Question

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: Girls are smarter than boys. Girls in the debate club always argue better than boys. And the mean grade-point average of the girls in the glee club is higher than that of the boys in the club.

Answer 1

CHECK #1: The appropriate population is being sampled. The sample are individuals in the debate club and glee club.

CHECK #2: The sample truly is not random. The sample consists of all individuals which have participated in the debate club or a memeber of glee club. Any individual which have not participated in the debate club or is not a memeber of glee club will not have any chance to be picked up in the sample. Thus it is not a random sample where the probability to get picked in the sample should be uniform.

CHECK #3: We assume that the sample size of individuals in the debate club or  in the glee club are sufficient to carry out the study.

As Check #2 failed, we cannot generalize the study on the population of all girls aand boys.