Question 45:

A Cause and Effect Diagram is used to:

Answers:

A. Prioritize relationships between several inputs and outputs

B. Help visualize relationships between several inputs and a given output and provide a guide for discussion

C. Prioritize risks

D. Obtain MSA data for your project


Question 45:

Given the following, calculate the Z value

(LSL = 150; USL = 215; mean = 213; s = 8, b=20%)

Answers:

A. 0.0031

B. 0.3682

C. 0.9999

D. 0.2500Z = (X – m)/s = (215 – 213) / 8 = 0.25

E. 0.5987


Question 46:

Provide the DPMO for the following process data

(Defects 30, Units 120, Opportunities per Unit 3)

Answers:

A. 750,000

B. 166,666

C. 83,333

DPMO = Defects/Opportunities * 1,000,000

Opportunities = Units*Opportunities/Unit

Defect = 30 Units = 120

Opportunities/Unit = 3

DPMO = 30/(120*3)*1000000 = 83,333

D. 987,000


Question 1:

Why should one learn the Central Limit Theorem?

Answers:

A. Applying the central limit theorem can reduce measurement error

B. Confidence Intervals are derived from the Central Limit Theorem

C. The Central Limit Theorem is the fundamental concept for inferential statistics

D. All of the Above


Question 2:

From history you know the variance of the population is 400.

You take 25 samples with a sample size of 16.

What is the standard error of the means?

Answers:

A. 16

B. 5

C. 4

Variance = σσσσ2

SE =

= sqrt( 400) / sqrt ( 25) = 20/5 = 4

D. 25

nX

σσ =

(see BBTM p350)

Question 3:

For a given standard deviation, the spread of the sampling distribution

________ when sample size _________

Answers:

A. Stays the same, decreases

B. Increases, stays the same

C. decreases, decreases

D. Decreases, increases

The spread of the sampling distribution is determined by the standard error.

Also, as n increases, the denominator increases and the overall standard error decreases.

nX

σσ =

(see BBTM pp348-349)

Question 4:

Simply stated, the Central Limit Theorem means;

Answers:

A. The more samples you have, the more normally distributed your sample means become.

B. CLT says that as n increases, distribution of sample means will approach a normal distribution with mean m and standard deviation

C. For a given standard deviation, the spread of the sampling distribution decreases when sample size increases (i.e. we have more confidence in our results when sample size is large)

D. All of the above


Question 5:

Which following statement is true about multi-vari analysis?

Answers:

A. Multi-vari analysis is a data analysis tool to study the relationship between

various continuous X’s and continuous response Y’s

B. Multi-vari analysis is a data analysis tool to study the relationship between

various categorical X’s and categorical response Y’s.

C. Multi-vari analysis is a graphical tool to analyze the effects of various categorical X’s on continuous response Y’s.

D. Multi-vari analysis is a graphical tool to analyze the effects of various

categorical X’s on categorical response Y’s.

1 2

1 2 1 2

0.01

0.02

0.03

0.04

0.05

Line

Impurity

1

2

3

4

Multi-Vari Chart for Impurity by Part - LineShif t

Part

(see BBMJ p127,

BBTM p416)

Question 6:

The Null and Alternate Hypotheses (H0 and HA) are statements about:

Answers:

A. Sampling statistics

B. Population parameters

C. Samples parameters

D. All of the above

(see BBTM p366)

Question 7:

Hypothesis testing for variances can be used to …

Answers:

A. compare a sample variance to a target

B. compare one sample against another

C. compare multiple samples

D. all of the above

(see BBTM p377)

Question 8:

This test statistic is used in analyzing variance hypothesis tests.

Answers:

A. z score

B. F test

This can be found on the Hypothesis Testing Roadmap

C. Chi squared

D. t test

(see BBTM p377)

Question 9:

This variance test is used in analyzing non-normal data

Answers:

A. Levene’s test

This can be found on the Hypothesis Testing Roadmap

B. Bartlett’s test

C. F test

D. Anderson-Darling

(see BBTM p377)

Question 10:

What is Correlation?

Answers: A. A way to show that there is always a relationship

between two variables

B. A way of measuring how much linear association exists between two quantitative variables.

C. A way to imply causation.

D. An equation describing the nature of a relationship of two independent variables.


Question 12:

When should a significance level less than 0.05 be used?

Answers:

A. Never, the 0.05 level of significance is the internationally recognized statistical standard.

B. When major rework, injury or death may result.

C. When the impact could be additional scrap or minor rework.

D. When you want to increase the power of your test.

E. Both B and D


Question 13:

When p = 0.04 and α = 0.05, we know:

Answers:

A. The Null Hypothesis is definitely false.

B. The Null Hypothesis is definitely true.

C. There is a 5% chance that the Null Hypothesis is false.

D. There is a 4% chance that rejecting the Null Hypothesis would be wrong.:


Question 14:

What is Β risk?

Answers:

A. Risk of making a Type II error.

B. Risk of not finding a difference when there really is one.

C. Consumers' Risk

D. All of the above


Question 15:

Given the following Minitab output from a Two Sample Paired-t Test, would you accept or reject the null hypothesis?

