Six Sigma Green Belt Practice Test SkillS

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Six Sigma Green Belt Practice Test SkillS
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2014-06-28 18:00:09
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  1. Which Method of quantifying measurements error combines repeatability and reproducibility together in the analysis system?

    A. Average and Range method
    B. ANOVA method
    C. Analysis of Variance method
    D. Range method
    Answer: D. Range method
  2. Which two design methodologies are commonly used in Design for Six Sigma (DFSS) projects?

    A. DMAIC and IDOV
    B. DMADV and IDOV
    C. DMADV and PDSA
    D. DMAIC and PDSA
    Answer: B. DMADV and IDOV
  3. Each member of a team silently selects three problems from a pre-generated list of nine issues. The most often selected issues become the focus of an improvement project. Which team tool was used in this scenario?

    A. Nominal Group Technique
    B. Brainstorming
    C. Groupthink
    D. Multivoting
    Answer: D. Multivoting
  4. Which tool is used to translate general customer requirements into specific requirements?

    A. Critical to quality tree
    B. Affinity Diagram
    C. Quality Function deployment
    D. Kano Analysis
    Answer: A. Critical to quality tree
  5. What is the correct order of control plan phases as defined by the Advance Product Quality Planning Reference manual?

    A. Prototype, pre-lunch, production
    B. Production, Pre-lunch, Protype
    C. Production, Trototype, pre-lunch
    D. Pre-lunch, Prototype, Production
    Answer: A. Prototype, pre-lunch, production
  6. What is the advantage of manual project management methods versus automatic management methods?

    A. Manual project management methods make displaying large projects easier
    B. Manual Project management are easier to learn
    C. Automatic project management methods do not support changes in reporting formats
    D. Automatic project management methods are not easily transportable
    Answer: B. Manual Project management are easier to learn
  7. Which method of quantifying measurement errors is the accurate?

    A. Average and Range method
    B. Analysis of Variance method
    C. Percent Agreement method
    D. Range method
    Answer: B. Analysis of Variance method
  8. A sample of 50 computer chips is taken from a continuous process. The current defect rate for this process is 5%. What is the probability of finding four defects in a sample using the Poisson distribution?

    A. 2.50%
    B. 76.57%
    C. 13.36 %
    D. 39.06%
    Answer: C. 13.36 %

    The Poisson distribution is applied to situations involving defect counts. When a sample size multiplied by the probability  of the defect rate results in a value less than 5, it is appropriate to apply the Poisson distribution as follow:

    P(r) = (np)^r * e^(-np) / r!

    • n = Size of the given sample
    • r = occurrences of the number of defective computer chips  
    • p = Probability of defective computer chips

    The calculation using this formulas is as follow:

    • P(4) = (50*0.05)^4 *e^-(50*0.50)/4!
    • P(4) = (39.0626) *e^-2.5/24
    • P(4) = (39.0626)/292.379855
    • P(4) = 0.1336 = 13.36%
  9. What is the effect of automating a poorly designed process?

    A. Defect levels will only stabilize
    B. Defect levels will not be affected
    C. Defect levels will stabilize  or decrease
    D. Defect levels will stabilize or increase
    Answer: C. Defect levels will stabilize  or decrease
  10. Using the Z test, how is a left one-tailed test denoted?

    A. The sing for the null hypothesis is =.
    B. The sign for the alternate hypothesis is !=
    C. The sign for the null hypothesis is <
    D. The sign for the alternate hypothesis is <
    Answer: D. The sign for the alternate hypothesis is <

    In the Z test hypothesis test, you compare a test to a critical value. The critical value is based on a confidence interval and is taken from a standard Z table. You can denote the test as a two tail, right one-tail with the comparison operator specified in the alternate hypothesis. If the sing in the alternate hypothesis is not equal(!=), the test is a two tailed test. If the greater than sing (>) is used for an alternate hypothesis, it is a right  one-tailed test. A left one-tailed test is indicated by a less than sign (<) in the alternate hypothesis.
  11. A regression analysis has been performed on the study for Customer Complaints versus Time for Training. The p-value is a calculated to be 0.04. What is the indicate about the Time for Training?

    A. It is a practically significant factor contributing to the customer complaints.
    B. It is not significant statistical factor contributing to customer complaints
    C. It is a highly significant statistical factor contributing to customer complaints
    D. It is a statistical significant factor contributing to the customer complaints
    Answer: D. It is a statistical significant factor contributing to the customer complaints
  12. In which measurement scale is the central location determined by the mode of the data?

    A. Ordinal 
    B. Nominal
    C. Interval
    D. Ratio
    Answer: B. Nominal
  13. Which formula would you use to calculate the value of sigma for  use in calculating Ppk?

    A. Square root (Sum (X - X-bar)^2 / (n-1))
    B. (USL - X-bar)/3
    C. (USL - LSL)/6
    D. R-bar / d2
    Answer: A. Square root (Sum (X - X-bar)^2 / (n-1))

    The process performance index (Ppk) is an actual measure of a process's performance. To calculate Ppk, the formula should be used:

    Ppk = minimum ( (USL - X-bar) / 3 sigma, (x-bar - LSL) / 3 sigma)

    The value of sigma in this formula must be the actual observed sigma. This means that sigma is calculated  using the following formula:

    Sigma = Square root(Sum(X - Xbar)^2 / (n-1))
  14. Which on the diagrams in the following Exhibit represent a control chart? 



