Question 1

Which of the following is NOT an example of continuous data?

Accepted Answer

Treatment conditions (A or B) are not continuous data.
Key Takeaway: Continuous data indicates that observations are numerical values and not limited to nominal categories (such as gender or employment status). For example, the temperature in a standard over would often range from zero degrees Celsius to over 500. The same can be said of other continuous measures such as money spent and gas mileage in a vehicle. A treatment condition comprised of two levels (A or B) is considered to be categorical data.

Question 2

Accuracy in data describes how _____ measurements are while precision describes how _____ they are in comparison to actual variation.

Accepted Answer

Accuracy in data describes how centered measurements are while precision describes how dispersed they are in comparison to actual variation.
Key Takeaway: Accuracy and precision are two descriptors of a measurement system. Accuracy in data describes how centered measurements are; for example, it measure how well data gathered from average production cycle times are centered in relation to actual variation. Precision, on the other hand, measures how widely spread or dispersed those measures are.

Question 3

In a measurement system, repeatability means that you are recording variation in a process output such as the amount of time it takes to install bolts to a machine with the same conditions. As part of measurement system variation, repeatability can be thought of as:

Accepted Answer

Repeatability can be thought of as the short-term component of measurement system variation.
Key Takeaway: Repeatability means that you are repeating measurements of a process with the same tools using the same measurement and under the same conditions. Together with reproducibility, repeatability represents captures a measurement system's precision.

Question 4

In a simple linear regression line, the rate of change of one variable is measured against another. The resulting equation is listed below. What does the term (b0) stand for?

Accepted Answer

The term b0 stands for intercept.
Key Takeaway: In a simple linear regression equation an unknown value of variable Y is predicted from a known value of variable X. The other components of the equation include two coefficients that are derived from a set of data that match values of variables X and Y. b0 represents the y-intercept value (when x=0) when this data is plotted and a line of best fit is drawn.

Question 5

A Black Belt practitioner is using preliminary data that correlates a vehicle's weight to its gas mileage. The goal of the study is to predict gas mileage (Y) in liters/40 miles from vehicle weight (X) in tons as seen in the equation below. What is the gas mileage of a car that weighs 2.5 tons? Y_i = 3.5 + 5X_i + 0.025

Accepted Answer

The gas mileage of a car that weighs 2.5 tons is 16.025 liters/40 miles. Key Takeaway: A simple linear regression equation is constructed to calculate an unknown variable (Y) from a known one (X) given a previously calculated set of coefficients (slope, intercept, and random error term). In this case, the gas mileage of a car depending on its weight will be calculated as such: Y_i = 3.5 + 5X_i + 0.025 Y_i = 3.5 + 5(2.5) + 0.025 Y_i = 16.025

Question 6

When designing a survey or questionnaire as part of a marketing campaign, the following survey error occurs when an entire group is excluded from participating in the survey and has no chance of being included in the future:

Accepted Answer

Selection bias is a type of survey error when an entire group is excluded from participation.
Key Takeaway: When an entire group is excluded from participating in a survey and has no chance of being included in the future, this is referred to as a selection bias. A selection bias threatens to skew results from a survey, especially if the excluded group is large and/or particularly influential in their purchasing habits.

Question 7

In Six Sigma methodology, critical Xs (or CTx) are important in optimizing the output and proficiency of a business or industrial process. What does CTS stand for?

Accepted Answer

CTS stands for Critical to Satisfaction.
Key Takeaway: In Six Sigma methodology, it is important to identify those factors that are critical to optimizing the proficiency and output of a business or industrial process. Critical to Satisfaction or CTS defines specific areas of application that contribute to customer success. Key contributors to customer satisfaction are outlined and expanded upon in a CTS tree. This allows principal project members to understand and apply ways to optimize those contributing factors.

Question 8

A Black Belt practitioner is hired to identify a number of Critical to Price (CTP) factors in an effort to streamline and reduce costs associated with manufacturing Product A. The following are CTP factors EXCEPT:

Accepted Answer

Loan refinancing costs are not a CTP factor.
Key Takeaway: Critical to Price (CTP) factors are factors that influence the costs of a process. To manufacture Product A, a number of costs including components, assembly and shipping would be included in the construction of a CTP tree.

Question 9

In Failure Mode Effects Analysis (FMEA), a probability score is assigned to the likelihood that current controls in a business or industrial process will become aware of the causes of a failure. What is this FMEA element referred to?

Accepted Answer

This FMEA element is referred to as the likelihood of detection.
Key Takeaway: FMEA provides an individual or a team with a structured approach to identify potential ways that a product or a process can experience failure. The primary elements of FMEA are probability of a failure's occurrence, the severity of its impact, and the likelihood of detection.

Question 10

A Six Sigma practitioner is likely to use advanced quantitative analysis to optimize business or industrial processes. Through process mapping and modeling, the practitioner can match the processes inherent to the project to multiple variables required by requirement or customer needs. This tool is also referred to the:

Accepted Answer

This tool is also referred to as the capability-complexity analysis (CCA).
Key Takeaway: Capability-complexity analysis (CCA) is a Six Sigma analytic tool that matches the capability an organization's processes with the complex of products and services that are developed from these processes. CCA uses a number of quantitative, process mapping and modeling in order to optimize business or industrial processes.