Answers:

A. Fail to reject the null hypothesis because the P-Value is > a=0.05

B. Reject the null hypothesis, the means are different

C. Fail to reject the null hypothesis because the P-Value is < a=0.05

D. Cannot tell from this analysis

Paired T-Test and CI: Machine A, Machine B

Paired T for Machine A – Machine BN Mean StDev SE Mean

Machine A 18 1.699 0.824 0.194Machine B 18 1.650 0.972 0.229Difference 18 0.0491 0.2896 0.068395% CI for mean difference: (-0.0949, 0.1931)T-Test of mean difference = 0 (vs not = 0): T-Value = 0.72

P-Value = 0.482


Question 16:

Determine the Variance Confidence Interval for n=10, s^2=50,000 at 99% confidence

Answers:

A. 19,067-260,116

B. Not enough info to calculate

C. 25,000-75,000

D. 138-509


2

2,1

2

21,1

11

αα χσ

χ−−−

−≤≤

−

nn

ns

ns

Question 17:

Calculate the Mean Confidence Interval for n=31, Xbar=280, s=20 at 99% confidence

Answers:

A. 270 – 290 CI = Xbar +/- 2.750 (20/sqrt 31)

B. 271.5 - 288.5

C. 250 - 310

D. 275.5 - 284.5


n

stx

n 1,2

−±= αµ

Question 18:

The probability of correctly rejecting Ho when it is false is also known as:

Answers:

A. Alpha

B. Power

C. Beta

D. Z score

Decision

Fail to reject Ho

Truth

Ho true

Ha true

Type I Error(α(α(α(α-Risk or false

positive)

Type II Error(β (β (β (β -Risk or false

negative)

Correct Decision

CI = 1- αααα

Correct Decision

Power = 1- ββββ

Reject Ho

Consumers’ Risk

(see BBTM p455)

Producers’ Risk

Question 19:

What is the Beta risk?

Answers:

A. Risk of finding a difference when there is not one

B. Risk of NOT finding a difference when there is one

C. Producers risk

D. Type I error


Question 19:

You will accept an alpha risk of 1% (or less). You receive a P-value of 0.04. What do you do?

Answers:

A. Fail to reject the Ho hypothesis

B. Reject the Ho hypothesis

C. Change the alpha level to 0.05 and rerun the test

D. Rerun the test

(see BBTM p371)

Question 20:

A clinical study of 111 out of 143 adults suffering from migraine headaches reported relief from using Drug A. If test proportion standard is set to .75 and confidence level is set to 95%, what can we interpret?

Answers:

A. Sufficient evidence that the drug is more than 75% effective

B. Insufficient evidence that the drug is not more than 75% effective

C. 71% of the sampled adults reported relief with Drug A

D. 29% of the sampled adults reported relieft with Drug A

Test and CI for One Proportion

Test of p = 0.75 vs p > 0.75

Exact

Sample X N Sample p 95.0% Lower Bound P-Value

1 111 143 0.776224 0.71132 0.124

(see BBTM p371)

Question 21:

As the % confidence increases, what is the effect on the spread of the Confidence Interval?

Answers:

A. No effect

B. The Confidence Interval gets wider

C. The Confidence Interval is inversely proportional to the % confidence level

D. The Confidence Interval gets closer together


Question 22:

Which hypothesis test is suitable for comparing a sample mean to a target value when the population standard deviation is not known

Answers:

A. 1 sample-Z test

B. 1 sample-t test

Follow the Roadmap

C. One-way ANOVA test

D. 2 sample-t test

Question 23:

In hypothesis testing the power of the test is defined by …

Answers:

A. Α

B. 1-α

C. 1-β

D. β-α

(see BBTM p455)

Decision

Fail to reject Ho

Truth

Ho true

Ha true

Type I Error

(α(α(α(α-Risk or false positive)

Type II Error

(β (β (β (β -Risk or false negative)

Correct Decision

CI = 1- αααα

Correct Decision

Power = 1- ββββ

Reject Ho

Consumers’ Risk

Decision

Fail to reject Ho

Truth

Ho true

Ha true

Type I Error


Type II Error


Correct Decision

CI = 1- αααα

Correct Decision

Power = 1- ββββ

Reject Ho

Consumers’ Risk

Producers’ Risk

Question 24:Supplier's A & B are bidding for a contract to supply high tensile alloy bars to your engineering company. The

contract must be awarded to the supplier whose product has the least variation (both suppliers achieve the required mean target). You have been asked to carry out a test on samples provided by each supplier to see if there is any statistically significant difference in variation between the two company's products. Based on the hypothesis test results below, what does your analysis show?

Test for Equal Variances

Level1 SupplyA Level2 SupplyB ConfLvl 95.0000

Bonferroni confidence intervals for standard deviations

Lower Sigma Upper N Factor Levels

2.41049 3.17767 4.60949 26 SupplyA

2.30246 3.03526 4.40291 26 SupplyB

F-Test (normal distribution)

Test Statistic: 1.096 P-Value : 0.820

Levene's Test (any continuous distribution)

Test Statistic: 0.020 P-Value : 0.888

Answers:

A. The sample from supplier A has the least variation.

B. The sample from supplier B has the least variation.

C. There is no statistically significant difference in variation between the samples from the two suppliers.

D. Insufficient evidence to make a decision.

(see BBTM p371)

Question 24:

What distribution is used as the basis for the Confidence Interval computation of means where the population standard deviation is not known?

Answers:

A. The normal distribution

B. The Z-distribution

C. The Chi-Square distribution

D. The t-distribution

(see BBTM p359)

Question 25:

How do you compute the Confidence Interval of the Standard Deviation within Minitab for a set of variable data?

