Question

Inductive generalizations have this form:1. X percent of the observed members of group A have property...

Inductive generalizations have this form:1. X percent of the observed members of group A have property B. (the sample)2.Thus, about X percent of A have property B. (the generalization from the sample)For instance: 1. 40% of the pickles you have pulled out of the barrel are very good.2.Therefore, about 40% of the pickles in the barrel are very good.To assess the strength or weakness of inductive generalizations (arguments which generalize from sample sets), logicians run through 3 checks:

CHECK #1: Is the appropriate population being sampled? You would be making a logical error if you have a sample of female college freshman and you generalize to a conclusion about elderly men.

CHECK #2: Is the sample truly random? To be a good/strong argument, the sample must be representative of the population it is targeting. The easiest way to ensure this is to have a truly random sample. If the sample is not representative (e.g. if you ask those over 40 what they think about Avengers movies, then generalize what people think about Avengers movies, you have made a logical error: those over 40 are only one part of “people” and not representative of all people.)

CHECK #3: Are there enough members in the sample set? Even if someone is randomly chosen from the U.S. you cannot generalize and conclude with probability who will win the next presidential election from one person’s opinion. The sample set (one person to generalize about all Americans) is too small, even if he/she was randomly chosen.

Question: 2/3 of the randomly chosen adults in New York City identify themselves as “pro-choice” in the abortion debate. And 70% of the randomly chosen adults in San Francisco do. This makes the situation clear: A large majority of the people in this country are pro-choice.

Homework Answers

Answer #1

For the given problem: In order to reach the conclusion, a large majority of the people in this country are pro-choice, a sample of randomly chosen adults from two major cities is studied.

CHECK #1: Here, the population is the whole citizens of the country, The random sample is chosen from two major cities of the country. We find that the population being sampled is appropriate.

CHECK #2: As stated in the problem, the samples were chosen randomly. However, the samples are randomly chosen only from urban population of two of the most forward cities.Generalizing it to the population of the whole country would need a second look.

CHECK #3: The sample approximately accounts for 2% of the population, which might be adequate for generalization according to the maximum 10% rule for samples greater than 1000.

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