Lean Six Sigma Green Belt Practice Exam — All Questions

When testing whether a process change produced a statistically significant effect, a p-value of 0.02 against an alpha of 0.05 means:

• a.The effect size is guaranteed to be large
• b.Reject the null hypothesis; the result is statistically significant✓
• c.Fail to reject the null hypothesis; no significant effect
• d.The test is invalid and must be repeated

Because the p-value (0.02) is less than alpha (0.05), you reject the null hypothesis and conclude the effect is statistically significant. Statistical significance does not by itself measure the size or practical importance of the effect.

A Pareto chart supports the Analyze phase by helping the team:

• a.Focus on the 'vital few' categories that account for most of the problem✓
• b.Estimate the population standard deviation
• c.Prove causation between two variables
• d.Monitor a process over time for stability

The Pareto principle directs attention to the small number of categories that produce the majority of the defects or cost. It does not establish causation, track stability over time, or estimate spread.

A correlation coefficient (r) of 0.85 between two variables indicates:

• a.A strong negative linear relationship
• b.A strong positive linear relationship between the variables✓
• c.No relationship between the variables
• d.That one variable definitely causes the other

An r near +0.85 signals a strong positive linear association, meaning the variables tend to rise together. Correlation alone never proves causation, and a negative relationship would show a negative r.

The '5 Whys' technique is primarily used to:

• a.Drill down from a symptom to an underlying root cause✓
• b.Set the sample size for a study
• c.Build a control chart
• d.Calculate process capability indices

Asking 'why' repeatedly moves the team from the visible symptom toward the deeper root cause. It is a qualitative root-cause tool, not a method for capability, sampling, or control charting.

In hypothesis testing, a Type I error (alpha) occurs when you:

• a.Fail to reject a null hypothesis that is actually false
• b.Measure a part with the wrong gage
• c.Choose too large a sample size
• d.Reject a null hypothesis that is actually true (a false positive)✓

A Type I error is a false positive: concluding an effect exists when it does not, which happens with probability alpha. Failing to detect a real effect is a Type II (beta) error.

An Ishikawa (fishbone) diagram organizes potential causes into major 'bones.' Which set best represents the classic 6M categories for manufacturing?

• a.Suppliers, Inputs, Process, Outputs, Customers, and Costs across the value chain
• b.Plan, Do, Check, Act, Adjust, and Assess as the improvement wheel
• c.Sort, Set in order, Shine, Standardize, Sustain, and Safety, the workplace-organization method
• d.Machine, Method, Material, Measurement, Man/People, and Mother Nature (Environment)✓

The fishbone (cause-and-effect) diagram groups candidate causes into the 6Ms: Machine, Method, Material, Measurement, Man/People, and Mother Nature (Environment). It is a brainstorming and organizing tool for potential causes, not the 5S list, the PDCA cycle, or SIPOC.

A team lists 'inadequate operator training' as a cause of errors and keeps asking 'why.' This progression from a symptom toward a fixable systemic cause is the essence of which tool?

• a.The 5 Whys root-cause technique✓
• b.A full factorial Design of Experiments study
• c.A process capability (Cp/Cpk) analysis
• d.A time-ordered statistical control chart

The 5 Whys drills through layers of causation by repeatedly asking why until a root, systemic cause is reached that can be corrected. DOE tests factor effects, control charts monitor stability, and capability analysis compares spread to specifications.

In FMEA, the Risk Priority Number (RPN) is calculated as:

• a.The sum of the Severity, Occurrence, and Detection ratings
• b.Severity times Occurrence, then divided by the Detection rating
• c.The sum of Severity and Occurrence, multiplied by Detection
• d.Severity multiplied by Occurrence multiplied by Detection✓

RPN = Severity x Occurrence x Detection, the product of the three 1-to-10 ratings used to prioritize failure modes. Summing the ratings or dividing by detection would not reflect how the three risk dimensions multiply together.

A failure mode is rated Severity = 8, Occurrence = 4, and Detection = 5. What is its RPN?

• a.160, from multiplying all three ratings✓
• b.17, from adding the three ratings together
• c.80, from multiplying only Severity and Occurrence and doubling
• d.40, from multiplying only Occurrence and Detection twice

RPN = S x O x D = 8 x 4 x 5 = 160. Adding the ratings gives 17 and multiplying only two of the three factors gives 80 or 40, none of which is the correct product.

In a FMEA, a Detection rating of 10 (on the 1-to-10 scale) means that:

• a.There is almost no chance the current controls will detect the failure✓
• b.The failure is certain to be caught by controls before it reaches the customer
• c.The failure carries the lowest possible severity to the end user
• d.The failure is expected to occur only very rarely in production

On the FMEA Detection scale, a 10 means detection is nearly impossible (controls will almost never catch the failure), which raises the RPN. Low detectability is bad, not good, and Detection is separate from Severity and Occurrence.