Answers:

A. Use the "Display Descriptive Statistics" – Graphical Summary"

B. Use the "1-Sample t" test

C. Use the "1-Sample Z" test

D. Use the "1 Proportion" test

These are Hypothesis Tests

Question 26:

Which statement below is NOT TRUE for Hypothesis Testing?

Answers:

A. Statistical process to reject or fail to reject an initial statement that there is no difference in two statistical measures.

B. Hypothesis testing is a MUST for all 6 Sigma projects.

C. Used to determine if two statistical measures are equal or not.

D. Relatively small samples are used to answer questions about population parameters.

Question 27:

Which statement is TRUE about Alternate Hypothesis?

Answers:

A. Alternate hypothesis is always the main focus of the hypo. Testing.

B. Alternate hypothesis is done before null hypothesis.

C. You always need continuous variable data of mean to do the alternate hypothesis.

D. It is a statement of change or difference.

(see BBTM p442)

Question 27:

Which test is NOT used to test for means?

Answers:

A. Chi Square Test.

B. 1-Sample Z-test.

C. 2-Sample T-test.

D. 1 Sample T-test.

(see BBTM p444)

Question 28:

If the sample size gets bigger, what happens to the t-distribution?

Answers:

A. The distribution gets wider and flatter

B. Gets narrower and taller

C. Nothing

D. Gets flatter and narrower.

(see BBMJ p251)

Question 29:

In Hypothesis testing, the α-risk is _______________________

Answers:

A. a Type II error or Consumers risk.

B. risk of finding a difference when there really isn't one.

C. a Type I error or Producers' risk.

D. Both B and C above.

(see BBTM p367)

Question 30:

In Hypothesis testing if the p-value is greater than α you _________________

Answers:

A. fail to reject the Null Hypothesis, there is no difference.

B. reject the Null Hypothesis, there is a difference.

C. accept the Alternate Hypothesis, there is a difference.

D. accept the Alternate Hypothesis, there is no difference.

(see BBTM p371)

Question 31:

A casino owner suspects that a set of dice used by his croupiers are biased. He sends the suspect dice to you (the BB expert) to determine whether his suspicions have any foundation. You collect some data and notice that one number in particular on one die occurs more frequently than you believe it should. Which test should you apply to determine whether this event is due to random variation or foul play?

Answers:

A. 2 sample t

B. Chi square

C. 1 sample t

D. 2 Sample t-test for correlation


These are hypothesis tests for means

Question 32:

The finance department is developing a "rule of thumb" for calculating their accruals each month. They have pulled a sample of data and developed a rule based on that sample. However, the rule doesn't appear to be tracking very well to what was actually expected. They've asked you to determine if their rule is "good" or not at 95% confidence. Given the information below what do you recommend that they do:

Answers:

A. Reject their rule of thumb

B. Accept their rule of thumb

C. Tell them to gather more data

D.Tell them you don't have time to do the analysis.

Observed Expected

Feb 65 74

Jan 57 76

Dec 94 81

Nov 96 89

Oct 90 89

Sept 88 89

(see BBTM p384,

pp371-373)

( )

g

1j e

2

eo2

f

ff∑

=

−=χ

µµµµ0

Observed value of Test Statistic

Critical value

αααα-risk p- value

Question 33:

You must have how many observations in each cell to run a Chi Square?

Answers:

A. More than 5

B. More than 10

C. More than 20

D. The total number of observations should be at least 30

(see BBTM p385)

Question 34:

If you wanted to determine if there was a relationship between two attribute variables, what test would you run?

Answers:

A. 1-sample t-test

B. 2-sample t-test

C. Test for Association

D. F test

(see BBTM p380)

1 Proportion

Test

1 Sample

Comparing Proportions

2 Proportion

Test

Chi-Square

Test

More Than 2 Samples2 Samples

Test for

Association

Goodness

of Fit

To test if a

particular

distribution

(model) is a good

fit for a population

To test if a

relationship

between two

attribute

variables exists

Question 35:

Which distribution is used to determine if two population variances are statistically different?

Answers:

A. Normal distribution

B. Z-distribution

C. F-distribution

D. T-distribution

(see BBTM p377)

1 Variance

Test

1 Sample

Comparing Variances

2 Variance

Test

2 Sample

Test for Equal

Variance

More Than 2 Samples

Levene’s TestBartlett’s TestLevene’s TestF- TestDescriptiveStatistics

Question 36:

Which statement about Residuals (Overall and Within) and a factor contribution is true?

Answers:

A. They are all related to the grand Mean

B. The Residual are related to the grand mean

C. They are all related to individual observations

D. Residuals are related to individual observations

(see BBMJ p189, BBTM p422, P476)

Question 37:

Given this output

from Minitab:

What can be said?

Answers:

a. In order to detect a difference of 3.2 for a process with a variance of 2, the

probability of correctly rejecting the null hypothesis with a sample size of 9 is

at greater than .82

b. In order to detect a difference (shift) of 3.2 for a process with a variance of 4, the calculated sample size needs to be at least 9 to have a power of 80%

c. The maximum difference between the 3 levels means generates by the

process is 3.2 with a sample size of 9 and a beta of 10% is used, given that

the standard deviation is 2.

d. The maximum difference between the 3 levels means generates by the

process is 3.2 with a sample size of 9 and a beta of 10% is used, given that

the variance 2.(see BBTM p616)

Question 37:

To determine critical Chi-Square value, you need to know:

Answers:

A. The sample size and the degree of freedom

B. The alpha value and the sample size

C. The alpha value and the degree of freedom

D. The alpha value, the sample size and the degree of freedom.


Question 38:

Given following table, calculate the degrees of freedom needed to solve the equation for the observed Chi-Square value.

