IASSC Lean Six Sigma Black Belt Practice Questions — 10 Free (2026)

What does the Yates continuity correction do in a 2x2 chi-square test, and what is its side effect?

• A. It doubles each expected count, which raises the power
• B. It adds 0.5 to each observed count, inflating the statistic, no matter what the process capability figures imply
• C. It removes the largest cell from the sum, stabilising the p-value
• D. It shrinks each observed-minus-expected gap by 0.5 before squaring, making the test more conservative ✓
• E. It transfers one unit of count from the largest cell to the smallest cell, leaving the marginal totals of the table unchanged

The correction subtracts half a unit from the absolute gap in every cell before squaring, compensating for fitting a smooth chi-square curve to a statistic built from whole number counts. Because the gaps shrink, the statistic falls and the p-value rises, so the corrected test is conservative and can miss borderline real effects, which is why some analysts prefer Fisher's exact test instead. Nothing is added to observed counts, no cell is removed, and no counts are transferred between cells. IASSC Lean Six Sigma BOK, 3.5.8

Tool wear drifts a dimension upward at about 0.2 units per hour, and the team must sample often enough that the drift between successive samples never exceeds 1.6 units. Using interval = allowed drift / drift rate, what is the longest acceptable sampling interval?

• A. 2
• B. 4
• C. 8 ✓
• D. 12
• E. 16

The drift accumulates at 0.2 units per hour, so 1.6 units build up over 1.6 / 0.2 = 8 hours, which is the widest spacing that still meets the requirement. The value 16 doubles the correct interval and lets twice the allowed drift accumulate, while 4 and 2 sample two and four times as often as necessary, spending inspection effort without any added protection. The value 12 has no basis in the figures. Tying the sampling interval to the physics of how fast the process can change is the rational way to set frequency, and it beats copying whatever interval the last project happened to use. IASSC Lean Six Sigma BOK, 5.2.12

A sponsor points out that a process still has variation the team cannot remove within the project's timeframe, yet the customer expects a firm delivery date. What does a combined programme say about the choices available?

• A. The date must be refused until that variation has been removed at its source
• B. The variation has to be covered by stock, by spare capacity or by quoted time ✓
• C. The variation can be absorbed by tightening the standard work of the operators
• D. The variation is a quality matter and has no bearing on the delivery promise
• E. The date can be held by raising the utilisation of the resources in the stream

Variability that has not been removed does not disappear; it is paid for in one of three currencies, and the only real decision is which. Inventory buys protection with cash, spare capacity buys it with idle resource, and a longer quoted lead time buys it with the customer's patience. Naming the choice openly lets a sponsor decide deliberately rather than discovering later that the plant has been paying in all three at once. Raising utilisation removes the capacity buffer and so makes the position worse, and tightening standard work cannot absorb variation that originates in the inputs or the equipment rather than in the operator. IASSC Lean Six Sigma BOK, 1.4.3

Beyond the cause and effect diagram that carries his name, what did Ishikawa argue for that a modern deployment still depends on?

• A. That statistical work belongs with engineers and trained specialists only
• B. That quality is settled during design and not out on the production floor
• C. That suppliers should be audited each year rather than developed slowly
• D. That everyone at work can use a small set of tools on their own process ✓
• E. That improvement work is best driven by one central department of experts

His argument was that quality is a company wide activity and that a modest set of tools, taught widely, lets the people who run a process improve it themselves, which is the idea behind training belts at several levels rather than hiring a few statisticians. Reserving analysis for specialists is the position he wrote against, and a single central department reproduces the same bottleneck under another name. Design does matter, but treating it as the only lever writes off everything the operating process can contribute. Auditing suppliers annually belongs to a different tradition of assurance rather than to improvement. IASSC Lean Six Sigma BOK, 1.1.2

Coating thickness decays with time as y = 120 * exp(-0.08t), where t is in hours. How many hours pass before the predicted thickness reaches half its starting value?

• A. 6.25
• B. 8.66 ✓
• C. 12.50
• D. 25.00
• E. 60.00

Halving means the exponential factor must fall to 0.5, so minus 0.08 times t equals the natural log of 0.5 and t is the natural log of 2 divided by 0.08, which is 8.66 hours. Dividing 0.5 by the rate rather than the log of 2 gives 6.25, and dividing 1 by the rate gives 12.50, which is the time constant rather than the half life. Dividing 2 by the rate gives 25.00, and 60.00 is half the starting thickness, a response rather than a time. The starting value of 120 never enters the calculation, since the half life of an exponential does not depend on where it starts. IASSC Lean Six Sigma BOK, 4.2.1

Two weeks into Define, a team has drawn the process the way it believes the work ought to run and wants to take its baseline against that drawing. Why should the coach object?