    Diagram A is in the shape of an XY chart. The horizontal axis is labeled as Time. A lower control limit (LCL), control limit (CL), and upper control limit (UCL) have been m marked on the vertical axis of the chart. Lines zigzag up and down through the three control lines with sharp peaks and valleys. One point is above the UCL line. Three points lie below the LCL line.

    Diagram B contains a single middle line with an oval at the right end. There are also three lines that angle upwards from the central line, and three lines that angle downward. Each of these six lines contains an oval at
    their end farthest from the horizontal line. Each of the six angled lines has a branch that is parallel to the middle line. The end of these branch lines also contains an oval.

    Diagram C starts at the left with a rectangle. From this rectangle, three more rectangles branch off at the same level. Further branching occurs off two of the three rectangles.

    Diagram D starts at the left with a rectangle. From this rectangle, two lines, each with an arrow at the end, point to other rectangles.
    A line with an arrow extends from each of these other rectangles to another rectangle, and so on, until a final rectangle is drawn at the right side.
    Answer: A
  15. Kaplan's balance scorecard focuses on which four perspectives of vision and strategy?

    A. Research, development, production, and customers
    B. Financial, internal business process, learning and growth, and customers
    C. Research, learning and growth, production and customers
    D. Financial, development, learning and growth, and customers
    Answer: B. Financial, internal business process, learning and growth, and customers
  16. Which organization role supporting Six Sigma initiatives is normally trained as a black belt and facilitator?

    A. Coach
    B. Sponsor
    C. Team Member
    D. Team Leader
    Answer: D. Team Leader
  17. Which option represents the definition of a statistic?

    A. A controlled selection of sample items from a given population
    B. A random selection of sample items from a given population
    C. A data value from a sample that is the form of a number, which can be used to make an inference about a population
    D. A data value from a population that s the in the form of a number, which can be used  to make an inference about a sample
    Answer: C. A data value from a sample that is the form of a number, which can be used to make an inference about a population
  18. Which option represents the main characteristic indicating a significant interaction on an interaction plot?

    A. Non-parallel lines
    B. Steep lines
    C. Lines consistently far apart
    D. Parallel lines
    Answer: A. Non-parallel lines
  19. using the student test, how do you determine if the test is a two-tailed test?

    A. The signed for the null hypothesis is =.
    B. The sing for the alternate hypothesis is 1!.
    C. The sign for the null hypothesis is <.
    D. The sign for the alternate hypothesis is >.
    Answer: B. The sing for the alternate hypothesis is 1!.
  20. What is known as "a distribution based on a counted data"?

    A. Decision Distribution 
    B. Normal Distribution
    C. Continuous Distribution
    D. Discrete Distribution
    Answer:  D. Discrete Distribution

    A discrete Distribution is a type of distribution  based on counted data. A discrete distribution has finite number of data points. Example of discrete distributions include binomial, Poisson, and hypergeometric distributions.
  21. Why would an organization use Six Sigma processes?

    A. To acquire new customers by branching into new markets
    B. To reduce their number of defects to around 6,210 defects per million opportunities
    C. To consistently develop near perfect products and service
    D. To reduce their defective rate to 0.6%
    Answer: C. To consistently develop near perfect products and service
  22. Under which line item in a control plan would you find information on how to measurement are made?

    A. Gage Technique
    B. Control method
    C. Gage capability
    D. Specifications
    Answer: A. Gage Technique
  23. A six sigma improvement project has reduce the risk associated with a critical portion of a production process. The project team must  now focus on the next highest priority risk in the process. How can the next highest priority risk be found?

    A. Perform a measurement system capabilities re-analysis
    B. Hold a brainstorming session
    C. Develop a Control Plan 
    D. Perform a failure modes and effect analysis.
    Answer: D. Perform a failure modes and effect analysis.(FMEA)
  24. What is the purpose of a chi-squared test?

    A. To test two sample means for equality the variance is unknown but assumed to be equal 
    B. To compare the observed and expected frequencies of test outcomes
    C. To compare three or more population means
    D. To compare a population mean with fixed value when the population follows a normal distribution.
    Answer: B. To compare the observed and expected frequencies of test outcomes

    There are two applications for the chi-square test:

    Case 1: To compare the observed and expected frequencies of test outcomes (specially for attribute data)

    Case 2: To compare sample variances when population variance is known 

    The test statistic calculation differ depending on which case you  choose. The test statistic (X-squared) for case 1 is calculated as follows:

    X-squared = Sum of ((observed frequencies - expected frequencies) / expected frequencies)

    The test statistic (X-squared) for case 2 is calculated as follow: 

    X-squared = (number of samples - 1) * the sample variance / known population variance
  25. When performing a one-way analysis of variance (ANOVA) test, how many different degrees of freedom must be calculated?

    A. 3
    B. 2
    C. 1
    D. 4
    Answer: A. 3

    • There are 3 different degrees of freedom calculation that must be performed in a one-way ANOVA test. 
    • 1. Total degrees of freedom (Total DF): total number of data points minus 1
    • 2. treatment degrees of freedom (TDF): number of treatments minus 1
    • 3. Error degrees of freedom (EDF): Total DF - TDF
  26. Which statement is an example of a goal statement?

    A. Company shipment are often delayed by 3 days due to a poor packing process
    B. We experience a 20% drop in sales due to defects in our product
    C. We will increase customer satisfaction by reducing product defects by 10%
    D. Our product contains 10 defects on average
    Answer: C. We will increase customer satisfaction by reducing product defects by 10%
  27. The theory of Constraints (TOC) uses which of the basic measures to evaluate systems?