A. 4

B. 5

C. 8

D. 3

(r-1) x (c-1 ) = 3 x 1 = 3

Observed Expected

1 293 333

2 63 42

3 36 29

4 24 12

(see BBTM p400)

Question 39:Three locations are being analyzed to understand the impact of distance (in miles) on product shipping damage.

Location A is 200 miles from the customer.Location B is 500 miles , Location C is 50 miles from the customer.

In sampling 100 shipments of delivered product from each of the locations, the following was found:

Location A = 5% breakage Location B = 8% breakageLocation C = 10% breakage

Is the amount of breakage related to the distance the truck has to travel to the customer?

Α. χ2 = 1.789; p = 0.409; Reject HoΒ. χ2 = 5.99; p = 0.05; Fail to reject HoC. χ2 = 5.99; p = 0.05; Reject HoD. χ2 = 1.789; p = 0.409; Fail to reject Ho

(see BBTM p371 and example on pp391-395)

Question 40:

When testing for independence of attribute variables, reject the null hypothesis if …

Answers:

A. χ2 observed < χ2 critical or if p-value < α-value

B. χχχχ2 observed > χχχχ2 critical or if p-value < αααα-value

C. χ2 observed > χ2 critical or if p-value > α-value

D. The residuals are not normally distributed

(see BBMJ pp254-255, BBTM pp 371-372)

Question 41:

If you want to find out whether one attribute variable is independent of another attribute variable, use the ____________ .

Answers:

A. Chi-Square Goodness-of-Fit Test

B. Chi-Square Test for Association

C. 2-Proportion Test

D. Levene’s Test

1 Proportion

Test

1 Sample


2 Proportion

Test

Chi-Square

Test


Test for

Association

Goodness

of Fit

To test if a particular

distribution

(model) is a good fit for a population

To test if a relationship

between two

attribute variables exists

(see BBTM p380)

Question 41:

The Chi-square distribution

Answers:

A. uses attribute data

B. measures the difference between observed counts and expected counts

C. both a and b

D. none of the above

(see BBTM p385)

Question 42:

If the sample size is increased for chi-square Test for Association

Answers:

A. the degrees of freedom will be increased

B. the critical chi-square value will change

C. the calculated chi-square value will change

D. all of the above

(see BBMJ pp254-255,

BBTM p385)

Chi-square distribution

for various degrees of

freedom (ν)

0.1

1.2

2.3

3.4

4.5

5.6

6.7

7.8

8.9 10

11.1

12

.2

13

.3

14.4

15.5

16.6

17.7

18.8

19.9

χ2

Valu

e o

f th

e (

χ2)

dis

trib

ution

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

ν = 2

ν = 10

ν = 4

ν = 6

Question 42:

Tukey’s Quick Test compares __________ to determine if sample data originates from the same population.

Answers:

A. Distributions

B. Means

C. Variances

D. Medians

(See BBTM p413, p444, p475)

Variables

Tests ForMeans

Tests ForStandard

Deviations

One-sample Z-test

Samples Related

Paired

T-test

Samples Not Related

Two-sample

T-test

Tukey's Quick

Test

PlotOf Effects

Analysis Of

Means

No PlotOf Effects

Analysis Of

Variance

OnePopulation

TwoPopulations

Three Or MorePopulations

Chi-square TestFor OneStd Dev.

F-testFor The Ratio Of

Two Std Dev.

Homogeneity

Of Variance

Bartlett'sTest

Levene'sTest

OnePopulation

TwoPopulations


One-sample T-test

Pop. STD known

Pop. STD not known

Question 43:

What does a value of zero for the correlation coefficient (r) imply?

Answers:

A. The slope of the best-fit line is zero.

B. There is no relationship at all between the two variables.

C. No linear relationship between the two variables can be shown.

D. You can reject the null hypothesis that no correlation occurs.

(see BBTM p419)

Question 44:

You have created a fitted line plot for your sales outcome versus shelf space given to the product in question. What do the blue lines (95% PI) tell you?

Answers:

A. You can be 95% confident that new observations will fall within the interval indicated. (Prediction intervals estimate future values)

B. You can be 95% confident that the population mean for the response will fall within these lines.

C. With an alpha risk of 95%, you will find all response values within this range.

D. With a beta risk of 5%, you will find all response values within this range.

650600550

2000

1500

1000

500

Shelf Space

Sale

s

S = 87,2641 R-Sq = 95,7 % R-Sq(adj) = 95,3 %

Sales = -4710,51 + 10,0720 Shelf Space

95% PI

Regression

Regression Plot

(see BBTM p488)

Question 45:

The probability of correctly rejecting Ho when it is false is also known as:

Answers:

A. Alpha

B. Power

C. Beta

D. Z score

(see BBTM p455)

Decision

Fail to reject Ho

Truth

Ho true

Ha true

Type I Error


Type II Error


Correct Decision

CI = 1- αααα

Correct Decision

Power = 1- ββββ

Reject Ho

Consumers’ Risk

Decision

Fail to reject Ho

Truth

Ho true

Ha true

Type I Error


Type II Error


Correct Decision

CI = 1- αααα

Correct Decision

Power = 1- ββββ

Reject Ho

Consumers’ Risk

Producers’ Risk

Question 46:

What can a Chi-Square Goodness-of-Fit-Test be used for?

