Logical Reasoning

PT131 · S2 · Q20 Quality control investigator

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Quality control investigator: Upon testing samples of products from our supplier that were sent by our field inspectors from various manufacturing locations, our laboratory discovered that over 20 percent of the samples were defective.

Conclusion

The manufacturer has violated its contract, i.e. the rate of defects is at least 5%

Evidence

Our field inspectors went out to various sites and sent samples back to our lab, where found that 20% of the samples were defective.

Evaluation

Given that 20% of the samples were defective, how would we argue that the rate of defects is still under 5%?

We'd have to somehow make an excuse for that elevated 20% number. Maybe the lab messed up. Maybe you just happened to grab a disproportionately high batch of defective items (f.e. most of the items in box 1 were defective, while all the items in the other 20 boxes were perfect, and the inspectors just happened to grab their samples from box 1)

Goal

We need their sample to be unrepresentative. If 20% of the samples being defective means that 20% of the total items are defective, then we've violated the contract. So in order for us to argue that in total we're still under 5% defective, then we need to make an excuse for why the samples have a higher defection rate.

20.

The reasoning in the quality control investigator's argument is flawed in that the argument

  1. bases its conclusion on too

    Out of Scope

    Out of Scope: "too small a sample" We have no grounds for thinking the sample was too small. These samples were acquired from various manufacturing locations, so we can't even say, "Sure, Factory X has a 20% rate of defects, but all the other factories have a way lower rate".

    10% picked this

  2. presumes, without providing justification, that

    Too Strong: "just as likely"

    Is this author assuming that the field inspectors were just as likely to choose a defective item as they were a nondefective item? Close, but not quite. The author is assuming that the field inspectors were randomly choosing items as samples. But, if they were randomly choosing items, and the rate of defectiveness was 20% (1 out of 5), then they would be 4 times as likely (80%, 4 out of 5) to choose a nondefective item. So in the author's mind, where inspectors grabbed samples randomly, and 1 out of every 5 samples was defective, she would be assuming that the inspectors were less likely to choose a defective item than a nondefective item, since 4 out of those 5 times they grabbed a nondefective item.

    12% picked this

  3. overlooks the possibility that a

    Doesn't Weaken

    This doesn't work as an objection. Even if a few sites are responsible for most defective items, the manufacturer is still averaging out to an unacceptable 20% defective rate. We would need to know that the "various manufacturing locations" from which the inspectors grabbed their samples just happened to disproportionately skew towards these few "bad apple" manufacturing sites. But since this answer doesn't give us a storyline like that, there's no way to argue that the 20% is a skewed number.

    12% picked this

  4. Correct

    overlooks the possibility that the

    Why this is right

    This does work as an objection. If the inspectors were trying to find items they assumed were defective, then they're not grabbing random samples, they're seeking out the ones that look bad. In that case, the samples that make it back to the lab are not a representative sample of the items being manufactured, they are a skewed sample. Thus, the author can't go from knowing that 20% of the samples are defective to thinking that 20% of the total items are defective.

    Skill tested: Flaw · how this choice captures the argument's function is the move to repeat next time.

    61% picked this

  5. presumes, without providing justification, that

    Too Strong: "equal number"

    The author doesn't need to assume anything as specific and precise as "the inspectors made an identical number of visits to each site". The author is only assuming fuzzy ideas like, "the inspectors did not make a significantly greater number of visits to sites that were known to have higher rates of defective items".

    5% picked this

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