A Pareto analysis of 500 defects finds that 3 of 12 defect types account for 410 defects. The best Analyze-phase conclusion is to:

• a.Conclude that the process is already in statistical control
• b.Ignore the three largest types because they are the hardest to fix
• c.Spread the improvement effort evenly across all twelve defect types
• d.Concentrate improvement effort on those three 'vital few' types✓

The Pareto principle says a small number of categories cause most of the problem, so focusing on the 3 vital-few types (about 82% of defects) yields the greatest return. Spreading effort evenly or ignoring the biggest contributors wastes resources, and Pareto says nothing about statistical control.

In hypothesis testing, the null hypothesis (H0) typically states that:

• a.The process producing the data is out of statistical control
• b.The alternative claim being investigated is definitely true
• c.The sample size collected for the study is too small
• d.There is no difference or no effect (the status quo holds)✓

The null hypothesis expresses no difference, no change, or no effect, and the test looks for evidence to reject it. The claim of a real difference is the alternative hypothesis (Ha), not the null.

A two-sample t-test is the appropriate tool when you want to:

• a.Compare the means of two independent groups of continuous data✓
• b.Test the association between two categorical attribute variables
• c.Fit a straight line to predict a continuous output variable
• d.Compare the variances of five different machines simultaneously

A two-sample t-test compares the means of two independent groups measured on a continuous scale. Comparing many means uses ANOVA, categorical association uses chi-square, and predicting a continuous output uses regression.

A one-way ANOVA is used instead of running many separate t-tests when comparing several group means because it:

• a.Completely eliminates the need to check for normality
• b.Controls the overall Type I error rate across all comparisons✓
• c.Always produces a noticeably lower p-value than a t-test
• d.Requires no assumptions at all about the underlying data being tested here

Running many separate t-tests inflates the family-wise chance of a false positive; ANOVA tests all means simultaneously and holds the overall Type I error at alpha. It still assumes independence, roughly normal residuals, and equal variances.

In a one-way ANOVA comparing 4 groups with 40 total observations, the between-groups and within-groups degrees of freedom are:

• a.4 and 40
• b.3 and 39
• c.1 and 39
• d.3 and 36✓

Between-groups df = k - 1 = 4 - 1 = 3, and within-groups (error) df = N - k = 40 - 4 = 36. The total df is N - 1 = 39, which equals 3 + 36.

The F-statistic in ANOVA is fundamentally a ratio of:

• a.The overall standard deviation to the grand mean
• b.The total variation in the data to the residual error variation
• c.Between-group variance to within-group variance✓
• d.The total sample size to the number of groups compared

F = MS(between) / MS(within), comparing the variation among group means to the variation within groups. A large F means the group means differ more than random within-group noise would explain.

A chi-square test of independence is the right tool when you want to determine whether:

• a.Two continuous variables share a linear increasing trend
• b.A single sample mean differs from a target value
• c.Three or more group means are all equal to each other
• d.Two categorical (attribute) variables are related✓

The chi-square test of independence checks whether two categorical variables (for example, shift and defect type) are associated by comparing observed and expected counts. Continuous trends use regression, several means use ANOVA, and a single mean uses a one-sample t-test.

For a chi-square contingency table with 3 rows and 4 columns, the degrees of freedom equal:

• a.5, from subtracting one from the total of rows and columns
• b.12, from multiplying the rows by the columns directly
• c.6, from (rows minus 1) times (columns minus 1)✓
• d.7, from adding the number of rows and columns together

df = (rows - 1) x (columns - 1) = (3 - 1) x (4 - 1) = 2 x 3 = 6. Multiplying the raw counts (12) or adding them (7) does not give the correct degrees of freedom.

The chi-square statistic is computed by summing, over all cells, the quantity:

• a.(Observed minus Expected), squared, divided by Expected✓
• b.(Observed minus Expected), divided by the Observed count
• c.(Expected minus Observed), divided by the sample size n
• d.Observed multiplied by Expected for each single cell

Chi-square = sum of (O - E)^2 / E across all cells, which grows when observed counts depart from what independence would predict. Simple differences or products do not weight the deviation by the expected count.

A p-value of 0.001 in a hypothesis test with alpha = 0.05 tells you that:

• a.You reject the null hypothesis; the result is highly statistically significant✓
• b.The practical effect in the process is guaranteed to be large and important in practice
• c.You fail to reject the null hypothesis for lack of evidence
• d.The test is invalid and its result must be discarded entirely

Because 0.001 is far below alpha = 0.05, you reject the null and the result is strongly statistically significant. A small p-value indicates significance, not the magnitude or practical importance of the effect.

