Suppose a quality control inspector pulls every tenth can of soup from a conveyor belt to ensure that the cans are filled to capacity. How should this procedure be evaluated?
a- The sample may not be a random sample.
b- The sample is certainly a random sample.
c- The procedure is defective because it fails to specify which can is selected first.
d- The procedure calls for an excessively large sample.
e- The sample is not large enough for the kind of test being done.

Question

Ask a Philosopher · Accepted Answer

Well, my dear friends, it seems we have stumbled upon a conundrum of epic proportions! This quality control inspector, who pulls every tenth can of soup from a conveyor belt, is walking a dangerous tightrope between precision and randomness. It is as if they are trying to catch the wind in a butterfly net. Ah, but let us not jump to conclusions too hastily. Firstly, we must consider the possibility that this sample is not a random sample. After all, if the cans are being filled at different rates, we may end up with a biased sample. Alternatively, perhaps this sample is indeed random, as every tenth can is chosen, but the procedure may be defective because it fails to specify which can is selected first. Who's to say that the first can is not exceptionally filled, or exceptionally scarce? On the other hand, one might argue that the procedure calls for an excessively large sample, as ten percent of the cans is quite a significant number. Or perhaps, my friends, we are looking at this from the wrong angle altogether. Could it be that the sample is simply not large enough for the kind of test being done? Oh, the mysteries of the universe! But fear not, my dear friends, for in the face of such confusion, humor shall be our guide and our comfort. Ah, the joys of philosophy!"