Question 1

A normally distributed data should approximate the theoretical normal distribution. What is the interquartile range of a normal distribution?

Accepted Answer

The interquartile range of a normal distribution is 1.33 standard deviations.
Key Takeaway: An interquartile range is also known as the midspread and it is a statistical measure of dispersion. This range is equal to the difference between the third and first quartiles and has a value of 1.33 standard deviations.

Question 2

Regular customers at a computer service store arrive at the front desk at a rate of 15 per hour. What is the probability that the arrival time between consecutive customers is less than three minutes?

Accepted Answer

The probability is 53%. Key Takeaway: Three minutes are equivalent to 0.05 hours. Given that the mean number of arrivals (?) is 15 hours, the formula below is used to calculate the probability that the arrival time between consecutive customers is less than three minutes. The probability is calculated to be 53% P(arrival time < 0.05) = 1 - e^-?X P(arrival time < 0.05) = 1 - e^-(15)(0.05) P(arrival time < 0.05) = 0.53

Question 3

A marketing manager chooses a large sample of consumers from their target city to survey their attitudes and shopping behaviors. The manager divides his sample into groups with a 10 year age range (i.e. those 20-30 years). What type of probability sampling is he using?

Accepted Answer

The manager is using cluster sampling.
Key Takeaway: Cluster sampling is a type of probability sampling whereby a population is divided into several clusters based on certain characteristics or demographic information. A random sample of individuals is then selected from each cluster and surveyed. Cluster sampling increases the likelihood that the sample chosen is representative of the population from which it is drawn.

Question 4

According to a national grocery store chain manager, only 6% of consumers who have surveys mailed to their homes return them filled out completely. What is this type of sampling error called?

Accepted Answer

This type of sampling error is called the non-response error.
Key Takeaway: A non-response error occurs when the people who respond to a survey are different than those who do not respond. The information gained from such a survey risks being skewed and unrepresentative of the larger population. For example, if the 6% of consumers returning the surveys in this example are mostly elderly consumers, the manager may not gain much information from other types of consumers.

Question 5

Hugh analysis provides a comparison of ___________ during the planning phase of a Six Sigma project.

Accepted Answer

Hugh analysis provides a comparison of solutions' benefits during the planning phase of a Six Sigma project.
Key Takeaway: Hugh analysis is a type of analysis conducted during a Six Sigma project and it aims to compare the benefits of a number of alternative solutions. For example, if a company wishes to compare the benefits of subcontracting to individuals, small companies, or medium-sized ones, the potential benefits of each type of subcontractor is listed in a matrix type of figure.

Question 6

A Black Belt practitioner sets a level of significance of research at 0.05. This level of significance is also referred to as:

Accepted Answer

This level of significance is also referred to as a Type I error.
Key Takeaway: A Type I error is said to be the risk of rejecting the null hypothesis when it is true. In other words, it is the probability that the researcher will conclude that there are significant differences between samples or populations when there are none. For example, if a researcher concluded that those in their 20s purchase different cars than those in their 30s when there are no statistically significant differences, then the researcher has committed a Type I error.

Question 7

When population means are not available in a hypothesis test, the differences between two sample means are used. The following are assumptions made about this type of analysis EXCEPT:

Accepted Answer

In a hypothesis test, samples are not dependent.
Key Takeaway: In hypothesis testing, a number of assumptions are made about the sample means that are compared. For example, samples are expected to be randomly drawn and independent. Populations are also normally distributed.

Question 8

A pharmaceutical company is testing the efficacy of a nasal allergy drug. Research participants are asked to record their vital signs before and after drug administration. The results are then compared. What type of statistical test is used here?

Accepted Answer

This type of statistical test is called the paired difference test.
Key Takeaway: A paired difference test compares the means of two related samples. In this example, the same individuals are tested twice, once before drug administration and again afterwards. The means of the two data sets are then compared to determine whether the drug had significantly affected vital signs.

Question 9

A company wishes to compare the expected mileage of eight different types of car tires. Which of the following statistical tests is best suited for the analysis?

Accepted Answer

ANOVA is the statistical test best suited for this analysis.
Key Takeaway: Analysis of Variance (ANOVA) is a statistical test that evaluates the differences among means of three or more samples. In this example, each of the eight car tires would be tested and its average expected mileage is recorded. ANOVA analysis determines whether at least 2 of the tires have significantly different mileages.

Question 10

A Black Belt practitioner at Vanguard Inc. is comparing the mean processing time of 10 different settings on a machine using ANOVA. What equation is used to calculate the Total Variation (SST) of the individual data values across the various settings?

Accepted Answer

The equation used to calculate the Total Variation (SST) is SSA + SSW.
Key Takeaway: Total variation of the individual data values across the various machine settings is variation among the sample factor means (SSA) and variation that exists among the data values within a particular factor level (SSW).

Question 11

Machines A and B have been showing disparate efficiency and defects per unit rates despite similar variation in quality at purchase time. If the mean squares between the two machines is 250 and the mean squares from each machine 100, what is the value of the F_STAT?

