I'm working on my algebra test, and it one of the questions asked me which one is an inferential statistic. The answer choices were this; (A).Gina's test score is at the 45th percentile. (B). The food cans have a mean shelf life of 14 months. (C). A recent survey indicates that 73% of the voters disapprove of the sheriff's proposal. (D). The boxes have a mean weight of 3.3 kg and a standard deviation of 0.14 kg. Can you explain the answer, and why it is that answer? Thank you
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Answers (B), (C), and (D) are all descriptions of populations. In (B), we are not thinking of one food can from the group, but the whole group of food cans. The answer in (C) refers to the entire population of voters, not just a single voter. (D) is describing descriptive statistics for the entire population of boxes. Properties of populations are known as parameters, and they provide descriptive statistical information.
On the other hand, (A) describes the test score of a single person, Gina. It is a reasonable assumption to make that her single score is a sample from a population of all the students in her class who took the test. Since her score is a sample that represents an entire population, we can use her score to make generalizations (inferences) about the population we took her score from. Since we can make generalizations about an entire population based on a sample using Gina's test score, the situation involves inferential statistics.