Answers:

A. To test if a relationship between two attributes exists

B. To test if a population under consideration follows a specific distribution

C. To test for equal means


1 ProportionTest

1 Sample


2 ProportionTest

Chi-SquareTest


Test for Association

Goodness of Fit

To test if a particular

distribution (model) is a good fit for a population

To test if a relationship

between two attribute variables exists

(see BBTM p380)

Question 47:

At a roulette table 113 out of 200 results were red. 87 were black (ignore the green zero). Could this ratio of red and black occur by chance or is this roulette table biased?

Answers:

A. Assessment is “biased” at an alpha risk of 5%

B. Assessment is “not biased” when an alpha risk of 10% is established

C. Assessment is “not biased” when an alpha risk of 5% is established

D. B and C

Null Hyp: Expected Red = 100 and Expected Black =100

Alternate: Expected Red, Black not equal to 100

alpha risk 0.05

Observed Expected Chi Squared

Red 113 100 1.69

Black 87 100 1.69

3.38 Total Chi Squared

1 degrees of freedom

0.066 P-value

Do Not Reject Ho

(see BBMJ p254)

Question 48:

Which distribution is used to determine if two population variances are statistically different?

Answers:

A. F-distribution

B. Z-distribution

C. Χ2-distribution

D. T-distribution

(see BBTM p444)

Variables

Tests ForMeans

Tests ForStandard

Deviations

One-sample T-test

Samples Related

Paired

T-test

Samples Not Related

Two-sample

T-test

Tukey's Quick

Test

PlotOf Effects

Analysis Of

Means

No PlotOf Effects

Analysis Of

Variance

OnePopulation

TwoPopulations


Chi-square TestFor OneStd Dev.

F-testFor The Ratio Of

Two Std Dev.

HomogeneityOf Variance

Bartlett'sTest

Levene'sTest

OnePopulation

TwoPopulations


Question 49:

What is the definition of the within process variation?

Answers:

A. Within Variation is the sum of the individual observation divided by the group process mean.

B. Within Variation is the sum of the square of each delta between individual observation and the group process mean.

C. Within process variance is the sum of the squares of the factor contribution residual

D. Within process variance is the sum of the residual dividing by the degrees of freedom

2

11

.)(iij

n

j

k

i

Within yySS −= ΣΣ==

Total Variation

Question 50:

Select the statements about the Chi-Square Distribution which are true:

A) Measure of difference between observed counts and expected counts,

B) Observations must be dependent,

C) Works best with 5 or less observations in each cell,

D) Cells must be combined to pool observations.

Answers:

A. A and B

B. B and C

C. A and D

D. C and D

(see BBTM p385)

Question 51:

How do we calculate 'power' when conducting a Power and Sample Size test?

Answers:

A. 1 - ββββ

B. 1 + β

C. 1 - α

D. 1 + α

(see BBTM p616)

Question 52:

The minimum recommended number of samples for constructing a histogram is:

Answers:

A. 50

B. 40

C. 30

D. 20

(see BBTM p426)

Question 53:

How do we calculate degrees of freedom (df) in a frequency table?

Answers:

A. Rows * Columns ^2

B. (Rows –1) * (Columns-1)

C. Rows * Columns /2

D. Rows * Columns /Columns -1

(see BBTM p394)

Question 54:

What are the types of Chi-square tests?

Answers:

A. Linear, Polynomial

B. Analysis of Means, Levene’s test

C. Analysis of Variance, Levene’s test

D. Goodness of fit, test for association

1 Proportion

Test

1 Sample


2 Proportion

Test

Chi-Square

Test


Test for

Association

Goodness

of Fit

To test if a

particular

distribution

(model) is a good

fit for a population

To test if a

relationship

between two

attribute

variables exists(see BBTM p380)

Question 55:

What hypothesis test is used to determine if two populations are statistically different?

Answers:

A. 1 Sample Z test

B. 1 Sample t test

C. 2 Sample t test

D. Paired t test 3 or more

factors

Comparing Means

1 Factor

1-sampleZ-test

Two wayANOVA

ANOVAGLM

One wayANOVA

1-samplet-test

2-samplet-test

Pairedt-test

1 Sample 2 Samples 2 or more

samples

2 Factors

σσσσ not knownσσσσ known independent paired

(see BBTM p376)

Question 56:

What hypothesis test is used to determine if a population is statistically different from a target value and the standard deviation is not known?

Answers:

A. 1 Sample Z test

B. 1 Sample t test

C. 2 Sample t test

D. Paired t test

(see BBTM p376)

3 or more

factors

Comparing Means

1 Factor

1-sampleZ-test

Two wayANOVA

ANOVAGLM

One wayANOVA

1-samplet-test

2-samplet-test

Pairedt-test


samples

2 Factors


Question 56:

A Paired Comparison hypothesis test:

Answers:

A. Determines if the population is statistically different from the target value

B. Determines if two populations are statistically different

C. Determines if the difference between matched pairs is greater than zero

D. Determines if two reject percentages are statistically different

(see BBTM p461)

Question 56:

A paired t-test is used when:

Answers:

A. When we are using 2 samples

B. When we are looking for what is the same about 2 data sets

C. The value of data in one sample is dependent on the other sample

D. When data is independent

(see BBTM p461)

Question 57:

What hypothesis test of the mean is appropriate when comparing the population mean to a target and the standard deviation is known?

