CQPA Free Mock Exam (60 Minutes)

Free sample questions

3 questions from this set, shown in full with the correct answer and the reasoning behind it. Read them as a study resource.

1. Q1.Quality costs are broken down by product line.
   
   $$\begin{array}{l|r|r|r} \hline \textbf{Line} & \textbf{Prevention} & \textbf{Appraisal} & \textbf{Failure} \\ \hline \text{Alpha} & 40 & 60 & 90 \\ \text{Beta} & 15 & 95 & 310 \\ \text{Gamma} & 55 & 45 & 70 \\ \hline \end{array}$$
   
   Which line most clearly warrants investigation, and why?

   • A.Beta, because it carries the lowest prevention spending
   • B.Alpha, because its three categories are the most evenly balanced
   • C.Gamma, because its prevention spending exceeds its appraisal spending
   • D.Beta, because heavy appraisal is not preventing very high failure✓ Correct answer

   Explanation

   Beta spends the most on inspection yet still incurs failure costs roughly three times either other line, which is the signature of relying on detection instead of prevention. Low prevention spending on Beta is the primary foil and is part of the same story, but a low figure on its own says nothing until it is set against the failure cost it fails to prevent.

   Reference: CQPA BoK I

2. Q2.A histogram of 200 shaft diameters from a single machine is shown below.
   
   What is the most likely explanation for the shape?

   

   • A.The process mean drifted steadily during the sampling period
   • B.The measurement resolution is too coarse for the tolerance
   • C.A few extreme values have inflated the standard deviation
   • D.Two different machine setups have been combined✓ Correct answer

   Explanation

   Two separated modes almost always mean two populations were pooled, most often two setups, fixtures, spindles, or shifts. Steady drift is the strongest competing explanation, but drift produces a single widened or flattened mound rather than two distinct peaks with a valley between them.

   Reference: CQPA BoK II

3. Q3.Parts were classified by supplier and by inspection result.
   
   $$\begin{array}{l|c|c|c} \hline & \text{Pass} & \text{Fail} & \text{Total} \\ \hline \text{Supplier X} & 240 & 60 & 300 \\ \text{Supplier Y} & 80 & 20 & 100 \\ \hline \text{Total} & 320 & 80 & 400 \\ \hline \end{array}$$
   
   What do these data indicate about the relationship between supplier and inspection result?

   • A.Supplier X is worse, since it produced three times as many failures
   • B.No conclusion is possible without knowing the lot sizes shipped
   • C.The two are independent, since the fail rate is 20 percent for both✓ Correct answer
   • D.Supplier Y is worse, since its total failures are fewer but its lot is smaller

   Explanation

   The expected counts are calculated from the row and column totals under the assumption that supplier and inspection result are independent:
   
   $$E = \frac{(\text{row total})(\text{column total})}{\text{grand total}}$$
   
   For Supplier X failures:
   
   $$E = \frac{300(80)}{400} = 60$$
   
   For Supplier Y failures:
   
   $$E = \frac{100(80)}{400} = 20$$
   
   The expected pass counts are therefore 240 for Supplier X and 80 for Supplier Y, exactly matching the observed values.
   
   The chi-square statistic is:
   
   $$\chi^2 = \sum \frac{(O-E)^2}{E}$$
   
   Because every observed value equals its expected value:
   
   $$\chi^2 = 0$$
   
   This means the table shows no association between supplier and inspection result. Both suppliers have the same 20% failure rate, which is the relationship this item is built to show.

   Reference: CQPA BoK III

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