    A. Machine efficiency, equipment utilization and  downtime
    B. machine efficiency, equipment utilization, and operation expenses
    C. Throughput, inventory and operational expenses
    D. Throughput, inventory and downtime
    Answer: C. Throughput, inventory and operational expenses
  28. Given a standard deviation of 2 and specification limit range from 70 to 130, what is the ratio of the precision distribution to the precision total?

    A. -0.20
    B. -5.00
    C. 5.00
    D. 0.20
    Answer: D. 0.20

    The ratio of the precision distribution to the precision total, also known as the precision/tolerance ratio, is 0.20 in this example. This value was calculated by suing the following formula: 

    • 6*standard deviation / (USL - LSL)
    • 6*2 / (130 - 70)
    • 12/60 = 0.20
  29. Which attribute control chart count the number of defects in a products?

    A. p charts and np charts
    B. np charts and c charts
    C. u charts and c charts
    D. U charts and p charts
    Answer: C. u charts and c charts
  30. A six sigma improvement initiative failed to sufficiently improve a process. New ideas must be generated for continued improvement efforts. Which improvement method should be employed?

    A. Hold a brainstorming session
    B. Perform a failure modes and effects analysis
    C. Develop a control plan 
    D. perform a measurement system capability re-analysis
    Answer: A. Hold a brainstorming session
  31. Which lean concept refers to mistake-proofing a process?

    A. Poka-yoke
    B. Queue Time
    C. process flow chart
    D. Pull
    Answer: A. Poka-yoke
  32. Which model describes the factors that make up value in the eyes of the customer?

    A. SIPOC
    B. CQFA
    C. IDOV
    D. DMADV
    Answer: B. CQFA

    The cost, quality, features, and availability (CQFA) model describes the four factors that make up value in the eyes of the customer.
  33. Your company manufactures notebook for students. What is a true statement concerning the company's internal and external customers?

    A. A line worker is an external customer
    B. A high school student is an external customer
    C. The retailer that sells the notebooks is a internal customer
    D. A line worker's family is an internal customers
    Answer: B. A high school student is an external customer
  34. What is the mechanism by which the capability of a process is identified?

    A. Creating Flow charts
    B. Performing process mapping
    C. Creating rational subgroups
    D. Performing rational sampling
    Answer: C. Creating rational subgroups
  35. Which statement is true concerning short-term capability?

    A. Control limits are closer together for short-term process evaluation than long-term process evaluation
    B.Using attribute data, 25 to 30 groups of 5 samples each must be used to estimate process mean and variation
    C. Using variable data, 25 groups of 50 samples each must be used to estimate process mean and variation
    D. Control limits are further apart for short term process evaluation than long term process evaluation
    Answer: A. Control limits are closer together for short-term process evaluation than long-term process evaluation
  36. Which customer would influence the company at the operations level?

    A. A shareholder owing stock in the company
    B. A member of the company's top management
    C. A customer who purchase the company's product
    D. A supplier of raw material for the company's product
    Answer: C. A customer who purchase the company's product
  37. What is the range for the correlation coefficient r?

    A. 0 to 1
    B. -1 to 1
    C. -2 to 2
    D.-1 to 0
    Answer: B. -1 to 1

    The range of the correlation coefficient r is from -1 to 1. the correlation coefficient is a vital statistic in Six Sigma analysis. A comparison of correlation coefficient for various data pairs can give an indication of which are the stronger relationships and may help point the way for future analysis of causes.
  38. Which method for resolving conflict is the least assertive but the most cooperative?

    A. Collaborating
    B. Avoiding
    C. Competing
    D. Accomodating
    Answer: D. Accomodating

  39. Which data analysis tool would you use to prioritize the order in which problems should be address?

    A. Line Graph
    B. Matrix diagram
    C. Control Chart
    D. Pareto Diagram
    Answer: D. Pareto Diagram
  40. Given the following Data set table, which measure of central tendency is equal to 2?

    Data: 9, 3, 2, 7, 8, 2, 4, 1, 5

    A. Mode
    B. Range
    C. Median
    D. Mean
    Answer: A. Mode
  41. What is the probability of rolling either 1. 3. or 6 on a standard single die?

    A. 33.3%
    B. 100%
    C. 0%
    D. 50%
    Answer: D. 50%

    A standard single die is a made up of the numbers 1.2.3.4.5 and 6. The probability of rolling each individual number would be 1/6. The probability of rolling any one of three different numbers is the sum of the probabilities of rolling each individual number. Therefore, the calculation would be as follows:

    • P(1 or 3 or 6) = P(1) + P(3) + P(6)
    • P(1 or 3 or 6) = 1/6 + 1/6 + 1/6
    • P(1 or 3 or 6) = 3/6 =1/2 or 50%
  42. A plan to improve quality is carried out during step of the Plan_Do_Check_Act (PDCA) cycle?

    A. Act
    B. Do
    C. Check
    D. Plan
    Answer: B. Do
  43. Which is the best description of mutually exclusive events?

    A. All sample points not contained in event A
    B. Events A and B cannot occur at the same time
    C. Events A and B both occur at the same time
    D. All samples points contained in event A
    Answer: B. Events A and B cannot occur at the same time
  44. Which option refers to Type 1 Error?

