Question

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Twenty words are chosen randomly from a fifth-grade science book. Twenty random words are also chosen from a ninth-grade science book. The length of the words chosen are as follows:
5th Grade Textbook: 2, 4, 3, 6, 5, 5, 3, 7, 8, 4, 4, 1, 5, 2, 4, 1, 1, 4, 5, 3
9th Grade Textbook: 7, 9, 3, 4, 12, 9, 5, 3, 4, 3, 9, 4, 8, 6, 5, 7, 9, 4, 8, 6
By looking at the two data sets, which conclusion is reasonable?

A) The words in the ninth-grade sample are longer than the words in the fifth-grade sample.
B) The words the fifth-grade sample are more common than the words in the ninth-grade sample.
C) All ninth-grade science textbooks have longer words than all fifth-grade science textbooks.
D) The words in the ninth-grade sample are more difficult than the words in the fifth-grade sample.

Answer 1

A) The words in the ninth-grade sample are longer than the words in the fifth-grade sample.

Explanation:

Just by looking at the answer choices, we can eliminate B and D because we cannot infer that longer words = more common or more difficult.

We are looking between A and B, since the two random samples of 5th grade textbooks and 9th grade textbooks looks at word length only.

We want to determine if this sample is representative of the population of 5th grade textbooks and 9th grade textbooks.

To test this hypothesis, we would need to collect many more samples of the same size and form a sampling distribution of means, and from there we could compare the true mean of 5th grade textbook word length vs. 9th grade textbook average word length.

Therefore, the answer is A) The words in the ninth-grade sample are longer than the words in the fifth-grade sample. We do not have enough evidence that this sample is representative of the larger population.