A p-value of 0.18 tested against alpha = 0.05 leads you to:

• a.Conclude that the alternative hypothesis has now been proven
• b.Fail to reject the null hypothesis (insufficient evidence)✓
• c.Reject the null hypothesis and declare a significant effect
• d.Automatically accept that the observed effect is large

Since 0.18 exceeds alpha = 0.05, there is not enough evidence to reject the null, so you fail to reject it. Failing to reject is not the same as proving the null true; it means the data did not show a significant effect.

The significance level alpha in a hypothesis test represents:

• a.The practical size of the effect the study hopes to demonstrate
• b.The probability of rejecting a true null hypothesis (the Type I error risk)✓
• c.The probability of committing a Type II error and missing an effect
• d.The statistical power of the test to detect a real difference

Alpha is the pre-set risk of a Type I error, rejecting a null hypothesis that is actually true. The Type II error risk is beta, and power (1 - beta) is the chance of detecting a real effect.

The power of a hypothesis test is defined as:

• a.The probability of committing a Type II error in the test
• b.The probability of correctly rejecting a false null hypothesis (1 minus beta)✓
• c.The probability of committing a Type I error, a false positive, in the test itself somehow
• d.The significance level alpha chosen before collecting data

Power equals 1 - beta, the probability of detecting an effect that truly exists. Increasing sample size or effect size raises power; alpha and beta are the two error probabilities, not power itself.

A Type II error (beta) in hypothesis testing occurs when you:

• a.Fail to reject a null hypothesis that is actually false (a missed effect)✓
• b.Reject a null hypothesis that is in fact actually true (a false positive)
• c.Select the wrong significance level for the analysis
• d.Use continuous data where discrete data was required

A Type II error is a false negative: failing to detect a real difference, which happens with probability beta. Rejecting a true null is the Type I (alpha) error.

A 95% confidence interval for a process mean is calculated as [48.2, 51.8]. The best interpretation is:

• a.Exactly 5% of all parts produced by the process are defective
• b.We are 95% confident the true population mean lies between 48.2 and 51.8✓
• c.The sample mean has a 95% chance of being precisely equal to 50
• d.Exactly 95% of individual measurements fall between 48.2 and 51.8 within the collected sample

A 95% confidence interval means the method captures the true population mean 95% of the time, so we are 95% confident the mean lies within [48.2, 51.8]. It describes the mean, not the spread of individual values or a defect rate.

A sample of n = 100 has mean 50 and known population standard deviation 10. Using z = 1.96, the 95% confidence interval for the mean is approximately:

• a.[30.40, 69.60]
• b.[49.80, 50.20]
• c.[48.04, 51.96]✓
• d.[40.00, 60.00]

Standard error = sigma / sqrt(n) = 10 / sqrt(100) = 1.0, and the margin = 1.96 x 1.0 = 1.96, giving 50 +/- 1.96 = [48.04, 51.96]. Using sigma itself (10) instead of the standard error gives the wrong, much wider interval.

Holding everything else constant, increasing the sample size in a confidence-interval calculation will:

• a.Narrow the interval by reducing the margin of error✓
• b.Widen the interval and reduce the precision of the estimate
• c.Have no measurable effect at all on the interval width
• d.Change the true population mean the interval is estimating

Because the standard error is sigma / sqrt(n), a larger n shrinks the standard error and narrows the interval, giving a more precise estimate. Sample size does not change the true population mean.

A correlation coefficient r = -0.92 between machine speed and product yield indicates:

• a.A weak, unreliable relationship that should be ignored entirely by the team
• b.A strong negative linear relationship (yield falls as speed rises)✓
• c.That higher speed is proven to cause lower yield with certainty
• d.A strong positive linear relationship between the two variables

An r near -0.92 is a strong negative linear association: as one variable increases the other tends to decrease. A strong correlation still does not prove causation, and the sign shows the direction is negative, not positive.

In regression, a coefficient of determination R^2 = 0.81 means that:

• a.There is an 81% probability that the relationship is truly causal
• b.81% of the variation in the response is explained by the model✓
• c.Exactly 81% of the data points fall directly on the fitted line
• d.The correlation coefficient r between the variables equals 0.81

R^2 is the proportion of variation in the output explained by the regression model, so 0.81 means the model accounts for 81% of that variation. Here r would be sqrt(0.81) = 0.90, and R^2 speaks to explained variance, not causation or exact fit.

A simple linear regression yields the equation Y = 5 + 2X. When X = 10, the predicted value of Y is:

• a.7
• b.25✓
• c.20
• d.15

Substituting X = 10 gives Y = 5 + 2(10) = 5 + 20 = 25. Forgetting the intercept (20), the slope term alone, or adding the coefficients (7) all give wrong predictions.