    A. Not rejecting the null hypothesis when it is false
    B. Accepting the null hypothesis when is false
    C. Rejecting the null hypothesis when it is true
    D. Accepting the null hypothesis when it is true
    Answer: C. Rejecting the null hypothesis when it is true

    When performing a hypothesis test, rejecting the null hypothesis when it is true  is considered a Type I error. The symbol for alpha is used to denote the probability of making  they type of error.
  45. What is a work break structure (WBS)?

    A. A cumulative of yield over multiple process steps.
    B. A measurement of a system used to determine  the success of a project.
    C. A detailed listing or activities required to complete a project
    D. A secondary metric derived from a primary metric.
    Answer: C. A detailed listing or activities required to complete a project
  46. What consideration must be made regarding effective process performance metrics?

    A. Individuals should focus on a large number of metrics.
    B. Metrics should focus only on past performance data.
    C. To be effective, metric should not be changed
    D. Metric should not focus on a single individual measure.
    Answer: D. Metric should not focus on a single individual measure.
  47. Which option defines the central limit theorem's significance with respect to control charts?

    A. A process where  the data points are randomly situated around the standard deviation with a smaller number of data points approaching the upper and lower control limits. 
    B. Data can be validated within a certain range as the basis for drawing larger conclusions.
    C. A process where the data points are randomly situated around  the average  with a smaller number of data points approaching the upper and lower control limits.
    D. As a sample size increases, the distribution of averages calculated from the individual samples will approach a normal distribution.
    Answer: D. As a sample size increases, the distribution of averages calculated from the individual samples will approach a normal distribution.
  48. Which chart type presented in the following Exhibit?


    A. Control Chart
    B. Fishbone diagram
    C. Scatter diagram
    D. Pareto Chart
    Answer: A. Control Chart
  49. What could cause a lack of variability in average (X_bar) control chart?

    A. Incorrectly calculated control limits
    B. Machine deterioration
    C. Process is over controlled
    D. New machine operator
    Answer: A. Incorrectly calculated control limits
  50. When the same functions performed by the different machines produce different results, which type of variation can this be attribute to in multi-vari chart?

    A. Ordinal 
    B. Cyclical
    C. Positional
    D. Temporal
    Answer: B. Cyclical

    Cyclical variation refers to variation from piece or unit to unit. it can also be variation from one operator to another or from machine to machine. When the same functions performed by different produce different results, cyclical variation can be indicated on a multi-vari chart
  51. Which prject documentation tool graphically displays the start date, end date and duration of project activities? 

    A. Pareto diagram
    B. Work breakdown structure
    C. PERT chart
    D. Gantt chart
    Answer: D. Gantt chart
  52. You are constructing an X-bar control chart for a process that produces lenghts of pipes. During sampling, you acquire the following data, as presented in the control Chart sample data table.

    What are the UCL and LCL for the X-bar control chart?



    A. UCL = 13.410, LCL - 12.350
    B. UCL = 13.410, LCL - 0.000
    C. UCL = 13.336, LCL - 0.000
    D. UCL = 12.350, LCL - 1.336
    Answer: A. UCL = 13.410, LCL - 12.350

    To calculate the upper and lower control limitis (UCL, LCL) for the bar chart, you must first find the grand average (X-double bar). To find  the grand average, simply calculate the vaerage of all sample averages. In this case, the grand average is equal to 12.88. Youmust find  the average  of all sample ranges (R-bar). In this case, R-bar is equal to .52. The formula  for calculating control limits uses an A2 value, which is a constant taken from a table  of control  chart constants. A2 for lots of three samples each is 1.02 UCL and LCL are now calculated using the following formulas.

    • UCL = X-double bar + (A2 * R-bar)
    •        = 12.88 + (1.02 x 0.52)
    •       = 13.410

    • LCL = X-double bar - (A2 * R-bar)
    •       = 12.88 - (1.02 x 0.52)
    •      = 12.350
  53. Your manufacturing process has the following steps with the indicated yields: 

    -Step 1: 98%
    -Step 2: 95%
    -Step 3: 87%
    -Step 4: 90%
    -Step 5: 75%

    What is the rolled throughtput yield (RTY) of this process?

    A. 54.7%
    B. 89.0 %
    C. 55.0%
    D. 45.3%
    Answer: A. 54.7%

    • RTY = FTY1 * FTY2 * FTY3 * FTY4...
    • RTY= .98 * .95 * .87 * .90 * .75
    • RTY=.547 = 54.7%
  54. Refer to exhibit.Which step is defined with an X?

    A. Identify
    B. Communicate
    C. Analyze
    D. Track

    Answer: B. Communicate


    They show a continuous six-step process circling a seventh step, Communicate, as a transition to each other step.
  55. In Business process management (BPM), how does a project management approach help to improve quality?

    A. Processes no longer flow through multiple vertical functions or the company
    B. One person is responsible for the product through all stages of production
    C. Each stage of the overall process is managed separably
    D. Products no longer pass through multiple horizontal business levels of the company
    Answer: B. One person is responsible for the product through all stages of production
  56. the temperature fluctuates in the environment where your production process creates widgets. The temp is cool in the morning hours and  slowly shits to hot during the afternoon hours. The process is somewhat sensitive to temperature. How could  you expect this  to present itself on an average control chart for your process?

    A. Jumps in process levels
    B. lack of variability
    C. Recurring cycles
    D. Points near or outside the control limits
    Answer: C. Recurring cycles

    Recurring cycles on an average control chart (X-bar chart) can be caused by changes in the environment's temp and humidity. They may also be caused by a tired operator or by the regular rotation of a machine or operator. Recurring cycles can be corrected by ensuring that temp and humidity of the physical environment remains constant. it can also  be corrected by regularly servicing the equipment, rotating the operators and evaluating machine maintenance.
  57. Review the chart type in the following exhibit. Which chart type is being presented?