Answers:

A. 2- Sample T

B. 1 -Sample T

C. 1 -Sample Z


3 or more

factors

Comparing Means

1 Factor

1-sampleZ-test

Two wayANOVA

ANOVAGLM

One wayANOVA

1-samplet-test

2-samplet-test

Pairedt-test


samples

2 Factors


(see BBTM p376)

Question 58:

The technique known as analysis of variance (ANOVA) employs tests based on __________________ of “between” and “within” Mean Squared Error.

Answers:

A. Means

B. Variance Ratios

C. Variance

D. medians

(see BBTM p477)

Question 59:

One-way ANOVA is used to determine

Answers:

A. The effect of one independent variable or factor on another dependent variable

B. The effect of one dependent variable on another dependent variable

C. The effect of an independent variable on another independent variable


(see BBTM p512)

Question 60:

In ANOVA, if the factor contributions are zero then which of the following statements is true?

Answers:

A. Factor means are zero

B. Grand mean is zero

C. Factor means are all equal and equal to grand mean

D. Within variance is equal to Between variance

(see BBTM p476)

Question 61:

In ANOVA, if the within variance = 6 and the between variance = 24 then what is F-ratio?

Answers:

A. 0.25

B. 4 F ratio = MS between / MS within = 24/6 = 4

C. 18

D. 30

(See BBTM p477)

Question 62:

A dynamometer engine test is being planned to run with 3 different settings for VCT timing (15,20,25 degrees). Goal is to detect 10HP improvement from the test that has a variance of 25HP. Assuming a significance level of 5% and a beta risk of 20% how many test runs are recommended at a minimum?

Answers:

A. 2

B. 3

C. 12

D. 6

Power and Sample Size

One-way ANOVA

Sigma = 5 Alpha = 0.05 Number of Levels = 3

Sample Target Actual Maximum

SS Means Size Power Power Difference

50 6 0.8000 0.8053 10

(see BBTM p616)

Question 63:

What is the definition of the within process variation ?

Answers:

A. Within Variation is the sum of the individual observation divided by the group process mean.

B. Within Variation is the sum of the square of each delta between individual observation and the group process mean.

C. Within process variance is the sum of the squares of the factor contribution residual

D. Within process variance is the sum of the residual dividing by the degrees of freedom

y

A within residual is the difference from

observation and FACTOR mean

Question 64:

ANOVA (Analysis of Variance) is:

Answers:

A. Used to detect significant differences between variances of multiple samples

B. A hypothesis test for mean differences

C. Based on the Chi squared distribution

D. Is the best test to use when comparing 2 different means

3 or more

factors

Comparing Means

1 Factor

1-sampleZ-test

Two wayANOVA

ANOVAGLM

One wayANOVA

1-samplet-test

2-samplet-test

Pairedt-test


samples

2 Factors


(see BBTM p376)

Question 65:

You need to conduct analysis for an experiment.

You will be monitoring 6.8L engine mpg at different altitude settings:

NYC (sea level), Denver CO and Detroit Michigan.

After the data is collected, what is the appropriate test and H0 / Ha?

Answers:A. Two way ANOVA with

H0: no sig. difference in avg. mpg Ha: sig. difference in avg mpg

B. One way ANOVA with

H0: no sig. difference in avg. mpg Ha: sig. difference in avg mpg

C. Two way ANOVA with

H0: no sig. difference in mpg variance Ha: sig. difference in avg mpg

D. One way ANOVA with

H0: no sig. difference in mpg variance Ha: sig. difference in mpg variance

Question 66:

What is the difference between a One Way ANOVA and a Two Way ANOVA?

Answers:

A. One way ANOVAs are used to detect differences in variance with one variable at multiple settings. Two way ANOVAs detect differences in variance with multiple variables at multiple settings.

B. One way ANOVAs are used to detect differences in means with one variable at multiple settings. Two way ANOVAs detect differences in means with multiple variables at multiple settings.

C. Two way ANOVAs can detect differences in means at 3 or more level settings. One way ANOVAs are used for testing at two level settings.

D. Two way ANOVAs can be used if the design is unbalanced. One way ANOVAs required balanced designs.

(see BBTM p376)

Question 67:

____________________ estimate the future value of a single observation (or small number of observations) from a population.

Answers:

A. Prediction intervals

B. Confidence intervals

C. Standard error of the mean

D. Trend charts

(see BBTM p488)

650600550

2000

1500

1000

500

Shelf Space

S = 87.2641 R-Sq = 95.7 % R-Sq(adj) = 95.3 %

Sales = -4710.51 + 10.0720 Shelf Space

95% PI

95% CI

Regression

Regression Plot

95% confidence interval for the mean response

95% prediction interval for a single response

Sa

les

Question 1:

You are presented with the Main Effects Plots. Which factor has the greatest impact on the output?

A.

B

C

D

-1 1 -1 1

71

67

63

59 Grand Mean

55

A B

-1 1 -1 1

71

67

63

59 Grand Mean

55

C D

y

y

Question 2:

You run a 2k factorial and the final reduced model results are:

How much variation is explained by the model?

