Question

A geography test was given to a simple random sample of 250 high school students in a certain large school district. One question involved an outline map of Europe, with the countries identified by number only. The students were asked to pick out Great Britain and France. As it turned out, 65.8% could find France and 70.2% could find Great Britain. Is this difference statistically significant?

Group of answer choices

A. We can’t answer with the information given because this is a matched pairs situation, and we don’t know how many students knew both answers.

B. Yes, the two-sample P-value is small.

C. No, the two-sample P-value is large.

D. The question does not make sense. We should ask about practical importance.

E. We can’t answer because this was a census; no chance mechanism is present.

Answer 1

It is only appropriate to use the formula for the S.E. of the difference when the two samples are independent. In this situation, the samples are not independent, because both samples contain the same set of 250 students (as the first sample contains the proportion of people in this set that could find France and the second sample contains the proportion of people in this set that could find Great Britain). Since the samples are not independent, it is not appropriate to use the formula for the standard eror and thus it is not possible to exccute the two-sample z-test (as this test requires this standard error).

therefore,

We can’t answer with the information given because this is a matched pairs situation, and we don’t know how many students knew both answers.