    A. Flow Chart
    B. Process map 
    C. Pareto Chart
    D. gantt chart

    Answer: C. Pareto Chart
  58. A sample of 20 plastics bags is randomly taken from a continuous process where the population is 1000 plastics bags. Past studies  have demostrated that 15% of the bags contains defects. Which option represent the probability of finding 2 defective bags?

    A. 77.06%
    b. 85.00%
    C. 15.00%
    D. 22.94%
    Answer: D. 22.94% dat

    The binomial distribution is used to model discrete data in the situation with 2 possible outcomes. The possible outcomes are defective plastic bags and non-defective bags. The binomial distribution is generally applied in situations where the sample size is less than 10% of the population. Therefore we can use the binomial probability distribution function to determine the probability  of finding 2 defective bags within the sample. 

  59. When performing a one-way ANOVA, how is the treatment sum of squares calculated?

    A. By finding the sum of the squared deviations of each observation within a treatment from the treatment average
    B. By finding the different between  the total degrees of freedom and the treatment degrees of freedom
    C. By finding the different between the crude sum of squares and the correction factor. 
    D. By  finding the Sum of the squared deviation of each treatment average from the grand average
    Answer: D. By  finding the Sum of the squared deviation of each treatment average from the grand average.

    In a one-way analysis of variance (ANOVA), the treatment of sum of squares (SST) must be calculated to find the total sum of squares. To calculate SST, find the sum of the square deviations of each treatment average from the grand average.
  60. Which methods will be used to correct the problem of team members discussing issues unrelated to the purpose of a team meeting?

    A. Ask team members to provide relevant data
    B. Ensure team members follow the prearranged agenda
    C. Ask team members to provide different solutions to the problem
    D. Ensure team members are actively listening
    Answer: B. Ensure team members follow the prearranged agenda
  61. Under which lean philosophy is throughput increased by removing bottlenecks in a process?

    A. Theory of Constraints
    B. Total productive maintenance
    C. Kaizen
    D. Poka-yoke
    Answer: A. Theory of Constraints

    The theory of Constraints (TOC), also known as constraint management, focuses on improving a process by eliminating bottlenecks. TOC allows management to determine on which part of a process a Six Sigma project should be focused. A good first step is constraints management is to develop a process chart.
  62. A process is examined and four different types of errors are observed. These errors are classified such that a class I error is more critical than a class IV error. The errors and the number of times they were observed are presented in the following Error Classes - Observed Error table. Which measurement scale was used on this scenario?



    A. Interval
    B. Ratio
    C. Ordinal
    D. Nominal
    Answer: C. Ordinal

    Ordinal measurement scales are also known as ranking scales. This measurement scale arranges data in order but the differences between values are meaningless.
  63. Which test examines the variance of multiple sample means?

    A. MUDA
    B. F distribution
    C. Student's t Test
    D. ANOVA
    Answer: B. F distribution

    Named for its inventor Ronald Fisher, the F distribution tests the null hypothesis that the variance of all population means under study are equal. The F Distribution is similar to the student's t Test, except that it examines the variance of multiple sample means,, rather than the means themselves.
  64. In Statistic, which terms refers to "probably true" or " not due to chance" when it comes to research findings?

    A. Importance
    B. Random
    C. Usefulness
    D. Significant
    Answer: D. Significant

    In statistics, "significant" means probably true or not due to chance. It has nothing to do with the importance or usefulness of research being conducted. For example, research findings may be true but not important or useful. When testing statistical significance, a calculation is done based on sample information. This calculated value is compared to a critical value, p, to determine statistical significance. Critical values of 1% or 5% are generally used in this comparison. If the calculated values is less than the critical value, the findings are considered statistically significant.
  65. For which type of information would informal communication such as rumors, be an appropriate delivery system?

    A. An employee second reprimand offense
    B. A business agreement with another company
    C. News of an employee's willing retirement
    D. six Sigma being adopted as a strategic initiative
    Answer: C. News of an employee's willing retirement
  66. Given the following Data set table, which measure if central tendency is equal to 4?

    Data Set: 9,3,2,7,8,2,4,1,5

    A. Median
    B. Range
    C. Mean
    D. Mode
    Answer: A. Median
  67. Which key element of a project charter would contain a baseline measure?

    A. Milestones and deliverables
    B. Business Case
    C. Problem Statement
    D. Project Scope
    Answer: C. Problem Statement

    Problem statement needs to be descriptive. They should include details such as how long the problem has been occurring and the measurable item from which success or failure of the project can be measured. The success or failure of a project is determined by comparison with a baseline. A baseline is a measurement of the measurable item at the start of the project.
  68. What are the 5 steps in Six Sigma's DMAIC process?

    A. Define, Monitor, Analyze, Improve, Control
    B. Define Measure, analyze, Improve, Correct
    C. Design, measure, Automate, Improve, Control
    D. Define, measure, Analyze, Improve, Control
    Answer: D. Define, measure, Analyze, Improve, Control

    The five steps of the six sigma DMAIC process are as follows:

    • Define: Choose an appropriate target for the Six Sigma initiative
    • Measure: Gather data on the target to be implemented
    • Analyze: Identify the root cause or defects or deviations in the target
    • Improve: Implement a change to eliminate the cause or defects or deviation in the target
    • Control: Monitor the newly implemented process to ensure that improvements last
  69. Review the Capabilities Index Failure Rate  table for a list of the part per million of non-conformance for various Cp values. 

