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 only by number. The students were asked to pick out Great Britain and
France. As it turned out, 65.6% could find France, compared to 70.4% for Great Britain. Is the
difference statistically significant? Or can this be determined from the information given?
Explain.

Solution: This can’t be determined from the information given. The responses are correlated. If
we wanted to formulate this as a box model, the box should have four kinds of tickets, with values
f1; 1g; f1; 0g; f0; 1g; f0; 0g. Here, f1; 1g indicates that the student can find both France and Great
Britain, f1; 0g indicates that the student can find France but not Great Britain, and so on. If we
want to conduct a statistical test, it should be formulated in terms of this model; for instance, we
might want to test the null hypothesis that the proportion who can find France but not Great
Britain is equivalent to the proportion who can find Great Britain but not France. But this is a
different question, and we would need more data.