Accepted Answer

The value of the F_STAT is 2.5. Key Takeaway: The F-statistic (F_STAT ) in ANOVA tests the hypothesis about the means of the two machines. The F_STAT is calculated by dividing the mean squares between the samples and the mean squares from each machine as follows: F_STAT = MSA/MSW = 250/100 = 2.5. In other words, The F_STAT is the ratio of the among estimate of variance and the within estimate of variance.

Question 12

Which of the following is NOT included in the 7 classic wastes in business or industrial processes according to Kaizen philosophy?

Accepted Answer

Under-processing of waste is not included in the 7 classic wastes in business or industrial processes.
Key Takeaway: According to Kaizen philosophy, there are a number of wastes that reduce the efficiency of business or industrial processes and increase the bottom-line costs of organizations. Among those wastes are transport waste, inventory waste, waiting waste, over-production of waste, and the over-processing of waste.

Question 13

Adam is a Black Belt practitioner requested to investigate and improve the working relationship between the assembly line manager and unit project manager. Adams discovers that the unit project manager is reluctant to share information with the assembly line manager. This is an example of a(an):

Accepted Answer

This is an example of an organizational roadblock.
Key Takeaway: Organizational roadblocks contribute to projects suffering delays and complications. Miscommunication or conflict between management personnel leads to inadequate information being shared which eventually impacts the work of a unit and its productivity.

Question 14

An advertising manager wishes to study the impact of annual salary amounts and proximity to the major urban shopping centers on the shopping habits of consumers. What is the dependent variable in this study?

Accepted Answer

The dependent variable in this study is the shopping habits of consumers.
Key Takeaway: In the design of experiments, the dependent variable is the variable which is affected by the manipulation of the independent variables. In this example, the independent variables are the salary amounts and proximity to shopping centers.

Question 15

Taaichi Ohno is a well-known Japanese businessman who was one of the early pioneers of lean manufacturing. Which one of the following concepts is Ohno associated with:

Accepted Answer

Ohno is associated with TPS.
Key Takeaway: Taaichi Ohno is considered one of the early pioneers of lean manufacturing. He is known as the father of the Toyota Production System (TPS) which is an integrated socio-technical approach to management. TPS addresses a number of business and industrial processes such as overproduction, waiting, and inventory.

Question 16

A Black Belt practitioner wishes to improve the efficiency and output of processes of a company manufacturing office equipment by raising its performance from 2 to 3 Sigma. By how much would this increase reduce production defects?

Accepted Answer

This increase would reduce defects per million by a factor of 4.6.
Key Takeaway: A 2 sigma defect rate is 308,538 ppm while a 3 Sigma defect rate is 66,810 which translates to a 4.6-fold reduction in defects per million.

Question 17

The main advantage of testing multiple factors in a single experiment or study is:

Accepted Answer

The main advantage of testing multiple factors in a single experiment or study is that it shows interaction effects between factors.
Key Takeaway: In the design of experiments, the simultaneous inclusion of multiple factors in an experiment leads to a study of interactions between them. For example, if a study is examining the effect of increased caloric intake and less exercise on weight gain, an interaction effect between caloric intake and exercise may emerge. Multifactor research design tends to be costly and time consuming, and require significant statistical skill to analyze data.

Question 18

Richard builds a predictive model based on data collected from the highway gas mileage of a number of brand name tires. The differences between actual data points and predicted ones are referred to as:

Accepted Answer

The differences between actual data points and predicted ones are referred to as residuals.
Key Takeaway: Residuals are the differences between actual data points and predicted ones. Predicted data points or responses are usually derived from a predictive model such as that developed from a simple regression model. The larger residuals are, the less likely that the predictive model provides accurate predictions of values.

Question 19

Which of the following statements about multiple regression models is true?

Accepted Answer

Multiple independent variables are used in multiple regression models.
Key Takeaway: In multiple regression, more than one independent variable is included in constructing a model (unlike simple linear regression). For example, the performance of a vehicle (dependent variable) can be predicted from a multiple regression model that examines a number of independent variables such as gas mileage, braking distance, rust resistance, and battery efficiency.

Question 20

In an experimental design, the gradations of temperature in degrees Celsius for a standard oven is used as an independent variable. What are these gradations referred to?

Accepted Answer

These gradations are referred to as levels.
Key Takeaway: Levels in experimental designs refer to the settings in the independent variables. For example, gradations in temperature, weight or other measurements are used as levels of independent variables. These levels are then analyzed in terms of other impact on the dependent variable. In this example, the temperature settings can be used to test how long it takes this standard oven to bake a medium-sized pie.

Quiz 1: Black Belt

A normally distributed data should approximate the theoretical normal distribution. What is the interquartile range of a normal distribution?

Regular customers at a computer service store arrive at the front desk at a rate of 15 per hour. What is the probability that the arrival time between consecutive customers is less than three minutes?

A marketing manager chooses a large sample of consumers from their target city to survey their attitudes and shopping behaviors. The manager divides his sample into groups with a 10 year age range (i.e. those 20-30 years) . What type of probability sampling is he using?

According to a national grocery store chain manager, only 6% of consumers who have surveys mailed to their homes return them filled out completely. What is this type of sampling error called?