    A process has the capability index rating (Cp) of 1:30. What percentage of production from this  process is expected to be nonconforming?

    A. 0.27%
    B. 0.0063%
    C. 4.55%
    D. 0.0096%

    Answer: D. 0.0096%

    A process with a Cp of 1.30 is expected t have a 96 nonconforming parts per million produce. This value of 96 non conforming parts can be found in the table provided by  looking up the Cp value of 1.30 and checking to see the corresponding value in the parts per million of noncorformance column. 

    To find the percentage, simple divide 96 by a million, A process with a Cp of 1.30 is expected to have 0.0096% of its products be nonconforming.
  70. Which statement is true about the null hypothesis?

    A. the null hypothesis can be rejected  or failed to be rejected.
    B. The null hypothesis asserts that something important is occurring
    C. It can be accepted if the evidence does not support rejecting it. 
    D. The assumption with the null hypothesis is that the variation is non-random
    Answer: A. the null hypothesis can be rejected  or failed to be rejected.
  71. Your manufacturing process uses a special part. This part is delivered to you from three separate manufacturing plants. Each of the manufacturing plants uses a different process to build this particular part. Which sampling technique would you use to test the part before incorporating it into your manufacturing process?

    A. Stratified sampling
    B. Random sampling
    C. Multiple sampling
    D. Sequential sampling
    Answer: A. Stratified sampling

    A lot of parts produce from different sources and produce using different machines or processes is said to be a stratified group. TO properly take different in the source part into account, stratified sampling must be performed. Stratified sampling randomly selects samples from each distinct group of parts.  For example, in the given scenario, parts from each of the manufacturing plats would be considered a separate group. This allows the number of samples from each group to be change based on the proportion of parts being used from that group.
  72. Which type of team is best suited for handling issues related to an organization policies, practices and operations?

    A. Quality Teams
    B. Six Sigma Teams
    C. Cross Functional Teams
    D. Project teams
    Answer: C. Cross Functional Teams
  73. Which Six sigma concept involves creating value for stakeholders by understanding, controlling and improving business processes?

    A. PDCA
    B. BPM
    C. FMEA
    D. QFD
    Answer: B. BPM

    Business process improvement (BPM) focuses on creating value for stakeholders by focusing on overall business processes. Instead of focusing processes within individual vertical units in the organization, BPM looks at the processes overall, and looks at the process flows through each unit.
  74. Which option best describes an analytical study?

    A. Descriptive statistic are used to describe a current process.
    B. the nature of what is occurring in a given process is described. 
    C. An observation is made about the location, spread and shape of data distribution around a central tendency.
    D. A sample is used to make judgement about a population
    Answer: D. A sample is used to make judgement about a population

    Analytical studies use inferential statistics to predict what a process is capable of doing. Six sigma relies on inferential statistics to help explain why a variation is occurring, whether it can be attribute to a given cause, and how reliable the inference itself may be. Sampling distributions, confidence intervals, and hypothesis testing are commonly used as the bases for making inference about a population.
  75. Your company is building a balance scorecard. The scope of the card has been defined. A facilitator has gather information from senior management and executive workshop has been conducted to draft the measure for the balance scorecard.What is the next step in the development process?

    A. Another workshop is held to refine the balance scorecard.
    B. A task team develops an implementation plan
    C. The facilitator creates a drafts of the balance scorecard.
    D. The balance scorecard is periodically reviewed.
    Answer: C. The facilitator creates a drafts of the balance scorecard.

    There are typically eight steps performed when developing a balance scorecard: 

    • Step1: The scope of the card is defined
    • Step2: A facilitator gathers information from senior management for the scorecard.
    • Step3: The facilitator presents the gather information at an executive workshop to develop a draft of the scorecard's measures. 
    • Step4: The facilitator creates a rough draft of the scorecard and a new report.
    • Step5: A second executive workshop is held to refine the drafted scorecard and objectives for the measure are defined.
    • Step6: A third workshop is conducted to finalized vision, objectives and measures.
    • Step7: A task team develops an implements plan.
    • Step8: The balance scorecard is periodically reviewed.
  76. Process capabilities is calculated as the average number of non-conformities in a sample of fixed size when using which type of chart?

    A. c charts
    B. u charts
    C. p charts
    D. np charts
    Answer: A. c charts

    A count chart, also known as a c hart, is a control chart for evaluating the stability of a process. It does this by counting the number of specified events classes in a sample. Process capability can be determined, using a count chart, by finding the average number of non-conformities in a sample of fixed size.
  77. Which option describes a paired t test inference test?

    A. The difference in mean is calculated from 2 sample with unknown, but assumed equal, variance.
    B. The variance of 2 sample's data are compared for equality.
    C. The difference in mean is calculated from 2 samples with unknown, but assumed unequal, variances.
    D. The difference in mean is calculated from data collected in tandem from 2 samples.
    Answer: D. The difference in means is calculated from data collected in tandem from 2 samples. 

    The paired t test is used to test the difference between 2 sample means. Data collected in pairs from the 2 sample. The difference (d) between the collected data is then calculated for each pair. after the difference has been calculated for each pair, the mean of the differences(d-bar) and the standard deviation of the differences (s) are calculated. The critical value t is then calculated using the following formula:

    t = d-bar / (s / square root of number of samples)

    This critical value is then compared to a value from a t distribution table to determine if the null hypothesis can be rejected.
  78. Which action is taken in the COntrol Step of the define, measure, analyze, improve, control (DMAIC) process?