Question 11

Which type of statistical analysis requires at least 50 data points in sequence in order to provide inferential capability?

Accepted Answer

Time-series analysis must be done with at least 50 data points in sequence.
Key Takeaway: Time-series analyses are done with at least 50 data points in sequence for them to provide inferential capability. This type of analyses provides information on trends decompositions and moving averages. For example, a weather prediction must take into account at least 50 consecutive days in any given season to provide prediction capability.

Question 12

Researchers at a car manufacturing plant are conducting a double-blind, controlled study to compare 2 brake systems. What does double-blind mean in this context?

Accepted Answer

Double-blind experimental design means that samples are kept confidential from testers.
Key Takeaway: To make sure that testers' knowledge of which brake system is being tested, they are kept unaware until the experiments are finished. This type of experimental design is also referred to as a double-blind study and it is used extensively to increase the validity of experimental data.

Question 13

The length of training offered to newly hired interns is strongly correlated with their monthly performance sales' figures. With a correlation coefficient of +0.72, this does NOT imply that:

Accepted Answer

This example does not imply that training causes high sales' figures.
Key Takeaway: In correlational studies, it is understood that only the relationship between two variables is explored without assigning causation. In other words, length of training and sales' figures may simply occur together or they may have a common contributing factor.

Question 14

The following are examples of One Way Analysis of Variance (ANOVA) EXCEPT:

Accepted Answer

Tukey multiple comparison is not an example of ANOVA.
Key Takeaway: ANOVA is a type of inferential analysis that compares the means of several populations. For example, a car manufacturer may be interested in the mean highway gas mileage of several of its mid-sized models. Tukey multiple comparison is an example of ANOVA.

Question 15

A company of over 13,000 employees conducted a survey and assigned numbers to those employees who have been hired within the previous 5 years (1) and in increments of 5 years from there on. Eight people have been with the company for 20 years. What is the plot below referred to?

Accepted Answer

This plot is referred to as stem-and-leaf.
Key Takeaway: A stem-and-leaf display of data is a simply way of distributing a data set so that areas of concentration are apparent. The data is arranged so that the major groupings (the stem) are on the left while their frequency (the leaves) is on the right.

Question 16

A company's marketing research reveals that in their target customer area, 50% of people are under the age of 39 years while 50% of people make over $80,000 per year. What is this descriptive statistic referred to?

Accepted Answer

This statistic is referred to as a median.
Key Takeaway: Median calculations are considered descriptive statistics and they shed light on a point in a data set whereby 50% of the data fall above while 50% fall below. This is a common descriptive used in large census projects as well as marketing campaigns.

Question 17

Which one of the following descriptive statistics is most affected by an outlier data point?

Accepted Answer

Range is a descriptive statistic that is most affected by an outlier data point.
Key Takeaway: Outliers are infrequent data points that fall outside of 2 or 3 standard deviations from the mean. Outliers have the potential to skew data statistics and the range of a data set is most affected by their presence. For example, if a group of individuals have an average age of 32 years with 99% of individuals placed between 20 and 45 years, a single data point of a 70 year old individual gives the data a range of 20-70 years.

Question 18

In the coefficient of variation formula below, what does the (S) stand for?

Accepted Answer

The S stands for standard deviation.
Key Takeaway: The Coefficient of Variation measures relative variation in a data set and is always shown as a percentage. The standard deviation of a data set is divided by the mean which shows a variation relative to the mean of the data set. This type of statistic can be used to measure the variation of two data sets; for example, the dimensions of pencils produced by two machines can be compared in terms of variation to gauge their precision.

Question 19

Jason is a Black Belt practitioner who is commissioned to compare the variations in Stocks A and B. Stock A has an average price of $80 with a standard deviation of $8 while Stock B has an average price of $120 with a standard deviation of $6. What is the variation of both Stocks A and B?

Accepted Answer

The variation of Stock A is 10% and the variation of Stock B is 5%.
Key Takeaway: The Coefficient of Variation measures the variation of a data set around the mean. This allows the comparison of two data values or sets such as Stocks A and B. To calculate variation, the following formula is used:
Stock A: CV = ($8/$80) * 100% = 10%
Stock B: CV = ($6/$120) * 100% = 5%

Question 20

Christina is the newest intern hired in the accounting department. According to her high school records, Christina scored a 650 on her math SAT. The mean score and deviation are 450 and 100, respectively. How many standard deviations above the mean did Christina score?

Accepted Answer

Christina's score is 2 standard deviations above the mean.
Key Takeaway: To calculate how much a data point deviates from the mean, it is important to calculate the Z-statistic as seen in the formula below. Using this formula, Christina scored 2 standard deviations above the mean so would not be considered an outlier.
Z = (650 - 450)/100 = 2

Quiz 1: Black Belt