• A. A should-be map is not allowed until the Improve phase has been approved
• B. The team has not yet been trained on the software used to draw such maps
• C. The map will have to be redrawn whenever a team member is replaced
• D. A baseline taken against an imagined flow measures nothing that exists ✓
• E. Should-be maps belong to the process owner rather than to the team

A baseline has to describe the process as it actually runs, because the whole project is an argument that the current performance can be changed, and that argument collapses if the starting figure came from a flow nobody has ever run. Measuring against the intended design also hides the very gap between intention and practice that usually holds the improvement. There is no rule reserving should-be maps for a later phase, and drawing tools and team turnover are irrelevant to the validity of a baseline. The should-be map is useful, but as a target, not as a measuring stick. IASSC Lean Six Sigma BOK, 1.2.1

A response plan for one characteristic runs to three pages and eleven branches. On nights a single operator covers four machines. What is the sound way to make that response work at three in the morning?

• A. One page: what to do first, what to hold, and who to call ✓
• B. The same document
• C. A note telling nights to wait for days if the plan is unclear
• D. The plan laminated and hung on the machine in a larger print
• E. The eleven branches kept, but numbered for reference

A response is used rarely, under pressure, often by someone who was not there when it was written, so it has to be readable in a few seconds and reduce to three decisions: make it safe, contain the product, and call the named person. The detail behind those steps still exists and can live in the procedure the plan points to, but it must not stand between the operator and the first action. Repeating training every six months tries to fix a design problem with memory, and enlarging or numbering the same eleven branches makes an unusable document easier to read without making it usable. Telling nights to wait for days leaves eight hours of production running against a known signal, which is the failure the plan was meant to prevent. IASSC Lean Six Sigma BOK, 5.3.3

Two studies each estimate the same 3 percent yield gain. One used 20 units per group and returned p equal to 0.21; the other used 500 per group and returned p equal to 0.001. How should the pair be read?

• A. The larger study found a bigger gain than the smaller one did
• B. The smaller study shows that the 3 percent gain is not real
• C. The two studies conflict, so neither result should be stated
• D. The estimated benefit agrees and only the precision differs ✓
• E. The larger study must have used a looser alpha to reach 0.001

Both studies point to the same estimated gain, so the effect size they report is identical and the disagreement is only in how tightly each one pins that estimate down. The larger study has a smaller standard error, so the same gain sits many more standard errors away from zero and the p value falls. A high p value from a small study is a statement about the precision of that study rather than evidence that the gain is absent. Alpha plays no part, because it is a threshold the team sets and not an input to the p value the data yields. IASSC Lean Six Sigma BOK, 3.3.2

Readings are recorded to the nearest whole unit while the process standard deviation is about 0.4 of a unit, so most moving ranges come out as either zero or one. What is the effect on an individuals and moving range chart?

• A. The readings take only a few values ✓
• B. The chart gains sensitivity, because rounding removes measurement noise
• C. The centre line drifts upward, since rounding always pushes values higher
• D. The moving range chart becomes an averages chart with a subgroup of two
• E. The limits are unaffected, as rounding cancels out over enough readings

A measurement unit that is large next to the process spread leaves the data in a few discrete steps, and the plotted points then form horizontal bands rather than a scatter. The average moving range is built almost entirely from zeros and ones, so it is a crude and often biased estimate of the spread, and the limits calculated from it can be far too tight or far too wide depending on where the rounding falls. The usual guidance is that the measurement increment should be no more than about a fifth of the process spread, and the remedy is a finer resolution rather than more data. Rounding does not remove noise, does not bias the average in one direction and certainly does not cancel out in a way that repairs the limits. IASSC Lean Six Sigma BOK, 2.4.2

The target spread used in a one sample variance test is itself an estimate taken from thirty historical parts. What does that do to the test?

• A. Nothing, because the target is treated as fixed by the arithmetic
• B. It removes the need to check normality of the current readings
• C. It makes the degrees of freedom climb to fifty nine for this test
• D. It adds uncertainty the chi-square test never accounts for ✓
• E. It turns that question into a test of a single sample mean

The chi-square test treats the target as a constant known without error, so every scrap of uncertainty in the comparison is charged to the current sample. When the target is itself an estimate from thirty historical parts it carries sampling variation of its own, and ignoring that makes the test more willing to declare a change than the stated alpha suggests. The proper comparison is then between two estimated spreads, which is a different procedure with its own degrees of freedom. Nothing about the origin of the target excuses the normality check, and the degrees of freedom of the test still come from the current sample alone. IASSC Lean Six Sigma BOK, 3.4.2