In the regression equation Y = 12 - 3X, the slope of -3 means that for each one-unit increase in X, Y is predicted to:

• a.Increase by 12 units, matching the intercept value
• b.Stay exactly the same regardless of the value of X
• c.Decrease by 3 units for every additional unit of X✓
• d.Increase by 3 units for every additional unit of X

The slope is the change in Y per one-unit change in X, so a slope of -3 means Y decreases by 3 for every unit increase in X. The intercept 12 is the predicted Y when X is zero, not the rate of change.

A residual in regression analysis is:

• a.The slope of the best-fit regression line drawn through all of the data points
• b.The difference between an observed value and the model's predicted value✓
• c.The correlation between the input X and the output Y
• d.The intercept where the regression line crosses the axis

A residual is the observed value minus the predicted (fitted) value, showing how far a point lies from the regression line. Analyzing residuals checks whether the model assumptions hold; it is not the slope, intercept, or correlation.

The caution 'correlation does not imply causation' warns the Analyze team that:

• a.Regression analysis should never be used in a Six Sigma project
• b.A statistical association may be coincidental or driven by a lurking variable✓
• c.A high correlation coefficient r is always a sign of measurement error somewhere in the data set
• d.Two variables can never actually be causally related to each other

A strong correlation shows two variables move together but does not prove one causes the other; a third (lurking) variable or coincidence may explain it. Confirming causation usually requires a designed experiment, not correlation alone.

A scatter diagram is used in the Analyze phase primarily to:

• a.Visualize the relationship between two continuous variables✓
• b.Display the five-number summary of a single variable
• c.Map the suppliers and inputs feeding into a process
• d.Rank defect categories from the largest to the smallest strictly by their count

A scatter diagram plots paired continuous values to reveal the direction, strength, and shape of a relationship before quantifying it with correlation or regression. Ranking categories is a Pareto chart and a five-number summary is shown by a box plot.

In Lean, 'value-added' activity is best defined as work that:

• a.Inspects the finished product to detect and screen out defects
• b.Is any step at all that the operator happens to be paid to perform during the shift
• c.The customer will pay for, physically transforms the product, and is done right the first time✓
• d.Moves material or product between two adjacent workstations

A value-added step meets three tests: the customer will pay for it, it changes the product toward what the customer wants, and it is done correctly the first time. Movement and inspection are classic non-value-added (though sometimes necessary) activities.

The eight wastes of Lean are often remembered by the acronym DOWNTIME. The 'D' stands for:

• a.Defects, meaning work that must be scrapped or reworked✓
• b.Delay, meaning the time products spend queued between steps
• c.Downtime, meaning idle equipment awaiting repair or setup
• d.Distance, meaning how far material and people must travel

In DOWNTIME the letters are Defects, Overproduction, Waiting, Non-utilized talent, Transportation, Inventory, Motion, and Excess processing, so 'D' is Defects. Defects waste material and time because work must be scrapped or reworked.

During value stream analysis, waiting time between two process steps is categorized as:

• a.Value-added time that the paying customer is happy to fund
• b.Takt time, the pace at which the customer demands the product
• c.Non-value-added time, a form of Lean waste✓
• d.Cycle-time reduction achieved by the improvement team

Waiting is one of the eight wastes because the product sits idle without being transformed, adding lead time but no value. It inflates the total lead time on a value stream map without contributing anything the customer would pay for.

Process cycle efficiency (PCE) is calculated as:

• a.Value-added time divided by the total process lead time✓
• b.The available production time divided by the customer demand
• c.Total process lead time divided by the value-added time
• d.The number of defects divided by the number of opportunities

PCE = value-added time / total lead time, expressing what fraction of the time the product is actually being improved. A low PCE reveals large amounts of waiting and other waste in the value stream; available time over demand is takt time.

A process has 45 minutes of value-added time within a total lead time of 900 minutes. Its process cycle efficiency is:

• a.20%
• b.5%✓
• c.0.5%
• d.50%

PCE = value-added time / lead time = 45 / 900 = 0.05 = 5%. This low efficiency shows that most of the lead time is non-value-added waiting or handling rather than transformation.

A histogram examined during Analyze that shows two distinct peaks (bimodal) most often suggests:

• a.Two different populations or conditions are mixed in the data✓
• b.A calculation error must have occurred while plotting
• c.The data follow a perfectly normal bell-shaped distribution in shape
• d.The underlying process has essentially zero variation

A bimodal histogram typically means the sample combines two different sources, such as two machines, shifts, or materials, that should be stratified and analyzed separately. It is a signal to segment the data, not evidence of normality or zero variation.