A. 99.6% Look at the residual error Seq SS (5.5 of 1306 total)

Variation explained by model = 1- 5.5/1306 = 99.6%

B. 0.4%

C. 0.1%

D. 99.9%

Fractional Factorial Fit: sales(k) versus AdMethod, Incentive, Coupon

Estimated Effects and Coefficients for sales(k) (coded units)

Term Effect Coef SE Coef T P

Constant 157.500 0.4787 329.01 0.000

AdMethod 23.000 11.500 0.4787 24.02 0.000

Incentiv -4.500 -2.250 0.4787 -4.70 0.018

Coupon 1.000 0.500 0.4787 1.04 0.373

AdMethod*Coupon 10.000 5.000 0.4787 10.44 0.002

Analysis of Variance for sales(k) (coded units)

Source DF Seq SS Adj SS Adj MS F P

Main Effects 3 1100.50 1100.50 366.833 200.09 0.001

2-Way Interactions 1 200.00 200.00 200.000 109.09 0.002

Residual Error 3 5.50 5.50 1.833

Total 7 1306.00

Question 4:

When analyzing the assumptions for 2K Full Factorial DOE….

Answers:

A. The data must be normally distributed

B. The residuals must be normally distributed

C. The factors are dependent on each other

D. A & C

100-10

8

7

6

54

3

2

1

0

Residual

Fre

quency

Histogram of Residuals

403020100

20

10

0

-10

-20

Observation Number

Resid

ual

I Chart of Residuals

Mean=-3.2E-15

UCL=17.63

LCL=-17.63

908070

10

5

0

-5

-10

-15

Fit

Resid

ual

Residuals vs. Fits

210-1-2

10

5

0

-5

-10

-15

Normal Plot of Residuals

Normal Score

Resid

ual

Checking for reasonable

equal variances

Checking for reasonable normality

Checking for Independence

Question 5:

In DOE with blocking, blocks are free of confounding with other terms in the model when

Answers:

A. there is no replication in the DOE.

B. number of blocks is more than the number of replications.

C. number of blocks is equal to number of replications.

D. Blocks are found to be not significant after model reduction

Question 6:

When conducting a DOE, a factor level is

Answers:

A. The key output that is linked to the Customer CTQ or CTD or CTC

B. The full operating range of factors under study

C. The level the factor contributes to the Response

D. The value of a factor (hi, low,+1, –1)

Question 7:

A 3 factor, 2 levels, 3 replicates with additional 2 center point tests will have how many TOTAL number of runs?

Answers:

A. 24

B. 26 23 x 3 = 24 + 2 = 26

C. 10

D. 20.

Question 8:

Sparsity of Effects Principle states that:

Answers:

A. Most systems are driven by main effects and low order interactions

B. Most systems are driven by higher order interactions

C. Interactions are not important


(See BBTM p160)

Question 9:

Which main factors and interactions are not confounded with a Resolution IV Fractional Factorial Design:

Answers:

A. Main Effects with 3-way interactions.

B. 2-way interactions with 2-way

C. Main Effects with 4-way interactions

Resolution IV confounds the following:

Main + 3 way interactions (1 + 3 = 4)

2 way & 2 way interactions (2 + 2 = 4)


Question 10:

What does 23-1 represent in a fractional factorial experiment?

Answers:

A. 3 factors, 2 levels, 8 runs

B. 2 factors, 3 levels, 6 runs

C. 3 factors, 2 levels, 4 runs

D. 1 factor, 3 levels, 4 runs

E. 2 factors, 3 levels, 4 runs

23-1Levels

Factors3-1 = 2, 22=4= number of runs

Question 11:

Center points can:

Answers:

A. Determine whether curvature exists in the system

B. Be used in both 2k full and fractional designs

C. Increase power of the design without replication of base design

D. All of the above

(See BBTM p601)

Question 12:

After checking for curvature and finding none, the model is approximately linear between the high and the low values of the inference space.

Answers:

A. True

B. False

(see BBTM p604)

Question 13:

When reviewing the regression residual plots for evaluating a regression model, the I Chart of Residuals can show what?

Answers:A. Validates the assumption of Normality

B. Possible existence of a missing term in the equation shown by a pattern

C. Validates the assumption of Equal Variance

D. Validates the assumption of Independence

100-10

8

7

6

54

3

2

1

0

Residual

Fre

quency

Histogram of Residuals

403020100

20

10

0

-10

-20

Observation Number

Resid

ual

I Chart of Residuals

Mean=-3.2E-15

UCL=17.63

LCL=-17.63

908070

10

5

0

-5

-10

-15

Fit

Resid

ual

Residuals vs. Fits

210-1-2

10

5

0

-5

-10

-15

Normal Plot of Residuals

Normal Score

Resid

ual

Checking for reasonable

equal variances

Checking for reasonable normality

Checking for Independence

Question 14:

In regression, process inputs are also known as:

Answers:

A. KPOV's

B. Predictors

C. Defects

D. Responses

Question 15:

R2 is:

Answers:

A. The difference between a fitted value and an actual experimental value

B. Used to compare models with different numbers of terms

C. A measure of correlation

D. A measure of how much variation can be explained by the regression equation

(See BBTM p622)

Question 16:

Which regression parameter is used to help determine which multiple regression model should be selected:

Answers:

A. Mallow's C-p statistic

B. R2

Χ. α

D. Adjusted R2

(See BBTM p622)

Question 17:

What is the difference between R2 and R2 adjusted?

