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A dairy union drew milk samples from 8 of the 200 farms that supply its chilling plant. All 8 stand within two kilometres of the plant. Every sample met the fat standard, and the union announced that milk from all 200 farms meets the standard. Which of the following best states what the union's evidence can and cannot show?

Competition practiceLogical / Critical
  • AIt shows that all 200 farms meet the standard, since 8 farms are enough to test
  • BIt shows that these 8 nearby farms met the standard on the day they were tested, but supports nothing about the remaining farms, which were not sampled and which differ from the 8 in a respect that could well matter
  • CIt shows nothing whatever, because no test of milk can be relied on
  • DIt shows that the farms lying further from the plant do not meet the standard

Step-by-Step Solution

Eight farms out of two hundred would be a thin basis even if they had been picked at random, and these were not: every one of them is close to the plant, which is exactly the distance over which milk is least likely to be affected in transit. The evidence therefore stands for the 8 and no further. Dismissing all milk testing goes too far in the other direction, and nothing in the samples speaks about the distant farms one way or the other.
Answer: B) It shows that these 8 nearby farms met the standard on the day they were tested, but supports nothing about the remaining farms, which were not sampled and which differ from the 8 in a respect that could well matter

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