    A. Customers and their requirements and expectations are outlined.
    B. An ongoing monitoring plan is developed.
    C. Data is collected to determine the current status of the process.
    D. Root causes of defects and opportunities for improvement are found.
    Answer: B. An ongoing monitoring plan is developed.
  79. Ultimately, who defines a product's value?

    A. Managers
    B. Customers
    C. Engineers
    D. Salespeople
    Answer: B. Customers
  80. Which tool can be used to break down a problem into manageable pieces?

    A. Histogram
    B. Control Chart
    C. Cause and Effect Diagram
    D. Normal Distribution
    Answer: C. Cause and Effect Diagram
  81. A bag contains 20 blue poker chips, 35 green poker chips, and 24 red poker chips. What is the probability of pulling out a blue chip, followed by a green chip, followed by a red chip?

    A. 5.9%
    B. 3.5 %
    C. 2.1%
    D. 3.4%
    Answer: B. 3.5 %

    The events in this situation are dependant. This is known as conditional probability, and the multiplicative law will be employed when finding the probability. It is calculated by multiplying together the probabilities of each event occurring given that the sample space is reduce at each step. 

  82. A six sigma project has reduce the variability in a process. What should be done to facilitate further reduction in variability?

    A. perform a failure modes and effects analysis.
    B. Hold a brainstorming session
    C. Develop a control plan
    D. Perform a measurement system capabilities re-analysis.
    Answer: D. Perform a measurement system capabilities re-analysis.

    The sensitivity of the measurement system in place plays a large part in detecting variability. If a Six sigma initiative has already reduce the variability of a process, the measurement system in place may not be sensitive enough to facilitate further improvement efforts. A measurement system capability re-analysis will help determine if more precise measuring instruments are required.
  83. Four police dogs are being evaluated for use on a drug detection team. To test the dogs 20 packages of drugs are hidden throughout a lot of luggage. The results of the test appear in the Drug Finding Test Results table. 

    You need to determine whether there is  significant difference between the dogs abilities to find drugs based on this test. Yu decide to use the chi-squred test. Given a confidence interval of 95%, what is the critical value (X-squared)?

    A. 7.81
    B. 0.325
    C. 0.1026
    D. 5.99

    In this scenario given, the null hypothesis is that there is no difference between the dogs' ability to find drugs (H0: pi = p2 = p3 = p4). To find the critical vale, when comparing observed and expected frequencies of test outcomes for attribute data we need two pieces of information: confidence interval and degrees of freedom. 

  84. A process capability study has been performed on a manufacturing process. It is found that the process spread is the same as the specification spread. What action should be taken?

    A. Take no action
    B. Center the process
    C. Change the specification
    D. Reduce variability
    Answer: B. Center the process

    A process may need to be centered when the process spread is approximately the same as the specification spread. Simply adjusting the centering of the process may bring the majority of the product back into the specifications limits.
  85. What is an advantage to using focus groups to gather customer feedback?

    A. Results from focus groups typically have high face validity
    B. There is a large degree of control involved in a focus group
    C. Dialogue is a focus group is easy to analyze
    D. Anyone can be a good interviewer for a focus group.
    Answer: A. Results from focus groups typically have high face validity

    There are many advantages to using focus groups to gather customer feedback. Typically a focus group will produce a greater number of comments than individuals interviews. This due to members of the group simulating each other's responses. The group's interviewer is able to direct conversations with probing questions to clarity the group's comments. The results from a focus group are expressed in the participant's own words, which lend to high face validity.
  86. Which option only appears in a project's milestone report?

    A. The project's status
    The Project's objectives
    C. The project's roadblocks
    D. The project's budget
    Answer: C. The project's roadblocks
  87. Which option represents the differences between observed values and the corresponding values predicted by your equation?

    A. Precision
    B. Sensitivity
    C. Residuals
    D. Qualitative
    Answer: C. Residuals

    Residuals are the difference between observed values and the corresponding values predicted by a model. In regression analysis, for example, once you have come up with a line that fits the data, you can determine how well the line fits by looking at the residuals.
  88. Many stakeholders within a project act as both suppliers and customers in the Supplier, input, Process, Output, Customer (SIPOC) model. Which stakeholders within a project would expect career growth as an output of the process?

    A. Suppliers and society
    B. Community and customers
    C. Stockholders and employees
    D. Employees and managers
    Answer: D. Employees and managers

    When suppliers in the SIPOC model are also customers, communication is channeled through internal company processes. Each supplier/customer supplies a different input and expects a different output from the process. In the case of employees and managers, the input is commitment and leadership respectively and the expected output is pay and career growth.
  89. What are process level metrics?

    A. Measures that relate the cost and time required manufacture products. 
    B. Executive level measurements of operation and results
    C. Metrics that are indicative of the customer's exposure to variation over the long term.
    C. Metrics that are indicative of the customer's exposure to variation over the long term.
    D. measurements made by workers and machinery to ensure normal oprations
    Answer: D. measurements made by workers and machinery to ensure normal oprations

    Measurements made by workers and machinery to ensure normal operations are process level metrics are vital to the measure, analyze, improve and control (MAIC) phases of Six Sigma.
  90. A comparison of engineering specification to chance causes of variation is done using which Six Sigma tool?