Hugh analysis provides a comparison of ___________ during the planning phase of a Six Sigma project.

A Black Belt practitioner sets a level of significance of research at 0.05. This level of significance is also referred to as:

When population means are not available in a hypothesis test, the differences between two sample means are used. The following are assumptions made about this type of analysis EXCEPT:

A pharmaceutical company is testing the efficacy of a nasal allergy drug. Research participants are asked to record their vital signs before and after drug administration. The results are then compared. What type of statistical test is used here?

A company wishes to compare the expected mileage of eight different types of car tires. Which of the following statistical tests is best suited for the analysis?

A Black Belt practitioner at Vanguard Inc. is comparing the mean processing time of 10 different settings on a machine using ANOVA. What equation is used to calculate the Total Variation (SST) of the individual data values across the various settings?

Machines A and B have been showing disparate efficiency and defects per unit rates despite similar variation in quality at purchase time. If the mean squares between the two machines is 250 and the mean squares from each machine 100, what is the value of the F_STAT?

Which of the following is NOT included in the 7 classic wastes in business or industrial processes according to Kaizen philosophy?

Adam is a Black Belt practitioner requested to investigate and improve the working relationship between the assembly line manager and unit project manager. Adams discovers that the unit project manager is reluctant to share information with the assembly line manager. This is an example of a(an) :

An advertising manager wishes to study the impact of annual salary amounts and proximity to the major urban shopping centers on the shopping habits of consumers. What is the dependent variable in this study?

Taaichi Ohno is a well-known Japanese businessman who was one of the early pioneers of lean manufacturing. Which one of the following concepts is Ohno associated with:

A Black Belt practitioner wishes to improve the efficiency and output of processes of a company manufacturing office equipment by raising its performance from 2 to 3 Sigma. By how much would this increase reduce production defects?

The main advantage of testing multiple factors in a single experiment or study is:

Richard builds a predictive model based on data collected from the highway gas mileage of a number of brand name tires. The differences between actual data points and predicted ones are referred to as:

Which of the following statements about multiple regression models is true?

In an experimental design, the gradations of temperature in degrees Celsius for a standard oven is used as an independent variable. What are these gradations referred to?

Quiz 1: Black Belt

A normally distributed data should approximate the theoretical normal distribution. What is the interquartile range of a normal distribution?

Regular customers at a computer service store arrive at the front desk at a rate of 15 per hour. What is the probability that the arrival time between consecutive customers is less than three minutes?

A marketing manager chooses a large sample of consumers from their target city to survey their attitudes and shopping behaviors. The manager divides his sample into groups with a 10 year age range (i.e. those 20-30 years) . What type of probability sampling is he using?

According to a national grocery store chain manager, only 6% of consumers who have surveys mailed to their homes return them filled out completely. What is this type of sampling error called?

Hugh analysis provides a comparison of ___________ during the planning phase of a Six Sigma project.

A Black Belt practitioner sets a level of significance of research at 0.05. This level of significance is also referred to as:

When population means are not available in a hypothesis test, the differences between two sample means are used. The following are assumptions made about this type of analysis EXCEPT:

A pharmaceutical company is testing the efficacy of a nasal allergy drug. Research participants are asked to record their vital signs before and after drug administration. The results are then compared. What type of statistical test is used here?

A company wishes to compare the expected mileage of eight different types of car tires. Which of the following statistical tests is best suited for the analysis?

A Black Belt practitioner at Vanguard Inc. is comparing the mean processing time of 10 different settings on a machine using ANOVA. What equation is used to calculate the Total Variation (SST) of the individual data values across the various settings?

Machines A and B have been showing disparate efficiency and defects per unit rates despite similar variation in quality at purchase time. If the mean squares between the two machines is 250 and the mean squares from each machine 100, what is the value of the FSTAT?

Which of the following is NOT included in the 7 classic wastes in business or industrial processes according to Kaizen philosophy?

Adam is a Black Belt practitioner requested to investigate and improve the working relationship between the assembly line manager and unit project manager. Adams discovers that the unit project manager is reluctant to share information with the assembly line manager. This is an example of a(an) :

An advertising manager wishes to study the impact of annual salary amounts and proximity to the major urban shopping centers on the shopping habits of consumers. What is the dependent variable in this study?

Taaichi Ohno is a well-known Japanese businessman who was one of the early pioneers of lean manufacturing. Which one of the following concepts is Ohno associated with:

A Black Belt practitioner wishes to improve the efficiency and output of processes of a company manufacturing office equipment by raising its performance from 2 to 3 Sigma. By how much would this increase reduce production defects?

The main advantage of testing multiple factors in a single experiment or study is:

Richard builds a predictive model based on data collected from the highway gas mileage of a number of brand name tires. The differences between actual data points and predicted ones are referred to as:

Which of the following statements about multiple regression models is true?

In an experimental design, the gradations of temperature in degrees Celsius for a standard oven is used as an independent variable. What are these gradations referred to?

Machines A and B have been showing disparate efficiency and defects per unit rates despite similar variation in quality at purchase time. If the mean squares between the two machines is 250 and the mean squares from each machine 100, what is the value of the F_STAT?