Quality control investigator: Upon testing samples of products from our supplier that were sent by our field inspect...

Naz on March 24, 2014

Let's first identify the flaw in the stimulus. The investigator states that over 20% of the samples sent to them were defective. We know that their supplier is contractually obligated to limit the rate of defects among items it manufactures to below 5%. Thus, seeing as the sample had a rate of defect that was over 20%, the inspector infers that the items as a whole have the same rate of defect, concluding that the contract must have been violated.

But, the two percentages that the investigator cites do not refer to the same exact group; rather we are using evidence from a part of a group to conclude something about the group as a whole. First, the investigator states that of the samples sent to them, over 20% were defective. Then the investigator states that the contract stipulates that the rate of defect among the total items that the supplier manufactures must be below 5%. Just because the rate of defect in the samples sent by the field inspectors was higher than 5%, does not necessarily mean that the overall rate of defect is higher than 5%. We are faced with a part to whole flaw.

Answer choice (B) is incorrect because it is not a flaw. It states that the argument assumes, without any evidence, that the field inspectors were just as likely to choose a defective item for testing, as they were to choose a nondefective item. Let's put in real numbers to help visualize better. If the sample consisted of 10 items, then according to answer choice (B), 5 would be defective and 5 would be nondefective. That is entirely consistent with the field inspectors' findings that over 20% were defective. However, we have not addressed the part to whole flaw.

Answer choice (D) clearly addresses the flaw. The argument is flawed because it overlooks the possibility that the field inspectors tend to choose items for testing that they suspect are defective, i.e. overlooks the possibility that the field inspectors are not choosing a representative sample. What is the nature of a field inspector's job? They are supposed to look out for defective items. So it would make sense that the field inspectors would send back a sample with more defective items than are represented as a whole. Thus, the part does not necessarily represent the whole.

Hope this helps! Please let us know if you have any other questions.

mjhirsch on September 19, 2015

Why would the answer not be (A)? This seems to follow the same thinking - the conclusion is based on too small a sample of items tested by the laboratory. Just because 20% of the sample is defective does not mean over 5% of the whole population is, as it is only a sample.

Naz on September 24, 2015

The error is not that the sample is too small, it is that the field inspector may have a tendency to choose items that they suspect are defective, i.e. the portion of the whole that the inspector sent has a high defect rate. But, this doesn't mean that the entire whole has the same defect rate.

We have not been given any information on the amount of the sample. Thus, (A) cannot be correct.

The sample not being representative is not the same thing as the sample not being large enough. Remember, the point of a representative sample is that we can accurately use it to make inferences about the whole. The issue is that the sample is not representative of the whole since the inspector have have tended to choose more defects for the sample.

Hope that clears things up! Please let us know if you have any other questions.

Maybeillgetlucky on May 19, 2019

hey I was able to identify the flaw as being a part to whole flaw but I still got the answer choice wrong. any tips? is there another step that will allow me to deduce the right answer?

Henleys on April 17, 2020

I found the initial response to be very helpful. I never really thought of "completing the flaw". If I understood you correctly, then we're looking for something that makes the flaw. I chose B originally but I see what your saying with D. With D, we now have a flaw in the argument. Did I understand that correctly?

Henleys on April 17, 2020

"D" gives us something suspect...

4356 on April 20, 2020

Exactly my thinking ^ why is A not correct?

4356 on April 20, 2020

Disregard my previous question