Answers:

A. R2 adjusted accounts for a different number of terms in the model

B. R2 adjusted is used when dealing with non-normal data

C. R2 adjusted removes collinearity from the model

D. R2 adjusted accounts for the degrees of freedom in the model

(See BBTM p622)

Question 18:

What are residuals?

Answers:

A. Input variables not controlled in the experiment

B. Variables not used in the experiment

C. Difference between predicted response values and observed response variables

D. Difference between response and regressor variables

(See BBTM p622)

Question 19:

In multiple regression a variable is found to have a VIF higher than 10. This implies:

Answers:

A. It is a significant factor.

B. It is in an insignificant factor.

C. It has a high degree of multicollinearity.

- Ri2 is the R2 value obtained when Xi is regressed against other X’s

- A large VIF implies that at least one variable is redundant

- VIF > 10: high degree of multicollinearity - cause for serious concern (Ri

2 > .9 )

D. It is non-normally distributed.

1

1- Ri2

VIF =

(See BBTM p630)

Question 20:

What is correct regarding the Variance Inflation Factor (VIF)?

Answers:

A. A large VIF implies that at least one variable is redundant

B. VIF > 10: high degree of multicollinearity

C. VIF > 5: moderate degree of multicollinearity

D. VIF = 1/(1-Ri2)

E. All of the above

(See BBTM p630)

Question 1:

Which attribute control charts should be used if the sample sizes vary from subgroup to subgroup?

Answers:

A. p-chart and np-chart

B. p-chart and u-chart

C. u-chart and c-chart

D. All attribute control charts

Attribute

u-chartp-chart

Defects or defective?

Defects

Constant area of opportunity

n = const

Defectives

np-chart c-chart

YesNo YesNo

(See BBTM p630)

Question 2:

In a c-chart, what does the central line represent?

Answers:

A. Average number of defective units

B. Average number of defectives per subgroup

C. Average number of defects per unit

D. Average number of defects per subgroup

PaneNo White Specs

1 31

2 39

3 38

4 5

5 22

6 34

7 10

8 23

9 11

10 36

11 25

12 4

13 4

14 11

15 25

16 4

17 38

18 36

19 36

20 17

Average 22.45

One out of control

point

Question 3:

What type of variable control chart would you use if you have a large sample size ( greater than 10)

Answers:

A. X-bar and R

B. X and Rm

C. X-bar and s

D. c Chart

Variable

Xbar-R Chart

I-MR Chart

Xbar-s chart

N<10

No

Yes

N=1

NoYes

(see BBMJ p225)

Question 4:

The term "in control" implies that our process…

Answers:

A. Meets and complies customer's standards

B. Has consistent variation

C. Will no longer be affected by special causes,

since we are in control of them

D. All of the above

Question 5:

What is NOT a characteristic of using Center Points in DOE?

Answers:

A. Add significant cost to the experiment

B. Improved graphical representation of the system response.

C. Determine if curvature exists

D. May be used in both 2k full and fractional designs

(See BBTM p601)

Question 6:

When analyzing the main effects plot of a 2k Full Factorial with center points, we noted that the curvature is not significant; therefore, the interpolation within the inference space is:

Answers:

A. Not Acceptable

B. Random

C. Acceptable

D. Key Factor

(see BBTM pp601- 606)

Question 7:

For the choices below, pick the experimental design case for which center point run randomization would be most appropriate:

Answers:

A. When the center point matches the current process settings

B. When the design does not include repetition or replication

C. When standard operating procedure is half-way between the upper and lower factor levels

D. When the design includes 3 replications

(see BBTM pp601- 606)

Question 8:

When curvature is discovered, through the use of center points in a designed experiment, which of the following is an appropriate next step:

Answers:

A. Collect more data – convert experiment to a Central Composite Design

B. Set factor levels to center point values - these settings produce better output than either end point

C. Proceed with DOE model reduction - optimize process based on relevant main effects and interactions

D. Abandon DOE - systems with curvature are unstable and cannot be optimized

(see BBTM p606)

Question 9:

When reviewing the regression residual plots for evaluating a regression model, the I Chart of Residuals can show what?

Answers:

A. Validates the assumption of Normality

B. Possible existence of a missing term in the equation shown by a pattern

C. Validates the assumption of Equal Variance

D. Validates the assumption of Independence

(see BBTM p641)

Question 10:

What's the relationship between width of the X-bar control limits and subgroup sample size?

Answers:

A. Width of control limits gets smaller as subgroup sample size increases. (test by increasing the sample size in Minitab)

B. Width of control limits gets larger as subgroup sample size increases

C. Width of control limits gets smaller as subgroup sample size decreases

D. No relationship

10

9

8

7

6

5

4

3

2

1

0 0 5 10 15 20

LCL

- 3σσσσ

UCL

+ 3σσσσ

Mean

(see BBMJ p227)

Question 11:

In which of the following cases might you have a process that produces a product or service that's statistically consistent, but is not meeting the needs of the customer?

Answers:

A. A process that's Out of Specification, but In Control

B. A process that's In Specification, but Out of Control

C. A process that's In Specification and In Control

D. A process that's Out of Specification and Out of Control

practice questions11

Documents

process dpmo

bbmj p41

bbmj p90question

bbmj p248d

resolutionsee bbmj p74question

accuracysee bbmj p82question

timesee bbmj p45

sigma process short