    A. Process capabilities study
    B. Analysis of variance
    C. Design of experiments
    D. Pareto Analysis
    Answer: A. Process capabilities study

    A predictable pattern of statistically stable behavior in a process referred to a process capability. A process capability study compares engineering specifications to chance causes of variation. Process that have  a spread on a bell-shaped curve narrower than the tolerance range are said to be capable.
  91. While reviewing an X-Bar control chart, you notice a set of seven consecutively decreasing points. You check previous control charts and notice that this is not a regular occurrence. What could have caused this behavior?

    A. machine deterioration
    B. Incorrectly calculated control limits
    C. New machine operator
    D. Process is over-controlled
    Answer: A. machine deterioration

    A series of six or more consecutively rising or decreasing points on an average control chart indicate a trend. Trends are often caused by machine deterioration, tired operators, or tool wear. Common solutions  to trends include repairing the machine or using an alternate machine. Rotating operators, changing tools, or sharpening tools may also correct trends.
  92. Which project management and planning tool is used to plan form multiple contingencies and to steer events towards the ultimate complex goal?

    A. Affinity Diagrams
    B. Process decision programs charts
    C. Interrelation diagraphs
    D. Matrix Diagrams
    Answer: B. Process decision programs charts

    Process decision program chart (PDPCs) are used to chart a course of events from beginning to end. PDPCs map put as many contingencies as possible and plan are made for each of these contingencies. PDPCs are appropriate for new, unique and complex problems, Problems with multiple, complex steps are well suited for PDPCs.
  93. Which tool is used as a form of quality control and is deployed during process baseline estimation  to monitor the variables and parameters occurring with a particular process?

    A. Flow charts
    B. SPC charts
    C. Process maps
    D. Histograms
    Answer: B. SPC charts

    Statistical process control(SPC) charts are used as form of quality control. They are deployed during process baseline estimation to monitor the variables and parameters occurring within a particular process. The performance of these variables is tracked in relation to predetermined upper and lower control limits.
  94. Which index is an indicator of a long term process performance without taking centering into account?

    A. Cpk
    B. CP
    C.Pp
    D. Ppk
    Answer: C.Pp

    Pp is a process performance index that indicates a process's ability to produce products within specification over a long period of time. Pp does not take process centering into account. Pp is calculated using the  following formula:

    Pp = (USL - LSL) / 6 sigma

    In this formula, USL and LSL are the upper and lower specification limits.
  95. Which graphical method for displaying data is also  know as correlation chart?

    A. Pareto diagram
    B. Box and whisker plot
    C. Scatter diagram
    D. Stem and leaf plot
    • Answer: C. Scatter diagram 
    • Scatter diagrams, also known as correlation charts, display XY-coordinate data points to show a relationship between tow variables. Once data points are plotted, a correlation between the variables can be determine is a center line can easily be lifted between the data points. If the fitting center line is straight, it may indicate a positive or negative relationship between the variables, while a curved lines indicate non-linear relationship. If a center line cannot be easily drawn between the data points, it typically indicates no correlation.
  96. Which tool can be specifically used to help set priorities for key process output variables?

    A. Relational Matrix
    B. Control Charts
    C. Attributes Charts
    D. Check Sheets
    Answer: A. Relational Matrix

    A relational matrix is a tool that can be specifically used to help set priorities for key process outputs variables. In this matrix or chart process. input variables are aligned vertically in the chart and output variables are aligned horizontally in the chart. Each output is assigned a priority number.
  97. How are degrees of freedom determine in a 2 mean equal variance t test?

    A. The ratio between the squares of two sample's deviations
    B. The total number of measurements minus one
    C. The Welch-Satterthwaite equation
    D. The total number of measurements minus two.
    Answer: D. The total number of measurements minus two. 

    In a 2 mean equal variance t test, the difference between the mean (x1-bar, and x2-bar) or two sample set of data is tested. The poled standard deviation (Sp)is calculated for use in finding the critical value (t). The critical value is given by the following formula:

    t = A/B

    Where A and B are define as follows:

    • A = X1-bar - X2-bar
    • B = Sp * Square root of (1 / n1 + 1/ n2)

    • In this equation, n1 and n2 represent the number of measurements in each sample. Once the critical value is calculated, its value is compared to a value from the t distribution table based on the confidence level and the degrees of freedom (DF). DF is determined with the following formula: 
    • DF = n1 + n2 - 2
  98. Refer to the exhibit. Which process mapping represents the data symbol?

    A. D
    B. B
    C. A
    D. C

    Answer: B. B

    Process mapping, also known as flow charting, is a technique to describe a process using standard symbols, arrows joining the symbols, and words for labeling each symbol. A parallelogram represents the Data Symbol. This is also sometimes referred to as the Input/Output symbol.
  99. The effects of a change are observed during which step of the Deming-Shewhart cycle?

    A. Do
    B. Act
    C. Plan
    D. Study
    Answer: D. Study

    The Deming-Shewhart cycle is also known as the Plan-Do-Study-Act (PDSA) project methodology. The effects of a change or test that is enacted in the Do step of the cycle are observed, recorded, and analyzed in the study step.
  100. Which inference test would you use to test if variances of two samples are equal?

    A. F Test
    B. 2 mean equal variance t test
    C. Paired t test
    D. 2 mean unequal variance t test
    Answer: A. F Test

    The precision of measuring devices are often compare d to each other by testing the variances in their measurements. To facilitate this test, the variance of two samples are compared for equality . This is done using the F test paired-comparison test.

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